definition of analysis of research

Data Analysis

• Introduction to Data Analysis
• Quantitative Analysis Tools
• Qualitative Analysis Tools
• Mixed Methods Analysis
• Geospatial Analysis
• Further Reading

What is Data Analysis?

According to the federal government, data analysis is "the process of systematically applying statistical and/or logical techniques to describe and illustrate, condense and recap, and evaluate data" ( Responsible Conduct in Data Management ). Important components of data analysis include searching for patterns, remaining unbiased in drawing inference from data, practicing responsible  data management , and maintaining "honest and accurate analysis" ( Responsible Conduct in Data Management ). 

In order to understand data analysis further, it can be helpful to take a step back and understand the question "What is data?". Many of us associate data with spreadsheets of numbers and values, however, data can encompass much more than that. According to the federal government, data is "The recorded factual material commonly accepted in the scientific community as necessary to validate research findings" ( OMB Circular 110 ). This broad definition can include information in many formats. 

Some examples of types of data are as follows:

• Photographs 
• Hand-written notes from field observation
• Machine learning training data sets
• Ethnographic interview transcripts
• Sheet music
• Scripts for plays and musicals 
• Observations from laboratory experiments ( CMU Data 101 )

Thus, data analysis includes the processing and manipulation of these data sources in order to gain additional insight from data, answer a research question, or confirm a research hypothesis. 

Data analysis falls within the larger research data lifecycle, as seen below. 

( University of Virginia )

Why Analyze Data?

Through data analysis, a researcher can gain additional insight from data and draw conclusions to address the research question or hypothesis. Use of data analysis tools helps researchers understand and interpret data. 

What are the Types of Data Analysis?

Data analysis can be quantitative, qualitative, or mixed methods. 

Quantitative research typically involves numbers and "close-ended questions and responses" ( Creswell & Creswell, 2018 , p. 3). Quantitative research tests variables against objective theories, usually measured and collected on instruments and analyzed using statistical procedures ( Creswell & Creswell, 2018 , p. 4). Quantitative analysis usually uses deductive reasoning. 

Qualitative  research typically involves words and "open-ended questions and responses" ( Creswell & Creswell, 2018 , p. 3). According to Creswell & Creswell, "qualitative research is an approach for exploring and understanding the meaning individuals or groups ascribe to a social or human problem" ( 2018 , p. 4). Thus, qualitative analysis usually invokes inductive reasoning. 

Mixed methods  research uses methods from both quantitative and qualitative research approaches. Mixed methods research works under the "core assumption... that the integration of qualitative and quantitative data yields additional insight beyond the information provided by either the quantitative or qualitative data alone" ( Creswell & Creswell, 2018 , p. 4). 

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What Is Statistical Analysis?

Statistical analysis is a technique we use to find patterns in data and make inferences about those patterns to describe variability in the results of a data set or an experiment. 

In its simplest form, statistical analysis answers questions about:

• Quantification — how big/small/tall/wide is it?
• Variability — growth, increase, decline
• The confidence level of these variabilities

What Are the 2 Types of Statistical Analysis?

• Descriptive Statistics:  Descriptive statistical analysis describes the quality of the data by summarizing large data sets into single measures. 
• Inferential Statistics:  Inferential statistical analysis allows you to draw conclusions from your sample data set and make predictions about a population using statistical tests.

What’s the Purpose of Statistical Analysis?

Using statistical analysis, you can determine trends in the data by calculating your data set’s mean or median. You can also analyze the variation between different data points from the mean to get the standard deviation . Furthermore, to test the validity of your statistical analysis conclusions, you can use hypothesis testing techniques, like P-value, to determine the likelihood that the observed variability could have occurred by chance.

More From Abdishakur Hassan The 7 Best Thematic Map Types for Geospatial Data

Statistical Analysis Methods

There are two major types of statistical data analysis: descriptive and inferential. 

Descriptive Statistical Analysis

Descriptive statistical analysis describes the quality of the data by summarizing large data sets into single measures. 

Within the descriptive analysis branch, there are two main types: measures of central tendency (i.e. mean, median and mode) and measures of dispersion or variation (i.e. variance , standard deviation and range). 

For example, you can calculate the average exam results in a class using central tendency or, in particular, the mean. In that case, you’d sum all student results and divide by the number of tests. You can also calculate the data set’s spread by calculating the variance. To calculate the variance, subtract each exam result in the data set from the mean, square the answer, add everything together and divide by the number of tests.

Inferential Statistics

On the other hand, inferential statistical analysis allows you to draw conclusions from your sample data set and make predictions about a population using statistical tests. 

There are two main types of inferential statistical analysis: hypothesis testing and regression analysis. We use hypothesis testing to test and validate assumptions in order to draw conclusions about a population from the sample data. Popular tests include Z-test, F-Test, ANOVA test and confidence intervals . On the other hand, regression analysis primarily estimates the relationship between a dependent variable and one or more independent variables. There are numerous types of regression analysis but the most popular ones include linear and logistic regression .  

Statistical Analysis Steps  

In the era of big data and data science, there is a rising demand for a more problem-driven approach. As a result, we must approach statistical analysis holistically. We may divide the entire process into five different and significant stages by using the well-known PPDAC model of statistics: Problem, Plan, Data, Analysis and Conclusion.

In the first stage, you define the problem you want to tackle and explore questions about the problem. 

Next is the planning phase. You can check whether data is available or if you need to collect data for your problem. You also determine what to measure and how to measure it. 

The third stage involves data collection, understanding the data and checking its quality. 

4. Analysis

Statistical data analysis is the fourth stage. Here you process and explore the data with the help of tables, graphs and other data visualizations.  You also develop and scrutinize your hypothesis in this stage of analysis. 

5. Conclusion

The final step involves interpretations and conclusions from your analysis. It also covers generating new ideas for the next iteration. Thus, statistical analysis is not a one-time event but an iterative process.

Statistical Analysis Uses

Statistical analysis is useful for research and decision making because it allows us to understand the world around us and draw conclusions by testing our assumptions. Statistical analysis is important for various applications, including:

• Statistical quality control and analysis in product development 
• Clinical trials
• Customer satisfaction surveys and customer experience research 
• Marketing operations management
• Process improvement and optimization
• Training needs 

More on Statistical Analysis From Built In Experts Intro to Descriptive Statistics for Machine Learning

Benefits of Statistical Analysis

Here are some of the reasons why statistical analysis is widespread in many applications and why it’s necessary:

Understand Data

Statistical analysis gives you a better understanding of the data and what they mean. These types of analyses provide information that would otherwise be difficult to obtain by merely looking at the numbers without considering their relationship.

Find Causal Relationships

Statistical analysis can help you investigate causation or establish the precise meaning of an experiment, like when you’re looking for a relationship between two variables.

Make Data-Informed Decisions

Businesses are constantly looking to find ways to improve their services and products . Statistical analysis allows you to make data-informed decisions about your business or future actions by helping you identify trends in your data, whether positive or negative. 

Determine Probability

Statistical analysis is an approach to understanding how the probability of certain events affects the outcome of an experiment. It helps scientists and engineers decide how much confidence they can have in the results of their research, how to interpret their data and what questions they can feasibly answer.

You’ve Got Questions. Our Experts Have Answers. Confidence Intervals, Explained!

What Are the Risks of Statistical Analysis?

Statistical analysis can be valuable and effective, but it’s an imperfect approach. Even if the analyst or researcher performs a thorough statistical analysis, there may still be known or unknown problems that can affect the results. Therefore, statistical analysis is not a one-size-fits-all process. If you want to get good results, you need to know what you’re doing. It can take a lot of time to figure out which type of statistical analysis will work best for your situation .

Thus, you should remember that our conclusions drawn from statistical analysis don’t always guarantee correct results. This can be dangerous when making business decisions. In marketing , for example, we may come to the wrong conclusion about a product . Therefore, the conclusions we draw from statistical data analysis are often approximated; testing for all factors affecting an observation is impossible.

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• Korean J Anesthesiol
• v.71(2); 2018 Apr

Introduction to systematic review and meta-analysis

1 Department of Anesthesiology and Pain Medicine, Inje University Seoul Paik Hospital, Seoul, Korea

2 Department of Anesthesiology and Pain Medicine, Chung-Ang University College of Medicine, Seoul, Korea

Systematic reviews and meta-analyses present results by combining and analyzing data from different studies conducted on similar research topics. In recent years, systematic reviews and meta-analyses have been actively performed in various fields including anesthesiology. These research methods are powerful tools that can overcome the difficulties in performing large-scale randomized controlled trials. However, the inclusion of studies with any biases or improperly assessed quality of evidence in systematic reviews and meta-analyses could yield misleading results. Therefore, various guidelines have been suggested for conducting systematic reviews and meta-analyses to help standardize them and improve their quality. Nonetheless, accepting the conclusions of many studies without understanding the meta-analysis can be dangerous. Therefore, this article provides an easy introduction to clinicians on performing and understanding meta-analyses.

Introduction

A systematic review collects all possible studies related to a given topic and design, and reviews and analyzes their results [ 1 ]. During the systematic review process, the quality of studies is evaluated, and a statistical meta-analysis of the study results is conducted on the basis of their quality. A meta-analysis is a valid, objective, and scientific method of analyzing and combining different results. Usually, in order to obtain more reliable results, a meta-analysis is mainly conducted on randomized controlled trials (RCTs), which have a high level of evidence [ 2 ] ( Fig. 1 ). Since 1999, various papers have presented guidelines for reporting meta-analyses of RCTs. Following the Quality of Reporting of Meta-analyses (QUORUM) statement [ 3 ], and the appearance of registers such as Cochrane Library’s Methodology Register, a large number of systematic literature reviews have been registered. In 2009, the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) statement [ 4 ] was published, and it greatly helped standardize and improve the quality of systematic reviews and meta-analyses [ 5 ].

Levels of evidence.

In anesthesiology, the importance of systematic reviews and meta-analyses has been highlighted, and they provide diagnostic and therapeutic value to various areas, including not only perioperative management but also intensive care and outpatient anesthesia [6–13]. Systematic reviews and meta-analyses include various topics, such as comparing various treatments of postoperative nausea and vomiting [ 14 , 15 ], comparing general anesthesia and regional anesthesia [ 16 – 18 ], comparing airway maintenance devices [ 8 , 19 ], comparing various methods of postoperative pain control (e.g., patient-controlled analgesia pumps, nerve block, or analgesics) [ 20 – 23 ], comparing the precision of various monitoring instruments [ 7 ], and meta-analysis of dose-response in various drugs [ 12 ].

Thus, literature reviews and meta-analyses are being conducted in diverse medical fields, and the aim of highlighting their importance is to help better extract accurate, good quality data from the flood of data being produced. However, a lack of understanding about systematic reviews and meta-analyses can lead to incorrect outcomes being derived from the review and analysis processes. If readers indiscriminately accept the results of the many meta-analyses that are published, incorrect data may be obtained. Therefore, in this review, we aim to describe the contents and methods used in systematic reviews and meta-analyses in a way that is easy to understand for future authors and readers of systematic review and meta-analysis.

Study Planning

It is easy to confuse systematic reviews and meta-analyses. A systematic review is an objective, reproducible method to find answers to a certain research question, by collecting all available studies related to that question and reviewing and analyzing their results. A meta-analysis differs from a systematic review in that it uses statistical methods on estimates from two or more different studies to form a pooled estimate [ 1 ]. Following a systematic review, if it is not possible to form a pooled estimate, it can be published as is without progressing to a meta-analysis; however, if it is possible to form a pooled estimate from the extracted data, a meta-analysis can be attempted. Systematic reviews and meta-analyses usually proceed according to the flowchart presented in Fig. 2 . We explain each of the stages below.

Flowchart illustrating a systematic review.

Formulating research questions

A systematic review attempts to gather all available empirical research by using clearly defined, systematic methods to obtain answers to a specific question. A meta-analysis is the statistical process of analyzing and combining results from several similar studies. Here, the definition of the word “similar” is not made clear, but when selecting a topic for the meta-analysis, it is essential to ensure that the different studies present data that can be combined. If the studies contain data on the same topic that can be combined, a meta-analysis can even be performed using data from only two studies. However, study selection via a systematic review is a precondition for performing a meta-analysis, and it is important to clearly define the Population, Intervention, Comparison, Outcomes (PICO) parameters that are central to evidence-based research. In addition, selection of the research topic is based on logical evidence, and it is important to select a topic that is familiar to readers without clearly confirmed the evidence [ 24 ].

Protocols and registration

In systematic reviews, prior registration of a detailed research plan is very important. In order to make the research process transparent, primary/secondary outcomes and methods are set in advance, and in the event of changes to the method, other researchers and readers are informed when, how, and why. Many studies are registered with an organization like PROSPERO ( http://www.crd.york.ac.uk/PROSPERO/ ), and the registration number is recorded when reporting the study, in order to share the protocol at the time of planning.

Defining inclusion and exclusion criteria

Information is included on the study design, patient characteristics, publication status (published or unpublished), language used, and research period. If there is a discrepancy between the number of patients included in the study and the number of patients included in the analysis, this needs to be clearly explained while describing the patient characteristics, to avoid confusing the reader.

Literature search and study selection

In order to secure proper basis for evidence-based research, it is essential to perform a broad search that includes as many studies as possible that meet the inclusion and exclusion criteria. Typically, the three bibliographic databases Medline, Embase, and Cochrane Central Register of Controlled Trials (CENTRAL) are used. In domestic studies, the Korean databases KoreaMed, KMBASE, and RISS4U may be included. Effort is required to identify not only published studies but also abstracts, ongoing studies, and studies awaiting publication. Among the studies retrieved in the search, the researchers remove duplicate studies, select studies that meet the inclusion/exclusion criteria based on the abstracts, and then make the final selection of studies based on their full text. In order to maintain transparency and objectivity throughout this process, study selection is conducted independently by at least two investigators. When there is a inconsistency in opinions, intervention is required via debate or by a third reviewer. The methods for this process also need to be planned in advance. It is essential to ensure the reproducibility of the literature selection process [ 25 ].

Quality of evidence

However, well planned the systematic review or meta-analysis is, if the quality of evidence in the studies is low, the quality of the meta-analysis decreases and incorrect results can be obtained [ 26 ]. Even when using randomized studies with a high quality of evidence, evaluating the quality of evidence precisely helps determine the strength of recommendations in the meta-analysis. One method of evaluating the quality of evidence in non-randomized studies is the Newcastle-Ottawa Scale, provided by the Ottawa Hospital Research Institute 1) . However, we are mostly focusing on meta-analyses that use randomized studies.

If the Grading of Recommendations, Assessment, Development and Evaluations (GRADE) system ( http://www.gradeworkinggroup.org/ ) is used, the quality of evidence is evaluated on the basis of the study limitations, inaccuracies, incompleteness of outcome data, indirectness of evidence, and risk of publication bias, and this is used to determine the strength of recommendations [ 27 ]. As shown in Table 1 , the study limitations are evaluated using the “risk of bias” method proposed by Cochrane 2) . This method classifies bias in randomized studies as “low,” “high,” or “unclear” on the basis of the presence or absence of six processes (random sequence generation, allocation concealment, blinding participants or investigators, incomplete outcome data, selective reporting, and other biases) [ 28 ].

The Cochrane Collaboration’s Tool for Assessing the Risk of Bias [ 28 ]

Data extraction

Two different investigators extract data based on the objectives and form of the study; thereafter, the extracted data are reviewed. Since the size and format of each variable are different, the size and format of the outcomes are also different, and slight changes may be required when combining the data [ 29 ]. If there are differences in the size and format of the outcome variables that cause difficulties combining the data, such as the use of different evaluation instruments or different evaluation timepoints, the analysis may be limited to a systematic review. The investigators resolve differences of opinion by debate, and if they fail to reach a consensus, a third-reviewer is consulted.

Data Analysis

The aim of a meta-analysis is to derive a conclusion with increased power and accuracy than what could not be able to achieve in individual studies. Therefore, before analysis, it is crucial to evaluate the direction of effect, size of effect, homogeneity of effects among studies, and strength of evidence [ 30 ]. Thereafter, the data are reviewed qualitatively and quantitatively. If it is determined that the different research outcomes cannot be combined, all the results and characteristics of the individual studies are displayed in a table or in a descriptive form; this is referred to as a qualitative review. A meta-analysis is a quantitative review, in which the clinical effectiveness is evaluated by calculating the weighted pooled estimate for the interventions in at least two separate studies.

The pooled estimate is the outcome of the meta-analysis, and is typically explained using a forest plot ( Figs. 3 and ​ and4). 4 ). The black squares in the forest plot are the odds ratios (ORs) and 95% confidence intervals in each study. The area of the squares represents the weight reflected in the meta-analysis. The black diamond represents the OR and 95% confidence interval calculated across all the included studies. The bold vertical line represents a lack of therapeutic effect (OR = 1); if the confidence interval includes OR = 1, it means no significant difference was found between the treatment and control groups.

Forest plot analyzed by two different models using the same data. (A) Fixed-effect model. (B) Random-effect model. The figure depicts individual trials as filled squares with the relative sample size and the solid line as the 95% confidence interval of the difference. The diamond shape indicates the pooled estimate and uncertainty for the combined effect. The vertical line indicates the treatment group shows no effect (OR = 1). Moreover, if the confidence interval includes 1, then the result shows no evidence of difference between the treatment and control groups.

Forest plot representing homogeneous data.

Dichotomous variables and continuous variables

In data analysis, outcome variables can be considered broadly in terms of dichotomous variables and continuous variables. When combining data from continuous variables, the mean difference (MD) and standardized mean difference (SMD) are used ( Table 2 ).

Summary of Meta-analysis Methods Available in RevMan [ 28 ]

The MD is the absolute difference in mean values between the groups, and the SMD is the mean difference between groups divided by the standard deviation. When results are presented in the same units, the MD can be used, but when results are presented in different units, the SMD should be used. When the MD is used, the combined units must be shown. A value of “0” for the MD or SMD indicates that the effects of the new treatment method and the existing treatment method are the same. A value lower than “0” means the new treatment method is less effective than the existing method, and a value greater than “0” means the new treatment is more effective than the existing method.

When combining data for dichotomous variables, the OR, risk ratio (RR), or risk difference (RD) can be used. The RR and RD can be used for RCTs, quasi-experimental studies, or cohort studies, and the OR can be used for other case-control studies or cross-sectional studies. However, because the OR is difficult to interpret, using the RR and RD, if possible, is recommended. If the outcome variable is a dichotomous variable, it can be presented as the number needed to treat (NNT), which is the minimum number of patients who need to be treated in the intervention group, compared to the control group, for a given event to occur in at least one patient. Based on Table 3 , in an RCT, if x is the probability of the event occurring in the control group and y is the probability of the event occurring in the intervention group, then x = c/(c + d), y = a/(a + b), and the absolute risk reduction (ARR) = x − y. NNT can be obtained as the reciprocal, 1/ARR.

Calculation of the Number Needed to Treat in the Dichotomous table

Fixed-effect models and random-effect models

In order to analyze effect size, two types of models can be used: a fixed-effect model or a random-effect model. A fixed-effect model assumes that the effect of treatment is the same, and that variation between results in different studies is due to random error. Thus, a fixed-effect model can be used when the studies are considered to have the same design and methodology, or when the variability in results within a study is small, and the variance is thought to be due to random error. Three common methods are used for weighted estimation in a fixed-effect model: 1) inverse variance-weighted estimation 3) , 2) Mantel-Haenszel estimation 4) , and 3) Peto estimation 5) .

A random-effect model assumes heterogeneity between the studies being combined, and these models are used when the studies are assumed different, even if a heterogeneity test does not show a significant result. Unlike a fixed-effect model, a random-effect model assumes that the size of the effect of treatment differs among studies. Thus, differences in variation among studies are thought to be due to not only random error but also between-study variability in results. Therefore, weight does not decrease greatly for studies with a small number of patients. Among methods for weighted estimation in a random-effect model, the DerSimonian and Laird method 6) is mostly used for dichotomous variables, as the simplest method, while inverse variance-weighted estimation is used for continuous variables, as with fixed-effect models. These four methods are all used in Review Manager software (The Cochrane Collaboration, UK), and are described in a study by Deeks et al. [ 31 ] ( Table 2 ). However, when the number of studies included in the analysis is less than 10, the Hartung-Knapp-Sidik-Jonkman method 7) can better reduce the risk of type 1 error than does the DerSimonian and Laird method [ 32 ].

Fig. 3 shows the results of analyzing outcome data using a fixed-effect model (A) and a random-effect model (B). As shown in Fig. 3 , while the results from large studies are weighted more heavily in the fixed-effect model, studies are given relatively similar weights irrespective of study size in the random-effect model. Although identical data were being analyzed, as shown in Fig. 3 , the significant result in the fixed-effect model was no longer significant in the random-effect model. One representative example of the small study effect in a random-effect model is the meta-analysis by Li et al. [ 33 ]. In a large-scale study, intravenous injection of magnesium was unrelated to acute myocardial infarction, but in the random-effect model, which included numerous small studies, the small study effect resulted in an association being found between intravenous injection of magnesium and myocardial infarction. This small study effect can be controlled for by using a sensitivity analysis, which is performed to examine the contribution of each of the included studies to the final meta-analysis result. In particular, when heterogeneity is suspected in the study methods or results, by changing certain data or analytical methods, this method makes it possible to verify whether the changes affect the robustness of the results, and to examine the causes of such effects [ 34 ].

Heterogeneity

Homogeneity test is a method whether the degree of heterogeneity is greater than would be expected to occur naturally when the effect size calculated from several studies is higher than the sampling error. This makes it possible to test whether the effect size calculated from several studies is the same. Three types of homogeneity tests can be used: 1) forest plot, 2) Cochrane’s Q test (chi-squared), and 3) Higgins I 2 statistics. In the forest plot, as shown in Fig. 4 , greater overlap between the confidence intervals indicates greater homogeneity. For the Q statistic, when the P value of the chi-squared test, calculated from the forest plot in Fig. 4 , is less than 0.1, it is considered to show statistical heterogeneity and a random-effect can be used. Finally, I 2 can be used [ 35 ].

I 2 , calculated as shown above, returns a value between 0 and 100%. A value less than 25% is considered to show strong homogeneity, a value of 50% is average, and a value greater than 75% indicates strong heterogeneity.

Even when the data cannot be shown to be homogeneous, a fixed-effect model can be used, ignoring the heterogeneity, and all the study results can be presented individually, without combining them. However, in many cases, a random-effect model is applied, as described above, and a subgroup analysis or meta-regression analysis is performed to explain the heterogeneity. In a subgroup analysis, the data are divided into subgroups that are expected to be homogeneous, and these subgroups are analyzed. This needs to be planned in the predetermined protocol before starting the meta-analysis. A meta-regression analysis is similar to a normal regression analysis, except that the heterogeneity between studies is modeled. This process involves performing a regression analysis of the pooled estimate for covariance at the study level, and so it is usually not considered when the number of studies is less than 10. Here, univariate and multivariate regression analyses can both be considered.

Publication bias

Publication bias is the most common type of reporting bias in meta-analyses. This refers to the distortion of meta-analysis outcomes due to the higher likelihood of publication of statistically significant studies rather than non-significant studies. In order to test the presence or absence of publication bias, first, a funnel plot can be used ( Fig. 5 ). Studies are plotted on a scatter plot with effect size on the x-axis and precision or total sample size on the y-axis. If the points form an upside-down funnel shape, with a broad base that narrows towards the top of the plot, this indicates the absence of a publication bias ( Fig. 5A ) [ 29 , 36 ]. On the other hand, if the plot shows an asymmetric shape, with no points on one side of the graph, then publication bias can be suspected ( Fig. 5B ). Second, to test publication bias statistically, Begg and Mazumdar’s rank correlation test 8) [ 37 ] or Egger’s test 9) [ 29 ] can be used. If publication bias is detected, the trim-and-fill method 10) can be used to correct the bias [ 38 ]. Fig. 6 displays results that show publication bias in Egger’s test, which has then been corrected using the trim-and-fill method using Comprehensive Meta-Analysis software (Biostat, USA).

Funnel plot showing the effect size on the x-axis and sample size on the y-axis as a scatter plot. (A) Funnel plot without publication bias. The individual plots are broader at the bottom and narrower at the top. (B) Funnel plot with publication bias. The individual plots are located asymmetrically.

Funnel plot adjusted using the trim-and-fill method. White circles: comparisons included. Black circles: inputted comparisons using the trim-and-fill method. White diamond: pooled observed log risk ratio. Black diamond: pooled inputted log risk ratio.

Result Presentation

When reporting the results of a systematic review or meta-analysis, the analytical content and methods should be described in detail. First, a flowchart is displayed with the literature search and selection process according to the inclusion/exclusion criteria. Second, a table is shown with the characteristics of the included studies. A table should also be included with information related to the quality of evidence, such as GRADE ( Table 4 ). Third, the results of data analysis are shown in a forest plot and funnel plot. Fourth, if the results use dichotomous data, the NNT values can be reported, as described above.

The GRADE Evidence Quality for Each Outcome

N: number of studies, ROB: risk of bias, PON: postoperative nausea, POV: postoperative vomiting, PONV: postoperative nausea and vomiting, CI: confidence interval, RR: risk ratio, AR: absolute risk.

When Review Manager software (The Cochrane Collaboration, UK) is used for the analysis, two types of P values are given. The first is the P value from the z-test, which tests the null hypothesis that the intervention has no effect. The second P value is from the chi-squared test, which tests the null hypothesis for a lack of heterogeneity. The statistical result for the intervention effect, which is generally considered the most important result in meta-analyses, is the z-test P value.

A common mistake when reporting results is, given a z-test P value greater than 0.05, to say there was “no statistical significance” or “no difference.” When evaluating statistical significance in a meta-analysis, a P value lower than 0.05 can be explained as “a significant difference in the effects of the two treatment methods.” However, the P value may appear non-significant whether or not there is a difference between the two treatment methods. In such a situation, it is better to announce “there was no strong evidence for an effect,” and to present the P value and confidence intervals. Another common mistake is to think that a smaller P value is indicative of a more significant effect. In meta-analyses of large-scale studies, the P value is more greatly affected by the number of studies and patients included, rather than by the significance of the results; therefore, care should be taken when interpreting the results of a meta-analysis.

When performing a systematic literature review or meta-analysis, if the quality of studies is not properly evaluated or if proper methodology is not strictly applied, the results can be biased and the outcomes can be incorrect. However, when systematic reviews and meta-analyses are properly implemented, they can yield powerful results that could usually only be achieved using large-scale RCTs, which are difficult to perform in individual studies. As our understanding of evidence-based medicine increases and its importance is better appreciated, the number of systematic reviews and meta-analyses will keep increasing. However, indiscriminate acceptance of the results of all these meta-analyses can be dangerous, and hence, we recommend that their results be received critically on the basis of a more accurate understanding.

1) http://www.ohri.ca .

2) http://methods.cochrane.org/bias/assessing-risk-bias-included-studies .

3) The inverse variance-weighted estimation method is useful if the number of studies is small with large sample sizes.

4) The Mantel-Haenszel estimation method is useful if the number of studies is large with small sample sizes.

5) The Peto estimation method is useful if the event rate is low or one of the two groups shows zero incidence.

6) The most popular and simplest statistical method used in Review Manager and Comprehensive Meta-analysis software.

7) Alternative random-effect model meta-analysis that has more adequate error rates than does the common DerSimonian and Laird method, especially when the number of studies is small. However, even with the Hartung-Knapp-Sidik-Jonkman method, when there are less than five studies with very unequal sizes, extra caution is needed.

8) The Begg and Mazumdar rank correlation test uses the correlation between the ranks of effect sizes and the ranks of their variances [ 37 ].

9) The degree of funnel plot asymmetry as measured by the intercept from the regression of standard normal deviates against precision [ 29 ].

10) If there are more small studies on one side, we expect the suppression of studies on the other side. Trimming yields the adjusted effect size and reduces the variance of the effects by adding the original studies back into the analysis as a mirror image of each study.

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Supplement to Analysis

Definitions and descriptions of analysis.

The older a word, the deeper it reaches. (Wittgenstein NB , 40) { §6.5 }

This supplement collects together various definitions and descriptions of analysis that have been offered in the history of philosophy (including all the classic ones), to indicate the range of different conceptions and the issues that arise. (There are also some remarks on related topics such as analyticity, definition, and methodology more generally.) In most cases, abbreviated references are given; full details can be found in the Annotated Bibliography on Analysis, in the section mentioned in curly brackets after the relevant definition or description. Where there is more than one passage quoted from a particular author, passages are numbered in chronological order of composition (as far as that can be determined).

• Cambridge Dictionary of Philosophy , 1999, ed. Robert Audi

Concise Oxford Dictionary , 1976, ed. J. B. Sykes

• Dictionary of Philosophy and Psychology , 1925, ed. James Mark Baldwin

A Kant Dictionary , 1995, by Howard Caygill

Oxford dictionary of philosophy , 1996, by simon blackburn, philosophielexikon , 1997, ed. a. hügli and p. lübcke, routledge encyclopedia of philosophy , 1998, entry under ‘analytical philosophy’ by thomas baldwin, routledge encyclopedia of philosophy , 1998, entry under ‘conceptual analysis’ by robert hanna, alexander of aphrodisias, arnauld, antoine and nicole, pierre, ayer, a. j., bentham, jeremy, bergson, henri, bos, henk j. m., bradley, f. h., brandom, robert b., carnap, rudolf, cassirer, ernst, cohen, l. jonathan, collingwood, r. g., davidson, donald, de chardin, teilhard, derrida, jacques, descartes, rené, frege, gottlob, geertz, clifford, hegel, georg w.f., heidegger, martin, hobbes, thomas, hodges, wilfrid, holton, gerald, husserl, edmund, kant, immanuel, lakatos, imre, leibniz, gottfried wilhelm, lichtenberg, georg christoph, locke, john, lodge, david, mendelssohn, moses, moore, g. e., newton, isaac, nietzsche, friedrich, poincaré, jules henri, polya, george, quine, w.v.o., rorty, richard, rosen, stanley, russell, bertrand, ryle, gilbert, schiller, friedrich, sellars, wilfrid, soames, scott, stebbing, l. susan.

• Strawson, F. Peter

Urmson, J. O.

Whitehead, alfred north, wilson, john cook, wittgenstein, ludwig, 1. definitions of analysis, cambridge dictionary of philosophy , 2nd ed., 1999, ed. robert audi.

the process of breaking up a concept, proposition, linguistic complex, or fact into its simple or ultimate constituents. { §1.1 }

1. Resolution into simpler elements by analysing (opp. synthesis ); statement of result of this; … 2. (Math.) Use of algebra and calculus in problem-solving. { §1.1 }

Dictionary of Philosophy and Psychology , 1925, ed. James Mark Baldwin, Vol. I

The isolation of what is more elementary from what is more complex by whatever method. { §1.1 }

Kant combines two senses of analysis in his work, one derived from Greek geometry, the other from modern physics and chemistry. Both remain close to the original Greek sense of analysis as a ‘loosening up’ or ‘releasing’, but each proceed in different ways. The former proceeds ‘lemmatically’ by assuming a proposition to be true and searching for another known truth from which the proposition may be deduced. The latter proceeds by resolving complex wholes into their elements. { §4.5 }

The process of breaking a concept down into more simple parts, so that its logical structure is displayed. { §1.1 }

Auflösung, Zerlegung in Bestandteile, im Gegensatz zu Synthese. { §1.1 }

Philosophical analysis is a method of inquiry in which one seeks to assess complex systems of thought by ‘analysing’ them into simpler elements whose relationships are thereby brought into focus. { §1.1 }

The theory of conceptual analysis holds that concepts – general meanings of linguistic predicates – are the fundamental objects of philosophical inquiry, and that insights into conceptual contents are expressed in necessary ‘conceptual truths’ (analytic propositions). { §1.1 }

Annotated Bibliography, §1.1

2. Descriptions of Analysis

And he [Aristotle] called them Analytics because the resolution of every compound into those things out of which the synthesis [is made] is called analysis . For analysis is the converse of synthesis. Synthesis is the road from the principles to those things that derive from the principles, and analysis is the return from the end to the principles. For geometers are said to analyze when, beginning from the conclusion they go up to the principles and the problem, following the order of those things which were assumed for the demonstration of the conclusion {1}. But he also uses analysis who reduces composite bodies into simple bodies {2}, and he analyzes who divides the word into the parts of the word {3}; also he who divides the parts of the word into the syllables {4}; and he who divides these into their components {5}. And they are severally said to analyse who reduce compound syllogisms into simple ones {6}, and simple ones into the premisses out of which they get their being {7}. And further, resolving imperfect syllogisms into perfect ones is called analyzing {8}. And they call analysis the reducing of the given syllogism into the proper schemata {9}. And it is especially in this meaning of analysis that these are entitled Analytics , for he describes for us a method at the end of the first book with which we shall be able to do this. ( Commentary on Aristotle’s Prior Analytics , §1.2.1 (7, lines 11-33); tr. in Gilbert 1960, 32; the square brackets are in the original translation, the curly brackets have been added here to highlight the nine senses that Alexander distinguishes) { §2.4 , §3.2 }

it is not the same thing to take an argument in one’s hand and then to see and solve its faults, as it is to be able to meet it quickly while being subjected to questions; for what we know, we often do not know in a different context. Moreover, just as in other things speed or slowness is enhanced by training, so it is with arguments too, so that supposing we are unpractised, even though a point is clear to us, we are often too late for the right moment. Sometimes too it happens as with diagrams; for there we can sometimes analyse the figure, but not construct it again: so too in refutations, though we know on what the connexion of the argument depends, we still are at a loss to split the argument apart. ( SR , 16, 175a20-30) { §2.4 }

We must next explain how to reduce syllogisms to the figures previously described; this part of our inquiry still remains. For if we examine the means by which syllogisms are produced, and possess the ability to discover them, and can also analyse [ analuoimen ] the syllogisms when constructed into the figures previously described, our original undertaking will be completed. (( PrA , I, 32, 46b40-47a6; Tredennick tr. slightly modified) { §2.4 }

Thus it is evident (1) that the types of syllogism which cannot be analysed in these figures [viz., second figure syllogisms into the third figure, and third figure syllogisms into the second figure] are the same as those which we saw could not be analysed into the first figure; and (2) that when syllogisms are reduced to the first figure these alone are established per impossibile .

It is evident, then, from the foregoing account [taken as including the discussion prior to chapter 45] how syllogisms should be reduced; and also that the figures can be analysed into one another. ( PrA , I, 45, 51a40-b5; Tredennick tr., substituting ‘analysed’ for ‘resolved’) { §2.4 }

If it were impossible to prove truth from falsehood, it would be easy to make analyses [ analuein ]; for then the propositions would convert from necessity. Let A be something that is the case; and if A is the case, then these things are the case (things which I know to be the case—call them B ). From the latter, then, I shall prove that the former is the case. (In mathematics conversion is more common because mathematicians assume nothing incidental—and in this too they differ from those who argue dialectically—but only definitions.) ( PoA , I, 12, 78a6-13) { §2.4 }

We deliberate not about ends but about means. For a doctor does not deliberate whether he shall heal, nor an orator whether he shall convince, nor a statesman whether he shall produce law and order, nor does any one else deliberate about his end. Having set the end, they consider how and by what means it is to be attained; and if it seems to be produced by several means they consider by which it is most easily and best produced, while if it is achieved by one only they consider how it will be achieved by this and by what means this will be achieved, till they come to the first cause, which in the order of discovery is last. For the person who deliberates seems to inquire and analyse in the way described as though he were analysing a geometrical construction (not all inquiry appears to be deliberation—for instance mathematical inquiries—but all deliberation is inquiry), and what is last in the order of analysis seems to be first in the order of becoming. And if we come on an impossibility, we give up the search, e.g. if we need money and this cannot be got; but if a thing appears possible we try to do it. ( NE , III, 3, 1112b8-27) { §2.4 }

The art of arranging a series of thoughts properly, either for discovering the truth when we do not know it, or for proving to others what we already know, can generally be called method.

Hence there are two kinds of method, one for discovering the truth, which is known as analysis , or the method of resolution , and which can also be called the method of discovery . The other is for making the truth understood by others once it is found. This is known as synthesis , or the method of composition , and can also be called the method of instruction .

Analysis does not usually deal with the entire body of a science, but is used only for resolving some issue. ( LAT , 233-4) { §4.1 }

Now analysis consists primarily in paying attention to what is known in the issue we want to resolve. The entire art is to derive from this examination many truths that can lead us to the knowledge we are seeking.

Suppose we wondered whether the human soul is immortal, and to investigate it we set out to consider the nature of the soul. First we would notice that it is distinctive of the soul to think, and that it could doubt everything without being able to doubt whether it is thinking, since doubting is itself a thought. Next we would ask what thinking is. Since we would see nothing contained in the idea of thought that is contained in the idea of the extended substance called body, and since we could even deny of thought everything belonging to body - such as having length, width, and depth, having different parts, having a certain shape, being divisible, etc. - without thereby destroying the idea we have of thought, from this we would conclude that thought is not at all a mode of extended substance, because it is the nature of a mode not to be able to be conceived while the thing of which it is a mode is denied. From this we infer, in addition, that since thought is not a mode of extended substance, it must be the attribute of another substance. Hence thinking substance and extended substance are two really distinct substances. It follows from this that the destruction of one in no way brings about the destruction of the other, since even extended substance is not properly speaking destroyed, but all that happens in what we call destruction is nothing more than the change or dissolution of several parts of matter which exist forever in nature. Likewise it is quite easy to judge that in breaking all the gears of a clock no substance is destroyed, although we say that the clock is destroyed. This shows that since the soul is in no way divisible or composed of parts, it cannot perish, and consequently is immortal.

This is what we call analysis or resolution . We should notice, first, that in this method - as in the one called composition - we should practice proceeding from what is better known to what is less known. For there is no true method which could dispense with this rule.

Second, it nevertheless differs from the method of composition in that these known truths are taken from a particular examination of the thing we are investigating, and not from more general things as is done in the method of instruction. Thus in the example we presented, we did not begin by establishing these general maxims: that no substance perishes, properly speaking; that what is called destruction is only a dissolution of parts; that therefore what has no parts cannot be destroyed, etc. Instead we rose by stages to these general notions.

Third, in analysis we introduce clear and evident maxims only to the extent that we need them, whereas in the other method we establish them first, as we will explain below.

Fourth and finally, these two methods differ only as the route one takes in climbing a mountain from a valley differs from the route taken in descending from the mountain into the valley, or as the two ways differ that are used to prove that a person is descended from St. Louis. One way is to show that this person had a certain man for a father who was the son of a certain man, and that man was the son of another, and so on up to St. Louis. The other way is to begin with St. Louis and show that he had a certain child, and this child had others, thereby descending to the person in question. This example is all the more appropriate in this case, since it is certain that to trace an unknown genealogy, it is necessary to go from the son to the father, whereas to explain it after finding it, the most common method is to begin with the trunk to show the descendants. This is also what is usually done in the sciences where, after analysis is used to find some truth, the other method is employed to explain what has been found.

This is the way to understand the nature of analysis as used by geometers. Here is what it consists in. Suppose a question is presented to them, such as whether it is true or false that something is a theorem, or whether a problem is possible or impossible; they assume what is at issue and examine what follows from that assumption. If in this examination they arrive at some clear truth from which the assumption follows necessarily, they conclude that the assumption is true. Then starting over from the end point, they demonstrate it by the other method which is called composition . But if they fall into some absurdity or impossibility as a necessary consequence of their assumption, they conclude from this that the assumption is false and impossible.

This is what may be said in a general way about analysis, which consists more in judgment and mental skill than in particular rules. ( LAT , 236-8) { §4.1 }

It is advisable to stress the point that philosophy, as we understand it, is wholly independent of metaphysics, inasmuch as the analytic method is commonly supposed by its critics to have a metaphysical basis. Being misled by the associations of the word ‘analysis’, they assume that philosophical analysis is an activity of dissection; that it consists in ‘breaking up’ objects into their constituent parts, until the whole universe is ultimately exhibited as an aggregate of ‘bare particulars’, united by external relations. If this were really so, the most effective way of attacking the method would be to show that its basic presupposition was nonsensical. For to say that the universe was an aggregate of bare particulars would be as senseless as to say that it was Fire or Water or Experience. It is plain that no such possible observation would enable to veify such an assertion. But, so far as I know, this line of criticism is in fact never adopted. The critics content themselves with pointing out that few, if any, of the complex objects in the world are simply the sum of their parts. They have a structure, an organic unity, which distinguishes them, as genuine wholes, from mere aggregates. But the analyst, so it is said, is obliged by his atomistic metaphysics to regard an object consisting of parts a , b , c , and d , in a distinctive configuration as being simply a + b + c + d , and thus gives an entirely false account of its nature.

If we follow the Gestalt psychologists, who of all men talk most constantly about genuine wholes, in defining such a whole as one in which the properties of every part depend to some extent on its position in the whole, then we may accept it as an empirical fact that there exist genuine, or organic, wholes. And if the analytic method involved a denial of this fact, it would indeed be a faulty method. But, actually, the validity of the analytic method is not dependent on any empirical, much less any metaphysical, presupposition about the nature of things. For the philosopher, as an analyst, is not directly concerned with the physical properties of things. He is concerned only with the way in which we speak about them.

In other words, the propositions of philosophy are not factual, but linguistic in character – that is, they do not describe the behaviour of physical, or even mental, objects; they express definitions, or the formal consequences of definitions. Accordingly, we may say that philosophy is a department of logic. For we shall see that the characteristic mark of a purely logical inquiry is that it is concerned with the formal consequences of our definitions and not with questions of empirical fact.

It follows that philosophy does not in any way compete with science. The difference in type between philosophical and scientific propositions is such that they cannot conceivably contradict one another. And this makes it clear that the possibility of philosophical analysis is independent of any empirical assumptions. That it is independent of any metaphysical assumptions should be even more obvious still. For it is absurd to suppose that the provision of definitions, and the study of their formal consequences, involves the nonsensical assertion that the world is composed of bare particulars, or any other metaphysical dogma.

What has contributed as much as anything to the prevalent misunderstanding of the nature of philosophical analysis is the fact that propositions and questions which are really linguistic are often expressed in such a way that they appear to be factual. A striking instance of this is provided by the proposition that a material thing cannot be in two places at once. This looks like an empirical proposition, and is constantly invoked by those who desire to prove that it is possible for an empirical proposition to be logically certain. But a more critical inspection shows that it is not empirical at all, but linguistic. It simply records the fact that, as the result of certain verbal conventions, the proposition that two sense-contents occur in the same visual or tactual sense-field is incompatible with the proposition that they belong to the same material thing. And this is indeed a necessary fact. But it has not the least tendency to show that we have certain knowledge about the empirical properties of objects. For it is necessary only because we happen to use the relevant words in a particular way. There is no logical reason why we should not so alter our definitions that the sentence ‘A thing cannot be in two places at once’ comes to express a self-contradiction instead of a necessary truth. (1936, 75-7) { §6.7 }

From our assertion that philosophy provides definitions, it must not be inferred that it is the function of the philosopher to compile a dictionary, in the ordinary sense. For the definitions which philosophy is required to provide are of a different kind from those which we expect to find in dictionaries. In a dictionary we look mainly for what may be called explicit definitions; in philosophy, for definitions in use . ...

We define a symbol in use , not by saying that it is synonymous with some other symbol, but by showing how the sentences in which it significantly occurs can be translated into equivalent sentences, which contain neither the definiendum itself, nor any of its synonyms. A good illustration of this process is provided by Bertrand Russell’s so-called theory of descriptions, which is not a theory at all in the ordinary sense, but an indication of the way in which all phrases of the form ‘the so-and-so’ are to be defined. ( Ibid ., 80-1) { §6.7 }

[A serious mistake in my account in Language, Truth and Logic ] was my assumption that philosophical analysis consisted mainly in the provision of ‘definitions in use’. It is, indeed, true that what I describe as philosophical analysis is very largely a matter of exhibiting the inter-relationship of different types of propositions; but the cases in which this process actually yields a set of definitions are the exception rather than the rule. ...

... Thus, when Professor Moore suggests that to say that ‘existence is not a predicate’ may be a way of saying that ‘there is some very important difference between the way in which “exist” is used in such a sentence as “Tame tigers exist” and the way in which “growl” is used in “Tame tigers growl”’, he does not develop his point by giving rules for the translation of one set of sentences into another. What he does is to remark that whereas it makes good sense to say ‘All tame tigers growl’ or ‘Most tame tigers growl’ it would be nonsense to say ‘All tame tigers exist’ or ‘Most tame tigers exist’. Now this may seem a rather trivial point for him to make, but in fact it is philosophically illuminating. For it is precisely the assumption that existence is a predicate that gives plausibility to ‘the ontological argument’; and the ontological argument is supposed to demonstrate the existence of a God. Consequently Moore by pointing out a peculiarity in the use of the word ‘exist’ helps to protect us from a serious fallacy; so that his procedure, though different from that which Russell follows in his theory of descriptions, tends to achieve the same philosophical end. (1946, 31-3) { §6.7 }

By the word paraphrasis may be designated that sort of exposition which may be afforded by transmuting into a proposition, having for its subject some real entity, a proposition which has not for its subject any other than a fictitious entity. ( EL , 246) { §5.6 }

By intuition is meant the kind of intellectual sympathy by which one places oneself within an object in order to coincide with what is unique in it and consequently inexpressible. Analysis, on the contrary, is the operation which reduces the object to elements already known, that is, to elements common both to it and other objects. To analyse, therefore, is to express a thing as a function of something other than itself. All analysis is thus a translation, a development into symbols, a representation taken from successive points of view from which we note as many resemblances as possible between the new object which we are studying and others which we believe we know already. In its eternally unsatisfied desire to embrace the object around which it is compelled to turn, analysis multiplies without end the number of its points of view in order to complete its always incomplete representation, and ceaselessly varies its symbols that it may perfect the always imperfect translation. It goes on, therefore, to infinity. But intuition, if intuition is possible, is a simple act. (1903, 6-7) { §5.1 }

[Analysis] operates always on the immobile, whilst intuition places itself in mobility, or, what comes to the same thing, in duration. There lies the very distinct line of demarcation between intuition and analysis. The real, the experienced and the concrete are recognised by the fact that they are variability itself, the element by the fact that it is invariable. And the element is invariable by definition, being a diagram, a simplified reconstruction, often a mere symbol, in any case a motionless view of the moving reality. (1903, 40-1) { §5.1 }

Modern science is neither one nor simple. It rests, I freely admit, on ideas which in the end we find clear; but these ideas have gradually become clear through the use made of them; they owe most of their clearness to the light which the facts, and the applications to which they led, have by reflection shed on them - the clearness of a concept being scarcely anything more at bottom than the certainty, at last obtained, of manipulating the concept profitably. At its origin, more than one of these concepts must have appeared obscure, not easily reconcilable with the concepts already admitted into science, and indeed very near the borderline of absurdity. This means that science does not proceed by an orderly dovetailing together of concepts predestined to fit each other exactly. True and fruitful ideas are so many close contacts with currents of reality, which do not necessarily converge on the same point. However the concepts in which they lodge themselves manage somehow, by rubbing off each other's corners, to settle down well enough together. (1903, 74) { §5.1 }

It may help to be reminded that many philosophers who might allow themselves to be described as “analysts” have been strongly influenced by the work of Russell, Moore, and Wittgenstein. For while all three have been engaged in “clarification of meaning” they have done so in different and distinctive ways; and the resulting divergences in conceptions of philosophical method have not yet been reconciled. This makes it hard to give any simple account of what is meant today by “philosophical analysis”. (1950a, 2) { §6.1 }

A man who had to describe “philosophical analysis” might resort to talking about a climate of opinion. The weather, he might say, is congenial to empiricists, naturalists, agnostics; the well acclimatized have admired the two Principia’s and the Tractatus and have read a hundred pages of Hume for one of Kant. Here rhetoric is viewed with suspicion and enthusiasm barely tolerated; this is a land of “prose writers, hoping to be understood” [J.M. Keynes, A Treatise on Probability , 1921, preface].

... If a formula or a slogan is wanted, it is easy enough to say that these writers (like Russell, Moore, and Wittgenstein before them) are engaged in clarification of meaning . ... And if those who are best at the work of clarification might feel embarrassed to provide a satisfactory analysis of “analysis”, that is perhaps no cause for apology or alarm. For it is a mark of life to resist arbitrary confinement, and “philosohical analysis” is still much alive. (1950a, 12-13) { §6.1 }

Analysis comprises mathematical methods for finding the solutions (in geometry: the constructions) of problems or the proofs of theorems, doing so by introducing unknowns. (2001, 129) { §4.2 }

It is a very common and most ruinous superstition to suppose that analysis is no alteration, and that, whenever we distinguish, we have at once to do with divisible existence. It is an immense assumption to conclude, when a fact comes to us as a whole, that some parts of it may exist without any sort of regard for the rest. Such naive assurance of the outward reality of all mental distinctions, such touching confidence in the crudest identity of thought and existence, is worthy of the school which so loudly appeals to the name of Experience. ... If it is true in any sense (and I will not deny it) that thought in the end is the measure of things, yet at least this is false, that the divisions we make within a whole all answer to elements whose existence does not depend on the rest. It is wholly unjustifiable to take up a complex, to do any work we please upon it by analysis, and then simply predicate as an adjective of the given these results of our abstraction. These products were never there as such, and in saying, as we do, that as such they are there, we falsify the fact. You can not always apply in actual experience that coarse notion of the whole as the sum of its parts into which the school of ‘experience’ so delights to torture phenomena. If it is wrong in physiology to predicate the results, that are reached by dissection, simply and as such of the living body, it is here infinitely more wrong. The whole that is given to us is a continuous mass of perception and feeling; and to say of this whole, that any one element would be what it is there, when apart from the rest, is a very grave assertion. We might have supposed it not quite self-evident, and that it was possible to deny it without open absurdity. ( PL , §64/ WLM , 77-8) { §5.6 }

judgement is the differentiation of a complex whole, and hence always is analysis and synthesis in one. ( AR , 149/ WLM , 158) { §5.6 }

At any moment my actual experience, however relational its contents, is in the end non-relational. No analysis into relations and terms can ever exhaust its nature or fail in the end to belie its essence. What analysis leaves for ever outstanding is no mere residue, but is a vital condition of the analysis itself. Everything which is got out into the form of an object implies still the felt background against which the object comes, and, further, the whole experience of both feeling and object is a non-relational immediate felt unity. The entire relational consciousness, in short, is experienced as falling within a direct awareness. This direct awareness is itself non-relational. It escapes from all attempts to exhibit it by analysis as one or more elements in a relational scheme, or as that scheme itself, or as a relation or relations, or as the sum or collection of any of these abstractions. And immediate experience not only escapes, but it serves as the basis on which the analysis is made. Itself is the vital element within which every analysis still moves, while, and so far as, and however much, that analysis transcends immediacy. ( ETR , 176/ WLM , 280-1) { §5.6 }

I would rather now lay more stress on the logical vice of all Analysis and Abstraction – so far as that means taking any feature in the Whole of Things as ultimately real except in its union with the Whole. ( Collected Works of F.H. Bradley: Selected Correspondence 1905-1924 , Bristol, Thoemmes Press, 1999, 275)

Analysis and synthesis I take in the end to be two aspects of one principle … Every analysis proceeds from and on the basis of a unity ... The point before us is the question as to how, without separation in its existence, we can discriminate ideally in analysis. ( ETR , 300)

Socratic method is a way of bringing our practices under rational control by expressing them explicitly in a form in which they can be confronted with objections and alternatives, a form in which they can be exhibited as the conclusions of inferences seeking to justify them on the basis of premises advanced as reasons, and as premises in further inferences exploring the consequences of accepting them. (2000, 56) { §6.9 }

I think of analytic philosophy as having at its center a concern with semantic relations between what I will call ‘vocabularies’. … Its characteristic form of question is whether and in what way one can make sense of the meanings expressed by one kind of locution interms of the meanings expressed by another kind of locution. So, for instance, two early paradigmatic projects were to show that everything expressible in the vocabulary of number-theory, and again, everything expressible using definite descriptions, is expressible already in the vocabulary of first-order quantificational logic with identity.

The nature of the key kind of semantic relation between vocabularies has been variously characterized during the history of analytic philosophy: as analysis, definition, paraphrase, translation, reduction of different sorts, truth-making, and various kinds of supervenience—to name just a few contenders. In each case, however, it is characteristic of classical analytic philosophy that logical vocabulary is accorded a privileged role in specifying these semantic relations. It has always been taken at least to be licit to appeal to logical vocabulary in elaborating the relation between analysandum and analysans —target vocabulary and base vocabulary—and, according to stronger versions of this thesis, that may be the only vocabulary it is licit to employ in that capacity. I will refer to this aspect of the analytic project as its commitment to ‘ semantic logicism ’. (2006, Lecture One, §1) { §6.9 }

What I want to call the “classical project of analysis”, then, aims to exhibit the meanings expressed by various target vocabularies as intelligible by means of the logical elaboration of the meanings expressed by base vocabularies thought to be privileged in some important respects—epistemological, ontological, or semantic—relative to those others. This enterprise is visible in its purest form in what I have called the “core programs” of empiricism and naturalism, in their various forms. In my view the most significant conceptual development in this tradition—the biggest thing that ever happened to it—is the pragmatist challenge to it that was mounted during the middle years of the twentieth century. Generically, this movement of thought amounts to a displacement from the center of philosophical attention of the notion of meaning in favor of that of use : in suitably broad senses of those terms, replacing concern with semantics by concern with pragmatics . ( Ibid ., Lecture One, §2) { §6.9 }

the analysis or, more precisely, quasi-analysis of an entity that is essentially an indivisible unit into several quasi-constituents means placing the entity in several kinship contexts on the basis of a kinship relation, where the unit remains undivided. (1928a, §71; English tr. by Rolf A. George slightly altered) { §6.7 }

The logical analysis of a particular expression consists in the setting-up of a linguistic system and the placing of that expression in this system. (1936, 143) { §6.7 }

That part of the work of philosophers which may be held to be scientific in its nature—excluding the empirical questions which can be referred to empirical science—consists of logical analysis. The aim of logical syntax is to provide a system of concepts, a language, by the help of which the results of logical analysis will be exactly formulable. Philosophy is to be replaced by the logic of science —that is to say, by the logical analysis of the concepts and sentences of the sciences, for the logic of science is nothing other than the logical syntax of the language of science . (1937, xiii) { §6.7 }

The task of making more exact a vague or not quite exact concept used in everyday life or in an earlier stage of scientific or logical development, or rather of replacing it by a newly constructed, more exact concept, belongs among the most important tasks of logical analysis and logical construction. We call this the task of explicating, or of giving an explication for, the earlier concept … (1947, 8-9) { §6.7 }

By the procedure of explication we mean the transformation of an inexact, prescientific concept, the explicandum , into a new exact concept, the explicatum . Although the explicandum cannot be given in exact terms, it should be made as clear as possible by informal explanations and examples. ...

The term ‘explicatum’ has been suggested by the following two usages. Kant calls a judgement explicative if the predicate is obtained by analysis of the subject. Husserl, in speaking about the synthesis of identification between a confused, nonarticulated sense and a subsequently intended distinct, articulated sense, calls the latter the ‘Explikat’ of the former. (For both uses see Dictionary of philosophy [1942], ed. D. Runes, p. 105). What I mean by ‘explicandum’ and ‘explicatum’ is to some extent similar to what C.H. Langford calls ‘analysandum’ and ‘analysans’: “the analysis then states an appropriate relation of equivalence between the analysandum and the analysans” [Langford 1942, 323 { §6.4 }]; he says that the motive of an analysis “is usually that of supplanting a relatively vague idea by a more precise one” ( ibid ., p. 329).

(Perhaps the form ‘explicans’ might be considered instead of ‘explicatum’; however, I think that the analogy with the terms ‘definiendum’ and ‘definiens’ would not be useful because, if the explication consists in giving an explicit definition, then both the definiens and the definiendum in this definition express the explicatum, while the explicandum does not occur.) The procedure of explication is here understood in a wider sense than the procedures of analysis and clarification which Kant, Husserl, and Langford have in mind. The explicatum (in my sense) is in many cases the result of analysis of the explicandum (and this has motivated my choice of the terms); in other cases, however, it deviates deliberately from the explicandum but still takes its place in some way; this will become clear by the subsequent examples. (1950, 3) { §6.7 }

[T]he sense of all objective judgments reduces to a final original relation, which can be expressed in different formulations as the relation of “form” to “content”, as the relation of “universal” to “particular”, as the relation of “validity [ Geltung ]” to “being [ Sein ]”. Whatever designation one may finally choose here, what is alone decisive is that the basic relation itself is to be retained as a strictly unitary relation, which can only be designated through the two opposed moments that enter into it – but never constructed out of them, as if they were independent constituents present in themselves. The original relation is not to be defined in such a way that the “universal” somehow “subsists” next to or above the “particular” – the form somehow separate from the content – so that the two are then melded with one another by means of some or another fundamental synthesis of knowledge. Rather, the unity of mutual determination constitutes the absolutely first datum, behind which one can go back no further, and which can only be analyzed via the duality of two “viewpoints” in an artificially isolating process of abstraction. It is the basic flaw of all metaphysical epistemologies that they always attempt to reinterpret this duality of “moments” as a duality of “elements”. (1913, 13-14; cited and tr. by Friedman 2000, 34) { §5.4 }

conceptual analysis typically relates one kind of reason for using a certain word to another. (1986, 51) { §6.9 }

When philosophical analysis proceeds from intuitively sanctioned premisses to a reasoned conclusion, it may be described as moving from analysandum to analysans. It seeks to ensure that any muddles or inconsistencies in our unreasoned inclinations and passive prejudices are replaced by an explicitly formulated, consciously co-ordinated, adequately reasoned, and freely adopted system of acceptable principles. (1986, 96) { §6.9 }

Socrates was essentially the inventor of a method. ... His revolt against the study of nature was essentially a revolt against observation in favour of thought; and whereas mathematical method, as an example of thought, had already been discovered by his predecessors, his own discovery was that a similar method, for which he invented an appropriate technique, could be applied to ethical questions. This technique, as he himself recognized, depended on a principle which is of great importance to any theory of philosophical method: the principle that in a philosophical inquiry what we are trying to do is not to discover something of which until now we have been ignorant, but to know better something which in some sense we knew already; not to know it better in the sense of coming to know more about it, but to know it better in the sense of coming to know it in a different and better way—actually instead of potentially, or explicitly instead of implicitly, or in whatever terms the theory of knowledge chooses to express the difference: the difference itself has been a familiar fact ever since Socrates pointed it out. (1933, 10-11) { §5.6 }

[The] work of disentangling and arranging questions, which ... I [call] analysis, may be alternatively described as the work of detecting presuppositions. ... The analysis which detects absolute presuppositions I call metaphysical analysis; but as regards procedure and the qualifications necessary to carry it out there is no difference whatever between metaphysical analysis and analysis pure and simple ... (1940, 39-40) { §5.6 }

It is only by analysis that any one can ever come to know either that he is making any absolute presuppositions at all or what absolute presuppositions he is making.

Such analysis may in certain cases proceed in the following manner. If the inquirer can find a person to experiment upon who is well trained in a certain type of scientific work, intelligent and earnest in his devotion to it, and unaccustomed to metaphysics, let him probe into various presuppositions that his ‘subject’ has been taught to make in the course of his scientific education, and invite him to justify each or alternatively to abandon it. If the ‘inquirer’ is skilful and the ‘subject’ the right kind of man, these invitations will be contemplated with equanimity, and even with interest, so long as relative presuppositions are concerned. But when an absolute presupposition is touched, the invitation wil be rejected, even with a certain degree of violence.

The rejection is a symptom that the ‘subject’, co-operating with the work of analysis, has come to see that the presupposition he is being asked to justify or abandon is an absolute presupposition; and the violence with which it is expressed is a symptom that he feels the importance of this absolute presupposition for the kind of work to which he is devoted. This is what ... I called being ‘ticklish in one’s absolute presuppositions’; and the reader will see that this ticklishness is a sign of intellectual health combined with a low degree of analytical skill. A man who is ticklish in that way is a man who knows, ‘instinctively’ as they say, that absolute presuppositions do not need justification. ( Ibid. , 43-4) { §5.6 }

metaphysical analysis, the discovery that certain presuppositions actually made are absolute presuppositions, is an integral part or an indispensable condition, you can put it whichever way you like, of all scientific work.( Ibid. , 84) { §5.6 }

In philosophy we are used to definitions, analyses, reductions. Typically these are intended to carry us from concepts better understood, or clear, or more basic epistemologically or ontologically, to others we want to understand. The method I have suggested fits none of these categories. I have proposed a looser relation between concepts to be illuminated and the relatively more basic. (‘Radical Interpretation’, 1972, Inquiries into Truth and Interpretation , Oxford: Oxford University Press, 2001, 137)

Unlike the primitives who gave a face to every moving thing, or the early Greeks who defined all the aspects and forces of nature, modern man is obsessed by the need to depersonalise (or impersonalise) all that he most admires. There are two reasons for this tendency. The first is analysis , that marvellous instrument of scientific research to which we owe all our advances but which, breaking down synthesis after synthesis, allows one soul after another to escape, leaving us confronted with a pile of dismantled machinery, and evanescent particles. The second reason lies in the discovery of the sidereal world, so vast that it seems to do away with all proportion between our own being and the dimensions of the cosmos around us. ( The Phenomenon of Man , 1955, 282; tr. Bernard Wall, Fontana, 1965; tr. first publ. 1959)

Up until now the idea of philosophy remained defined in a formal way as an idea of an infinite task theoria . Could a history of this infinite theoretical life, which merges itself in its efforts and failures with a simple realization of the self , take on the value of a genetic description? Will the history of the “transcendental motive” through all the stages of European philosophy, enlighten us at last on the genesis of transcendental subjectivity? But such a history presupposes the possibility of such a going backward, the possibility of finding again the originary sense of the former presents as such. It implies the possibility of a transcendental “regression” ( Ruckfrage ) through a history that is intelligible and transparent to consciousness, a history whose sedimentations can be unmade and remade without alteration. ( The Problem of Genesis in Husserl's Philosophy , The University of Chicago Press, 2003, 161; tr. Marian Hobson)

[discussing his ‘Rule Four’: “ We need a method if we are to investigate the truth of things ”] … the human mind has within it a sort of spark of the divine, in which the first seeds of useful ways of thinking are sown, seeds which, however neglected and stifled by studies which impede them, often bear fruit of their own accord. This is our experience in the simplest of sciences, arithmetic and geometry: we are well aware that the geometers of antiquity employed a sort of analysis which they went on to apply to the solution of every problem, though they begrudged revealing it to posterity. At the present time a sort of arithmetic called ‘algebra’ is flourishing, and this is achieving for numbers what the ancients did for figures. ( Rules for the Direction of the Mind , in PW , I, 16-17) { §4.2 }

As for the method of demonstration, this divides into two varieties: the first proceeds by analysis and the second by synthesis.

Analysis shows the true way by means of which the thing in question was discovered methodically and as it were a priori , so that if the reader is willing to follow it and give sufficient attention to all points, he will make the thing his own and understand it just as perfectly as if he had discovered it for himself. But this method contains nothing to compel belief in an argumentative or inattentive reader; for if he fails to attend even to the smallest point, he will not see the necessity of the conclusion. Moreover there are many truths which - although it is vital to be aware of them - this method often scarcely mentions, since they are transparently clear to anyone who gives them his attention.

Synthesis, by contrast, employs a directly opposite method where the search is, as it were, a posteriori (though the proof itself is often more a priori than it is in the analytic method). It demonstrates the conclusion clearly and employs a long series of definitions, postulates, axioms, theorems and problems, so that if anyone denies one of the conclusions it can be shown at once that it is contained in what has gone before, and hence the reader, however argumentative or stubborn he may be, is compelled to give his assent. However, this method is not as satisfying as the method of analysis, nor does it engage the minds of those who are eager to learn, since it does not show how the thing in question was discovered.

It was synthesis alone that the ancient geometers usually employed in their writings. But in my view this was not because they were utterly ignorant of analysis, but because they had such a high regard for it that they kept it to themselves like a sacred mystery.

Now it is analysis which is the best and truest method of instruction, and it was this method alone which I employed in my Meditations . As for synthesis, which is undoubtedly what you are asking me to use here, it is a method which it may be very suitable to deploy in geometry as a follow-up to analysis, but it cannot so conveniently be applied to these metaphysical subjects.

The difference is that the primary notions which are presupposed for the demonstration of geometrical truths are readily accepted by anyone, since they accord with the use of our senses. Hence there is no difficulty there, except in the proper deduction of the consequences, which can be done even by the less attentive, provided they remember what has gone before. Moreover, the breaking down of propositions to their smallest elements is specifically designed to enable them to be recited with ease so that the student recalls them whether he wants to or not.

In metaphysics by contrast there is nothing which causes so much effort as making our perception of the primary notions clear and distinct. Admittedly, they are by their nature as evident as, or even more evident than, the primary notions which the geometers study; but they conflict with many preconceived opinions derived from the senses which we have got into the habit of holding from our earliest years, and so only those who really concentrate and meditate and withdraw their minds from corporeal things, so far as is possible, will achieve perfect knowledge of them. Indeed, if they were put forward in isolation, they could easily be denied by those who like to contradict just for the sake of it. (‘Second Set of Replies’, in PW , II, 110-11) { §4.2 }

[interpolated into the text of the Elements ] What is analysis and what is synthesis. Analysis is the assumption of that which is sought as if it were admitted [and the arrival] by means of its consequences at something admitted to be true. Synthesis is an assumption of that which is admitted [and the arrival] by means of its consequences at something admitted to be true. ( E , Book XIII, Prop. 1; Vol. III, 442, where Heath comments on the interpolation) { §2.2 }

[In replying to the objections that Husserl had raised in his Philosophie der Arithmetik (1891) to Frege’s Grundlagen definitions] If words and combinations of words refer to [ bedeuten ] ideas, then for any two of them there are only two possibilities: either they designate the same idea or they designate different ideas. In the former case it is pointless to equate them by means of a definition: this is ‘an obvious circle’; in the latter case it is wrong. These are also the objections the author raises, one of them regularly. A definition is also incapable of analysing the sense, for the analysed sense just is not the original one. In using the word to be explained, I either think clearly everything I think when I use the defining expression: we then have the ‘obvious circle’; or the defining expression has a more richly articulated sense, in which case I do not think the same thing in using it as I do in using the word to be explained: the definition is then wrong. One would think that a definition was unobjectionable in the case where the word to be explained had as yet no sense at all, or where we were asked explicitly to regard its sense as non-existent so that it was first given a sense by the definition. But in the last case too, the author refutes the definition by reminding us of the difference between the ideas (p. 107). To evade all objections, one would accordingly have to create a new verbal root and form a word out of it. This reveals a split between psychological logicians and mathematicians. What matters to the former is the sense of the words, as well as the ideas which they fail to distinguish from the sense; whereas what matters to the latter is the thing itself: the Bedeutung of the words. The reproach that what is defined is not the concept but its extension actually affects all mathematical definitions. For the mathematician, it is no more right and no more wrong to define a conic as the line of intersection of a plane with the surface of a circular cone than to define it as a plane curve with an equation of the second degree in parallel coordinates. His choice of one or the other of these expressions or of some other one is guided solely by reasons of convenience and is made irrespective of the fact that the expressions have neither the same sense nor evoke the same ideas. I do not intend by this that a concept and its extension are one and the same, but that coincidence in extension is a necessary and sufficient criterion for the occurrence between concepts of the relation that corresponds to identity [ Gleichheit ] between objects. ( RH , 319-20/ FR , 225-6) { §6.2 }

We come to definitions . Definitions proper must be distinguished from elucidations [ Erläuterungen ]. In the first stages of any discipline we cannot avoid the use of ordinary words. But these words are, for the most part, not really appropriate for scientific purposes, because they are not precise enough and fluctuate in their use. Science needs technical terms that have precise and fixed Bedeutungen , and in order to come to an understanding about these Bedeutungen and exclude possible misunderstandings, we provide elucidations. Of course in so doing we have again to use ordinary words, and these may display defects similar to those which the elucidations are intended to remove. So it seems that we shall then have to provide further elucidations. Theoretically one will never really achieve one’s goal in this way. In practice, however, we do manage to come to an understanding about the Bedeutungen of words. Of course we have to be able to count on a meeting of minds, on others’ guessing what we have in mind. But all this precedes the construction of a system and does not belong within a system. In constructing a system it must be assumed that the words have precise Bedeutungen and that we know what they are. ( LM , 224/ FR , 313) { §6.2 }

We have ... to distinguish two quite different cases :

1. We construct a sense out of its constituents and introduce an entirely new sign to express this sense. This may be called a ‘constructive definition’ [‘ aufbauende Definition ’], but we prefer to call it a ‘definition’ tout court .

2. We have a simple sign with a long-established use. We believe that we can give a logical analysis [ Zerlegung ] of its sense, obtaining a complex expression which in our opinion has the same sense. We can only allow something as a constituent of a complex expression if it has a sense we recognize. The sense of the complex expression must be yielded by the way in which it is put together. That it agrees with the sense of the long established simple sign is not a matter for arbitrary stipluation, but can only be recognized by an immediate insight. No doubt we speak of a definition in this case too. It might be called an ‘analytic definition’ [‘ zerlegende Definition ’] to distinguish it from the first case. But it is better to eschew the word ‘definition’ altogether in this case, because what we should here like to call a definition is really to be regarded as an axiom. In this second case there remains no room for an arbitrary stipulation, because the simple sign already has a sense. Only a sign which as yet has no sense can have a sense arbitrarily assigned to it. So we shall stick to our original way of speaking and call only a constructive definition a definition. According to that a definition is an arbitrary stipulation which confers a sense on a simple sign which previously had none. This sense has, of course, to be expressed by a complex sign whose sense results from the way it is put together.

Now we still have to consider the difficulty we come up against in giving a logical analysis when it is problematic whether this analysis is correct.

Let us assume that A is the long-established sign (expression) whose sense we have attempted to analyse logically by constructing a complex expression that gives the analysis. Since we are not certain whether the analysis is successful, we are not prepared to present the complex expression as one which can be replaced by the simple sign A . If it is our intention to put forward a definition proper, we are not entitled to choose the sign A , which already has a sense, but we must choose a fresh sign B , say, which has the sense of the complex expression only in virtue of the definition. The question now is whether A and B have the same sense. But we can bypass this question altogether if we are constructing a new system from the bottom up; in that case we shall make no further use of the sign A – we shall only use B . We have introduced the sign B to take the place of the complex expression in question by arbitrary fiat and in this way we have conferred a sense on it. This is a definition in the proper sense, namely a constructive definition.

If we have managed in this way to construct a system for mathematics without any need for the sign A , we can leave the matter there; there is no need at all to answer the question concerning the sense in which – whatever it may be – this sign had been used earlier. In this way we court no objections. However, it may be felt expedient to use sign A instead of sign B . But if we do this, we must treat it as an entirely new sign which had no sense prior to the definition. We must therefore explain that the sense in which this sign was used before the new system was constructed is no longer of any concern to us, that its sense is to be understood purely from the constructive definition that we have given. In constructing the new system we can take no account, logically speaking, of anything in mathematics that existed prior to the new system. Everything has to be made anew from the ground up. Even anything that we may have accomplished by our analytical activities is to be regarded only as preparatory work which does not itself make any appearance in the new system itself.

Perhaps there still remains a certain unclarity. How is it possible, one may ask, that it should be doubtful whether a simple sign has the same sense as a complex expression if we know not only the sense of the simple sign, but can recognize the sense of the complex one from the way it is put together? The fact is that if we really do have a clear grasp of the sense of the simple sign, then it cannot be doubtful whether it agrees with the sense of the complex expression. If this is open to question although we can clearly recognize the sense of the complex expression from the way it is put together, then the reason must lie in the fact that we do not have a clear grasp of the sense of the simple sign, but that its outlines are confused as if we saw it through a mist. The effect of the logical analysis of which we spoke will then be precisely this – to articulate the sense clearly. Work of this kind is very useful; it does not, however, form part of the construction of the system, but must take place beforehand. Before the work of construction is begun, the building stones have to be carefully prepared so as to be usable; i.e. the words, signs, expressions, which are to be used, must have a clear sense, so far as a sense is not to be conferred on them in the system itself by means of a constructive definition.

We stick then to our original conception: a definition is an arbitrary stipulation by which a new sign is introduced to take the place of a complex expression whose sense we know from the way it is put together. A sign which hitherto had no sense acquires the sense of a complex expression by definition. ( LM , 227-9/ FR , 317-8) { §6.2 }

Analysis … is sorting out the structures of signification … and determining their social ground and import. ( The Interpretation of Cultures , New York: Basic Books, 1973, 9)

Cultural analysis is (or should be) guessing at meanings, assessing the guesses, and drawing explanatory conclusions from the better guesses, not discovering the Continent of Meaning and mapping out its bodiless landscape. ( Ibid ., 20)

The analysis of an idea, as it used to be carried out, was, in fact, nothing else than ridding it of the form in which it had become familiar. To break an idea up into its original elements is to return to its moments, which at least do not have the form of the given idea, but rather constitute the immediate property of the self. This analysis, to be sure, only arrives at thoughts which are themselves familiar, fixed, and inert determinations. But what is thus separated and non-actual is an essential moment; for it is only because the concrete does divide itself, and make itself into something non-actual, that it is self-moving. The activity of dissolution is the power and work of the Understanding , the most astonishing and mightiest of powers, or rather the absolute power. The circle that remains self-enclosed and, like substance, holds its moments together, is an immediate relationship, one therefore which has nothing astonishing about it. But that an accident as such, detached from what circumscribes it, what is bound and is actual only in its context with others, should attain an existence of its own and a separate freedom—this is the tremendous power of the negative; it is the energy of thought, of the pure ‘I’. Death, if that is what we want to call this non-actuality, is of all things the most dreadful, and to hold fast what is dead requires the greatest strength. Lacking strength, Beauty hates the Understanding for asking of her what it cannot do. But the life of Spirit is not the life that shrinks from death and keeps itself untouched by devastation, but rather the life that endures it and maintains itself in it. It wins its truth only when, in utter dismemberment, it finds itself. It is this power, not as something positive, which closes its eyes to the negative, as when we say of something that it is nothing or is false, and then, having done with it, turn away and pass on to something else; on the contrary, Spirit is this power only by looking the negative in the face, and tarrying with it. This tarrying with the negative is the magical power that converts it into being. This power is identical with what we earlier called the Subject, which by giving determinateness an existence in its own element supersedes abstract immediacy, i.e. the immediacy which barely is, and thus is authentic substance: that being or immediacy whose mediation is not outside of it but which is this mediation itself. ( PS , ‘Preface’, §32, 18-19)

[Summary of above passage offered by J.N. Findlay] The analysis of an idea is the removal of its familiarity, its reduction to elements that are the true possessions of the thinking self. In such reduction the idea itself changes and renders itself unreal. The force which effects analysis is that of the Understanding, the most remarkable and absolute of powers, the power of the thinking self and also of death. It is above all marvellous that this thinking self should be able to isolate, and to look at apart, what can only exist as an aspect or ‘moment’ in a living whole. Thinking Spirit can, however, only grasp such a whole by first tearing it into parts, each of which it must look at separately for a while, before putting them back in the whole. The thinking self must destroy an immediate, existent unity in order to arrive at a unity which includes mediation, and is in fact mediation itself. (‘Analysis of the Text’, §32, in PS , 499) { §5.2 }

What we are trying to bring to light here by means of phenomenological analysis in regard to the intentional structure of production is not contrived and fabricated but already present in the everyday, pre-philosophical productive behaviour of the Dasein. In producing, the Dasein lives in such an understanding of being without conceiving it or grasping it as such. (1927, §12, 114-15) { §5.8 }

every method by which we investigate the causes of things is either compositive, or resolutive, or partly compositive, partly resolutive. And the resolutive is usually called analytic, while the compositive is usually called synthetic. ( Logica , ‘On Method’, §1, 289) { §4.1 }

What philosophers seek to know. Philosophers seek scientific knowledge either simply or indefinitely, that is, they seek to knkow as much as they can when no definite question is proposed or the cause of some definite phenomenon or at least to discover something definite, such as what the cause of light is, or of heat, or gravity, of a figure which has been proposed, and similar things; or in what subject some proposed accident inheres; or which of many accidents is above all conducive to the production of some proposed effect; or in what way particular proposed causes ought to be conjoined in order to produce a definite effect. Because of the variety of the things sought for, sometimes the analytic method, sometimes the synthetic method, and sometimes both ought to be applied.

The first part, by which principles are found, is purely analytic. Seeing that the causes of all singulars are composed from the causes of universals or simples, it is necessary for those who are looking simply for scientific knowledge, which consists of the knowledge of the causes of all things insofar as this can be achieved, to know the causes of universals or those accidents which are common to all bodies, that is, to every material thing, before they know the causes of singular things, that is, of the accidents by which one thing is distinguished from another. Again, before the causes of those things can be known, it is necessary to know which things are universals. But since universals are contained in the nature of singular things, they must be unearthed by reason, that is, by resolution. For example, let any conception or idea of a singular thing be proposed, say a square. The square is resolved into: plane, bounded by a certain number of lines equal to one another, and right angles . Therefore we have these universals or components of every material thing: line, plane (in which a surface is contained), being bounded, angle, rectitude , and equality . If anyone finds the causes or origin of these, he will put them together as the cause of the square. Again, if he proposes to himself the conception of gold, the ideas of being solid, visible, and heavy (that is, of tending to the center of the earth or of motion downwards) and many others more universal than gold itself, which can be resolved further until one arrives at the most universal, will come from this by resolution. And by this same method of resolving things into other things one will know what those things are, of which, when their causes are known what those things are, of which, when their causes are known and composed one by one, the causes of all singular things are known. We thus conclude that the method of investigating the universal notions of things is purely analytic. ( Ibid ., §§ 3-4, 291-5) { §4.1 }

The method of scientific knowledge, civil as well as natural, [starting] from sense-experience and [going] to principles is analytic; while [starting] from principles is synthetic. ( Ibid ., §7, 301) { §4.1 }

it is obvious that in the investigation of causes there is a need partly for the analytic method, partly for the synthetic method. The analytic method is needed for understanding the circumstances of the effect one by one; the synthetic method for putting together those things which, single in themselves, act as one. ( Ibid ., §10, 311) { §4.1 }

that art of geometers which they call logistic is ... the method according to which by supposing that the thing asked about is true they come upon in reasoning either things known [to be true], from which they can prove the truth of the thing sought, or [they come upon] impossibilities, from which it can be understood that what was supposed [to be true] was false. ( Ibid ., §19, 329) { §4.1 }

[Logical analysis] stands somewhere between translating and paraphrasing. ( Logic , Harmondsworth: Penguin, 1977, 86)

The terms “analysis” and “synthesis” bring to mind, on the one hand, certain methodological practices in the works of Plato, Descartes, Newton, Kant, Hegel, and others and, on the other hand, techniques in fields as disparate as chemistry and logic, mathematics and psychology. The width of this spectrum of associations alerts us to the realization that at the base of these two related terms there lies a specific methodological thema-antithema ... pair. Indeed, it is one of the most pervasive and fundamental ones, in science and outside. This chapter attempts to uncover and identify this thematic content, to clarify the meanings and uses of the terms “analysis” and “synthesis”, and especially to distinguish among four general meanings: (1) Analysis and Synthesis, and particularly synthesis, used in the grand, cultural sense, (2) Analysis and Synthesis used in the reconstitutional sense (e.g., where an analysis, followed by a synthesis, re-establishes the original condition), (3) Analysis and Synthesis used in the transformational sense (e.g., where the application of Analysis and Synthesis advances one to a qualitatively new level), and (4) Analysis and Synthesis used in the judgmental sense (as in the Kantian categories and their modern critiques). (1998, 111) { §5.5 }

The point of view of function is the central one for phenomenology; the investigations radiating from it comprise almost the whole phenomenological sphere, and in the end all phenomenological analyses somehow enter into its service as component parts or preliminary stages. In place of analysis and comparison, description and classification restricted to particular experiences [ Erlebnisse ], the particulars are considered from the “teleological” point of view of their function, to make possible “synthetic unity”. ( IPP , I, §86; Kersten’s tr. modified) { §5.8 }

Explication is penetration of the internal horizon of the object by the direction of perceptual interest. In the case of the unobstructed realization of this interest, the protentional expectations fulfill themselves in the same way; the object reveals itself in its properties as that which it was anticipated to be, except that what was anticipated now attains original givenness. A more precise determination results, eventually perhaps partial corrections, or—in the case of obstruction—disappointment of the expectations, and partial modalization. ( EJ , §22, 105) { §5.8 }

The process of explication in its originality is that in which an object given at first hand is brought to explicit intuition. The analysis of its structure must bring to light how a twofold constitution of sense [ Sinngebung ] is realized in it: “object as substrate” and “determination α ...”; it must show how this constitution of sense is realized in the form of a process which goes forward in separate steps, through which, however, extends continuously a unity of coincidence —a unity of coincidence of a special kind, belonging exclusively to these sense-forms. ( EJ , §24a, 114) { §5.8 }

§1. MATHEMATICS ARRIVES AT ALL ITS DEFINITIONS SYNTHETICALLY, WHEREAS PHILOSOPHY ARRIVES AT ITS DEFINITIONS ANALYTICALLY

There are two ways in which one can arrive at a general concept: either by the arbitrary combination of concepts, or by separating out that cognition which has been rendered distinct by means of analysis. Mathematics only ever draws up its definitions in the first way. For example, think arbitrarily of four straight lines bounding a plane surface so that the opposite sides are not parallel to each other. Let this figure be called a trapezium . The concept which I am defining is not given prior to the definition itself; on the contrary, it only comes into existence as a result of that definition. Whatever the concept of a cone may ordinarily signify, in mathematics, the concept is the product of the arbitrary representation of a right-angled triangle which is rotated on one of its sides. In this and in all other cases the definition obviously comes into being as a result of synthesis .

The situation is entirely different in the case of philosophical definitions. In philosophy, the concept of a thing is always given, albeit confusedly or in an insufficiently determinate fashion. The concept has to be analysed; the characteristic marks which have been separated out and the concept which has been given have to be compared with each other in all kinds of contexts; and this abstract thought must be rendered complete and determinate. For example, everyone has a concept of time. But suppose that that concept has to be defined. The idea of time has to be examined in all kinds of relation if its characteristic marks which have been abstracted have to be combined together to see whether they yield an adequate concept; they have to be collated with each other to see whether one characteristic mark does not partly include another within itself. If, in this case, I had tried to arrive at a definition of time synthetically, it would have had to have been a happy coincidence indeed if the concept, thus reached synthetically, had been exactly the same as that which completely expresses the idea of time which is given to us. ( IDP , 2:276-7/ TP , 248-9) { §4.5 }

The true method of metaphysics is basically the same as that introduced by Newton into natural science and which has been of such benefit to it. Newton’s method maintains that one ought, on the basis of certain experience and, if need be, with the help of geometry, to seek out the rules in accordance with which certain phenomena of nature occur. ( IDP , 2:286/ TP , 259) { §4.5 }

What I am chiefly concerned to establish is this: in metaphysics one must proceed analytically throughout, for the business of metaphysics is actually the analysis of confused cognitions. If this procedure is compared with the procedure which is adopted by philosophers and which is currently in vogue in all schools of philosophy, one will be struck by how mistaken the practice of philosophers is. With them, the most abstracted concepts, at which the understanding naturally arrives last of all, constitute their starting point, and the reason is that the method of the mathematicians, which they wish to imitate throughout, is firmly fixed in their minds. This is why there is a strange difference to be found between metaphysics and all other sciences. In geometry and in the other branches of mathematics, one starts with what is easier and then one slowly advances to the more difficult operations. In metaphysics, one starts with what is the most difficult: one starts with possibility, with existence in general, with necessity and contingency, and so on – all of them concepts which demand great abstraction and close attention. And the reason for this is to be sought chiefly in the fact that the signs for these concepts undergo numerous and imperceptible modifications in use; and the differences between them must not be overlooked. One is told that one ought to proceed synthetically throughout. Definitions are thus set up right at the beginning, and conclusions are confidently drawn from them. Those who practise philosophy in this vein congratulate each other for having learnt the secret of thorough thought from the geometers. What they do not notice at all is the fact that geometers acquire their concepts by means of synthesis , whereas philosophers can only acquire their concepts by means of analysis – and that completely changes the method of thought. ...

Metaphysics has a long way to go yet before it can proceed synthetically. It will only be when analysis has helped us towards concepts which are understood distinctly and in detail that it will be possible for synthesis to subsume compound cognitions under the simplest cognition, as happens in mathematics. ( IDP , 2:289-90/ TP , 262-3) { §4.5 }

Such a system of pure (speculative) reason I hope myself to deliver under the title Metaphysics of Nature , which will be not half so extensive but will be incomparably richer in content than this critique, which had first to display the sources and conditions of its possibility, and needed to clear and level a ground that was completely overgrown. Here I expect from my reader the patience and impartiality of a judge , but there I will expect the cooperative spirit and assistance of a fellow worker ; for however completely the principles of the system may be expounded in the critique, the comprehensiveness of the system itself requires also that no derivative concepts should be lacking, which, however, cannot be estimated a priori in one leap, but must be gradually sought out; likewise, just as in the former the whole synthesis of concepts has been exhausted, so in the latter it would be additionally demanded that the same thing should take place in respect of their analysis , which would be easy and more entertainment than labor. ( CPR , Axxi) { §4.5 }

I understand by an analytic of concepts not their analysis, or the usual procedure of philosophical investigations, that of analyzing [ zergliedern ] the content of concepts that present themselves and bringing them to distinctness, but rather the much less frequently attempted analysis [ Zergliederung ] of the faculty of understanding itself, in order to research the possibility of a priori concepts by seeking them only in the understanding as their birthplace and analyzing its pure use in general; for this is the proper business of a transcendental philosophy; the rest is the logical treatment of concepts in philosophy in general. We will therefore pursue the pure concepts into their first seeds and predispositions in the human understanding, where they lie ready, until with the opportunity of experience they are finally developed and exhibited in their clarity by the very same understanding, liberated from the empirical conditions attaching to them. ( CPR , A65-6/B90-1) { §4.5 }

[in offering a refutation of Mendelssohn’s proof of the persistence of the soul] If we take the above propositions in a synthetic connection, as valid for all thinking beings, as they must be taken in rational psychology as a system, and if from the category of relation, starting with the proposition “All thinking beings are, as such, substances” we go backward through the series of propositions until the circle closes, then we finally come up against the existence of thinking beings, which in this system are conscious of themselves not only as independent of external things but also as being able to determine themselves from themselves (in regard to the persistence belonging necessarily to the character of a substance). But from this it follows that idealism , at least problematic idealism, is unavoidable in that same rationalistic system, and if the existence of external things is not at all required for the determination of one’s own existence in time, then such things are only assumed, entirely gratuitously, without a proof of them being able to be given.

If, on the contrary, we follow the analytic procedure, grounded on the “I think” given as a proposition that already includes existence in itself, and hence grounded on modality, and then we take it apart so as to cognize its content, whether and how this I determines its existence in space or time merely through it, then the propositions of the rational doctrine of the soul begin not from the concept of a thinking being in general but from an actuality; and from the way this is thought, after everything empirical has been detached from it, it is concluded what pertains to a thinking being in general ... ( CPR , B416-19) { §4.5 }

Give a philosopher the concept of a triangle, and let him try to find out in his way how the sum of its angles might be related to a right angle. He has nothing but the concept of a figure enclosed by three straight lines, and in it the concept of equally many angles. Now he may reflect on this concept as long as he wants, yet he will never produce anything new. He can analyze [ zergliedern ] and make distinct the concept of a straight line, or of an angle, or of the number three, but he will not come upon any other properties that do not already lie in these concepts. But now let the geometer take up this question. He begins at once to construct a triangle. Since he knows that two right angles together are exactly equal to all of the adjacent angles that can be drawn at one point on a straight line, he extends one side of his triangle, and obtains two adjacent angles that together are equal to two right ones. Now he divides the external one of these angles by drawing a line parallel to the opposite side of the triangle, and sees that here there arises an external adjacent angle which is equal to an internal one, etc. In such a way, through a chain of inferences that is always guided by intuition, he arrives at a fully illuminating and at the same time general solution of the question. ( CPR , A716-7/B744-5) { §4.5 }

although a mere plan that might precede the Critique of Pure Reason would be unintelligible, undependable, and useless, it is by contrast all the more useful if it comes after. For one will thereby be put in the position to survey the whole, to test one by one the main points at issue in this science, and to arrange many things in the exposition better than could be done in the first execution of the work.

Here then is such a plan subsequent to the completed work, which now can be laid out according to the analytic method , whereas the work itself absolutely had to be composed according to the synthetic method , so that the science might present all of its articulations, as the structural organization of a quite peculiar faculty of cognition, in their natural connection. ( PFM , 4:263/ 13) { §4.5 }

In the Critique of Pure Reason I worked on this question [Is metaphysics possible at all?] synthetically , namely by inquiring within pure reason itself, and seeking to determine within this source both the elements and the laws of its pure use, according to principles. This work is difficult and requires a resolute reader to think himself little by little into a system that takes no foundation as given except reason itself, and that therefore tries to develop cognition out of its original seeds without relying on any fact whatever. Prolegomena should by contrast be preparatory exercises; they ought more to indicate what needs to be done in order to bring a science into existence if possible, than to present the science itself. They must therefore rely on something already known to be dependable, from which we can go forward with confidence and ascend to the sources, which are not yet known, and whose discovery not only will explain what is known already, but will also exhibit an area with many cognitions that all arise from these same sources. The methodological procedure of prolegomena, and especially of those that are to prepare for a future metaphysics, will therefore be analytic . ( PFM , 4:274-5/ 25-6) { §4.5 }

[interpreting the method of analysis in ancient Greek geometry] Rule of analysis and synthesis: Draw conclusions from your conjecture, one after the other, assuming that it is true. If you reach a false conclusion, then your conjecture was false. If you reach an indubitably true conclusion, your conjecture may have been true. In this case reverse the process, work backwards, and try to deduce your original conjecture via the inverse route from the indubitable truth to the dubitable conjecture. If you succeed, you have proved your conjecture. (1978a, 72-3) { §2.2 }

Synthesis is when, beginning from principles and running through truths in order, we discover certain progressions and form tables, as it were, or sometimes even general formulae, in which the answers to what arises later can be discovered. Analysis, however, goes back to principles solely for the sake of a given problem, just as if nothing had been discovered previously, by ourselves or by others. It is better to produce a synthesis, since that work is of permanent value, whereas when we begin an analysis on account of particular problems we often do what has been done before. However, to use a synthesis which has been established by others, and theorems which have already been discovered, is less of an art than to do everything by oneself by carrying out an analysis; especially as what has been discovered by others, or even by ourselves, does not always occur to us or come to hand. There are two kinds of analysis: one is the common type proceeding by leaps, which is used in algebra, and the other is a special kind which I call ‘reductive’. This is much more elegant, but is less well-known. In practice, analysis is more necessary, so that we may solve the problems which are presented to us; but the man who can indulge in theorising will be content to practice analysis just far enough to master the art. For the rest, he will rather practise synthesis, and will apply himself readily only to those questions to which order itself leads him. For in this way he will always progress pleasantly and easily, and will never feel any difficulties, nor be disappointed of success, and in a short time he will achieve much more than he would ever have hoped for at the outset. ( USA , 16-17) { §4.4 }

Primary truths are those which either state a term of itself, or deny an opposite of its opposite. For example, ‘A is A’, or ‘A is not not-A’ ...

All other truths are reduced to primary truths by the aid of definitions—i.e. by the analysis of notions; and this constitutes a priori proof , independent of experience. ...

The predicate or consequent, therefore, is always in the subject or antecedent, and this constitutes the nature of truth in general, or, the connexion between the terms of a proposition, as Aristotle also has observed. In identities this connexion and inclusion of the predicate in the subject is express, whereas in all other truths it is implicit and must be shown through the analysis of notions, in which a priori demonstration consists. ( PT , 87-8) { §4.4 }

There are two kinds of truths , those of reason and those of fact . Truths of reason are necessary and their opposite is impossible; truths of fact are contingent and their opposite is possible. When a truth is necessary, its reason can be found by analysis, resolving it into simpler ideas and truths, until we come to those that are primitive. ( M , §33; tr. R. Latta) { §4.4 }

Our whole philosophy is rectification of colloquial linguistic usage. ( Aphorisms , 115) { §4.5 }

Writing is an excellent means of awakening in every man the system slumbering within him; and everyone who has ever written will have discovered that writing always awakens something which, though it lay within us, we failed clearly to recognize before. ( Ibid ., 119) { §4.5 }

Whichever way you look at it, philosophy is always analytical chemistry. The peasant employs all the propositions of the most abstract philosophy, only he employs them enveloped, concealed, compounded, latent, as the chemist and physicist says; the philosopher gives us the propositions pure. ( Ibid ., 162) { §4.5 }

There are therefore three ways whereby we get the complex Ideas of mixed Modes . 1. By Experience and Observation of things themselves. Thus by seeing two Men wrestle, or fence, we get the Idea of wrestling or fencing. 2. By Invention , or voluntary putting together of several simple Ideas in our own Minds: So he that first invented Printing, or Etching, had an Idea of it in his Mind, before it ever existed. 3. Which is the most usual way, by explaining the names of Actions we never saw, or Notions we cannot see; and by enumerating, and thereby, as it were, setting before our Imaginations all those Ideas which go to the making them up, and are the constituent parts of them. For having by Sensation and Reflection stored our Minds with simple Ideas , and by use got the Names, that stand for them, we can by those Names represent to another any complex Idea , we would have him conceive; so that it has in it no simple Idea , but what he knows, and has, with us, the same name for. For all our complex Ideas are ultimately resolvable into simple Ideas , of which they are compounded, and originally made up, though perhaps their immediate Ingredients, as I may so say, are also complex Ideas . Thus the mixed Mode , which the word Lye stands for, is made of these simple Ideas : 1. Articulate Sounds. 2. Certain Ideas in the Mind of the Speaker. 3. Those words the signs of those Ideas . 4. Those signs put together by affirmation or negation, otherwise than the Ideas they stand for, are in the mind of the Speaker. I think I need not go any farther in the Analysis of that complex Idea , we call a Lye : What I have said is enough to shew, that it is made up of simple Ideas : And it could not be an offensive tediousness to my Reader, to trouble him with a more minute enumeration of every particular simple Idea , that goes to this complex one; which, from what has been said, he cannot but be able to make out to himself. The same may be done in all our complex Ideas whatsoever; which however compounded, and decompounded, may at last be resolved into simple Ideas , which are all the Materials of Knowledge or Thought we have or can have. ( Essay , II, xxii, 9) { §4.3 }

Analysis has a way of unravelling the self: the longer you pull on the thread, the more flaws you find. ( Therapy , London, 31)

The certainty of mathematics is based upon the general axiom that nothing can be and not be at the same time. In this science each proposition such as, for example, “A is B”, is proven in one of two ways. Either one unpacks the concepts of A and shows “A is B”, or one unpacks the concepts of B and infers from this that not-B must also be not-A. Both types of proof are thus based upon the principle of contradiction, and since the object of mathematics in general is magnitude and that of geometry in particular extension , one can say that in mathematics in general our concepts of magnitude are unpacked and analyzed, while in geometry in particular our concepts of extension are unpacked and analyzed. In fact, since geometry lays nothing else as its basis than the abstract concept of extension and derives all its conclusions from this single source – deriving them, to be sure, in such a way that one recognizes distinctly that everything maintained in it is necessarily connected by the principle of contradiction with the abstracted concept of extension, there is no doubt that all geometric truths that geometry teaches us to unpack or untangle from the concept of extension must be encountered all tangled up in it. For what else can the profoundest inferences do but analyze a concept and make distinct what was obscure? Such inferences cannot bring in what is not to be found in the concept, and it is easy to see that it is also not possible, by means of the principle of contradiction, to derive from the concept what is not to be found in it. In the concept of extension, for example, there lies the inner possibility that a space is limited by three straight lines in such a way that two of them include a right angle. For it follows from the essence of extension that it is capable of many sorts of limitations and that the assumed sort of limitation of one of its level planes contains no contradiction. If one subsequently shows that the concept of this assumed limitation or of a right-angled triangle necessarily entails that the square of the hypotenuse is such-and-such, then it must have also been possible to find this truth originally and implicitly in the initial concept of extension. Otherwise it could never have been derived from it by means of the principle of contradiction. The idea of extension is inseparable from the idea of the possibility of such a limitation, as was previously assumed, and the limitation is in turn necessarily connected to the concept of the equality of the aforesaid square. Thus, this truth also lay tangled up, as one might say, in the original concept of extension, but it escaped our attention and could not be distinctly known and distinguished until, through analysis, we unpacked all the parts of this concept and separated them from one another. The analysis of concepts is for the understanding nothing more than what the maginfying glass is for sight. It does not produce anything that was not to be found in the object. But it spreads out the parts of the object and makes it possible for our senses to distinguish much that they would otherwise not have noticed. The analysis of concepts does nothing different from this; it makes the parts and members of these concepts, which were previously obscure and unnoticed, distinct and recognizable, but it does not introduce anything into the concepts that was not already to be found in them. (1763, §1/ PW , 257-8) { §4.5 }

It seems necessary, then, to regard the world as formed of concepts. These are the only objects of knowledge. They cannot be regarded fundamentally as abstractions either from things or from ideas; since both alike can, if anything is to be true of them, be composed of nothing but concepts. A thing becomes intelligible first when it is analysed into its constituent concepts. ( NJ , 8) { §6.4 }

It appears to me that in Ethics, as in all other philosophical studies, the difficulties and disagreements, of which its history is full, are mainly due to a very simple cause: namely to the attempt to answer questions, without first discovering precisely what question it is which you desire to answer. I do not know how far this source of error would be done away, if philosophers would try to discover what question they were asking, before they set about to answer it; for the work of analysis and distinction is often very difficult: we may often fail to make the necessary discovery, even though we make a definite attempt to do so. But I am inclined to think that in many cases a resolute attempt would be sufficient to ensure success; so that, if only this attempt were made, many of the most glaring difficulties and disagreements in philosophy would disappear. ( PE , vii) { §6.4 }

My point is that ‘good’ is a simple notion, just as ‘yellow’ is a simple notion; that, just as you cannot, by any manner of means, explain to any one who does not already know it, what yellow is, so you cannot explain what good is. Definitions of the kind that I was asking for, definitions which describe the real nature of the object or notion denoted by a word, and which do not merely tell us what the word is used to mean, are only possible when the object or notion in question is something complex. You can give a definition of a horse, because a horse has many different properties and qualities, all of which you can enumerate. But when you have enumerated them all, when you have reduced a horse to his simplest terms, then you no longer define those terms. They are simply something which you think of or perceive, and to any one who cannot think of or perceive them, you can never, by any definition, make their nature known. ( PE , 7) { §6.4 }

As in Mathematicks, so in Natural Philosophy, the Investigation of difficult Things by the Method of Analysis, ought ever to precede the Method of Composition. This Analysis consists in making Experiments and Observations, and in drawing general Conclusions from them by Induction, and admitting of no Objections against the Conclusions, but such as are taken from Experiments, or other certain Truths. For Hypotheses are not to be regarded in experimental Philosophy. And although the arguing from Experiments and Observations by Induction be no Demonstration of general Conclusions; yet it is the best way of arguing which the Nature of Things admits of, and may be looked upon as so much the stronger, by how much the Induction is more general. And if no Exception occur from Phænomena, the Conclusion may be pronounced generally. But if at any time afterwards any Exception shall occur from Experiments, it may then begin to be pronounced with such Exceptions as occur. By this way of Analysis we may proceed from Compounds to Ingredients, and from Motions to the Forces producing them; and in general, from Effects to their Causes, and from particular Causes to more general ones, till the Argument end in the most general. This is the Method of Analysis: and the Synthesis consists in assuming the Causes discover’d, and establish’d as Principles, and by them explaining the Phænomena proceeding from them, and proving the Explanations. ( Opticks , Book Three, Part I, 404-5) { §4.1 }

All concepts in which an entire process is semiotically telescoped elude definition. ( On the Genealogy of Morals , 1887, tr. Walter Kaufmann, New York: Random House, 1968, 80)

the most valuable insights are methods . ( The Antichrist , 1895, §13)

The so-called Treasury of Analysis [ analuomenos ] .. is, in short, a special body of doctrines furnished for the use of those who, after going through the usual elements, wish to obtain the power of solving theoretical problems, which are set to them, and for this purpose only is it useful. It is the work of three men, Euclid the author of the Elements , Apollonius of Perga, and Aristaeus the Elder, and proceeds by the method of analysis and synthesis.

Now analysis is the way from what is sought—as if it were admitted—through its concomitants [ akolouthôn ] in order to something admitted in synthesis. For in analysis we suppose that which is sought to be already done, and we inquire from what it results, and again what is the antecedent [ proêgoumenon ] of the latter, until we on our backward way light upon something already known and being first in order. And we call such a method analysis, as being a solution backwards [ anapalin lysin ].

In synthesis, on the other hand, we suppose that which was reached last in analysis to be already done, and arranging in their natural order as consequents [ epomena ] the former antecedents [ proêgoumena ] and linking them one with another, we in the end arrive at the construction of the thing sought. And this we call synthesis.

Now analysis is of two kinds. One seeks the truth, being called theoretical. The other serves to carry out what was desired to do, and this is called problematical. In the theoretical kind we suppose the thing sought as being and as being true, and then we pass through its concomitants [ akolouthôn ] in order, as though they were true and existent by hypothesis, to something admitted; then, if that which is admitted be true, the thing sought is true, too, and the proof will be the reverse of analysis. But if we come upon something false to admit, the thing sought will be false, too. In the problematic kind we suppose the desired thing to be known, and then we pass through its concomitants [ akolouthôn ] in order, as though they were true, up to something admitted. If the thing admitted is possible or can be done, that is, if it is what the mathematicians call given, the desired thing will also be possible. The proof will again be the reverse of analysis. But if we come upon something impossible to admit, the problem will also be impossible. ( PAC , tr. in Hintikka and Remes 1974, 8-10) { §2.2 }

For we should remember that if a person goes on analyzing names into words, and inquiring also into the elements out of which the words are formed, and keeps on always repeating this process, he who has to answer him must at last give up the inquiry in despair … But if we take a word which is incapable of further resolution, then we shall be right in saying that we at last reached a primary element, which need not be resolved any further. (‘Cratylus’, Benjamin Jowett (trans.), in Hamilton and Cairns (ed.), Collected Dialogues , New York: Pantheon Books, 421e)

Then, said I, is not dialectic the only process of inquiry that advances in this manner, doing away with hypotheses, up to the first principle itself in order to find confirmation there? And it is literally true that when the eye of the soul is sunk in the barbaric slough of the Orphic Myth, dialectic gently draws it forth and leads it up, employing as helpers and cooperators in this conversation the studies and sciences which we enumerated, which we called sciences often from habit, though they really need some other designation, connoting more clearness than opinion and more obscurity than science. ‘Understanding’ I believe was the term we employed. But, I presume we shall not dispute about the name when things of such moment lie before us for consideration. (‘Republic VII’, Paul Shorey (trans.), Ibid. , 533d)

Understand then, said I, that by the other section of the intelligible I mean that which the reason lays hold of by the power of dialectic, treating its assumptions not as absolute beginnings but literally as hypotheses, underpinnings, footings and springboards so to speak, to enable it to rise to that which requires no assumption and is the starting point of all, and after attaining to that again taking hold of the first dependencies from it, so to proceed downward to the conclusion, making no use whatever of any object of sense but only of pure ideas moving on through ideas to ideas and ending with ideas. (‘Republic VI’, Paul Shorey (trans.), Ibid ., 511b)

In mathematics logic is called analysis , and analysis means division , dissection . It can have, therefore, no tool other than the scalpel and the microscope. (‘Intuition and Logic in Mathematics’, 1900, in William Ewald, ed., From Kant to Hilbert , Oxford: Oxford University Press, 1996, 1018)

Nonmathematical illustration [of the method of analysis described by Pappus] . A primitive man wishes to cross a creek; but he cannot do so in the usual way because the water has risen overnight. Thus, the crossing becomes the object of a problem; “crossing the creek’ is the x of this primitive problem. The man may recall that he has crossed some other creek by walking along a fallen tree. He looks around for a suitable fallen tree which becomes his new unknown, his y . He cannot find any suitable tree but there are plenty of trees standing along he creek; he wishes that one of them would fall. Could he make a tree fall across the creek? There is a great idea and there is a new unknown; by what means could he tilt the tree over the creek?

This train of ideas ought to be called analysis if we accept the terminology of Pappus. If the primitive man succeeds in finishing his analysis he may become the inventor of the bridge and of the axe. What will be the synthesis? Translation of ideas into actions. The finishing act of the synthesis is walking along a tree across the creek.

The same objects fill the analysis and the synthesis; they exercise the mind of the man in the analysis and his muscles in the synthesis; the analysis consists in thoughts, the synthesis in acts. There is another difference; the order is reversed. Walking across the creek is the first desire from which the analysis starts and it is the last act with which the synthesis ends. (1957, 145) { §2.2 }

beauty and order are common to all branches of mathematics, as are the method of proceeding from things better known to things we seek to know and the reverse path from the latter to the former, the methods called analysis and synthesis. ( CEE , 8/6-7) { §2.2 }

as Nous is set over understanding and dispenses principles to it from above, perfecting it out of its own riches, so in the same way dialectic, the purest part of philosophy, hovers attentively over mathematics, encompasses its whole development, and of itself contributes to the special sciences their various perfecting, critical, and intellective powers—the procedures, I mean, of analysis, division, definition, and demonstration. Being thus endowed and led towards perfection, mathematics reaches some of its results by analysis, others by synthesis, expounds some matters by division, others by definition, and some of its discoveries binds fast by demonstration, adapting these methods to its subjects and employing each of them for gaining insight into mediating ideas. Thus its analyses are under the control of dialectic, and its definitions, divisions, and demonstrations are of the same family and unfold in conformity with the way of mathematical understanding. It is reasonable, then, to say that dialectic is the capstone of the mathematical sciences. It brings to perfection all the intellectual insight they contain, making what is exact in them more irrefutable, confirming the stability of what they have established and referring what is pure and incorporeal in them to the simplicity and immateriality of Nous, making precise their primary starting-points through definitions and explicating the distinctions of genera and species within their subject-matters, teaching the use of synthesis to bring out the consequences that follow from principles and of analysis to lead up to the first principles and starting-points. ( CEE , 42-3/35-6) { §2.2 }

Magnitudes, figures and their boundaries, and the ratios that are found in them, as well as their properties, their various positions and motions—these are what geometry studies, proceeding from the partless point down to solid bodies, whose many species and differences it explores, then following the reverse path from the more complex objects to the simpler ones and their principles. It makes use of synthesis and analysis, always starting from hypotheses and first principles that it obtains from the science above it and employing all the procedures of dialectic—definition and division for establishing first principles and articulating species and genera, and demonstrations and analyses in dealing with the consequences that follow from first principles, in order to show the more complex matters both as proceeding from the simpler and also conversely as leading back to them. ( CEE , 57/46) { §2.2 }

[Euclid’s Elements ] contains all the dialectical methods: the method of division for finding kinds, definitions for making statements of essential properties, demonstrations for proceeding from premises to conclusions, and analysis for passing in the reverse direction from conclusions to principles. ( CEE , 69/57) { §2.2 }

there are certain methods that have been handed down, the best being the method of analysis, which traces the desired result back to an acknowledged principle. Plato, it is said, taught this method to Leodamas, who also is reported to have made many discoveries in geometry by means of it. A second is the method of diaeresis , which divides into its natural parts the genus proposed for examination and which affords a starting-point for demonstration by eliminating the parts irrelevant for the establishment of what is proposed. This method also Plato praised as an aid in all the sciences. A third is the reduction to impossibility, which does not directly show the thing itself that is wanted but by refuting its contradictory indirectly establishes its truth. ( CEE , 211-12/165-6) { §2.2 }

for problems one common procedure, the method of analysis, has been discovered, and by following it we can reach a solution; for thus it is that even the most obscure problems are pursued. ( CEE , 242/189) { §2.2 }

In general we must understand that all mathematical arguments proceed either from or to the starting-points, as Porphyry somewhere says. Those that proceed from the starting-points are themselves of two kinds, as it happens, for they proceed either from common notions, that is, from self-evident clarity alone, or from things previously demonstrated. Those that proceed to the starting-points are either affirmative of them or destructive. But those that affirm first principles are called “analyses”, and their reverse procedures “syntheses” (for it is possible from those principles to proceed in orderly fashion to the thing sought, and this is called “synthesis”); when they are destructive, they are called “reductions to impossibility”, for it is the function of this procedure to show that something generally accepted and self-evident is overthrown. There is a kind of syllogism in it, though not the same as in analysis ... ( CEE , 255/198-9) { §2.2 }

A maxim of shallow analysis prevails: expose no more logical structure than seems useful for the deduction or other inquiry at hand. In the immortal words of Adolf Meyer, where it doesn’t itch don't scratch.

On occasion the useful degree of analysis may, conversely, be such as to cut into a simple word of ordinary language, requiring its paraphrase into a composite term in which other terms are compounded with the help of canonical notation. When this happens, the line of analysis adopted will itself commonly depend on what is sought in the inquiry at hand; again there need be no question of the uniquely right analysis, nor of synonymy. (1960, §33, 160-1) { §6.9 }

This construction [of the ordered pair as a class, such as Wiener’s identification of the ordered pair x , y > with the class {{ x }, { y , Λ}}] is paradigmatic of what we are most typically up to when in a philosophical spirit we offer an “analysis” or “explication” of some hitherto inadequately formulated “idea” or expression. We do not claim synonymy. We do not claim to make clear and explicit what the users of the unclear expression had unconsciously in mind all along. We do not expose hidden meanings, as the words ‘analysis’ or ‘explication’ would suggest; we supply lacks. We fix on the particular functions of the unclear expression that make it worth troubling about, and then devise a substitute, clear and couched in terms to our liking, that fills those functions. Beyond those conditions of partial agreement, dictated by our interests and purposes, any traits of the explicans come under the head of “don’t-cares” … Under this head we are free to allow the explicans all manner of novel connotations never associated with the explicandum. …

Philosophical analysis, explication, has not always been seen in this way. Only the reading of a synonymy claim into analysis could engender the so-called paradox of analysis, which runs thus: how can a correct analysis be informative, since to understand it we must already know the meanings of its terms, and hence already know that the terms which it equates are synonymous? The notion that analysis must consist somehow in the uncovering of hidden meanings underlies also the recent tendency of some of the Oxford philosophers to take as their business an examination of the subtle irregularities of ordinary language. And there is no mistaking the obliviousness of various writers to the point about the don’t-cares. …

... explication is elimination . We have, to begin with, an expression or form of expression that is somehow troublesome. It behaves partly like a term but not enough so, or it is vague in ways that bother us, or it puts kinks in a theory or encourages one or another confusion. But also it serves certain purposes that are not to be abandoned. Then we find a way of accomplishing those same purposes through other channels, using other and less troublesome forms of expression. The old perplexities are resolved.

According to an influential doctrine of Wittgenstein’s, the task of philosophy is not to solve problems but to dissolve them by showing that there were really none there. This doctrine has its limitations, but it aptly fits explication. For when explication banishes a problem it does so by showing it to be in an important sense unreal; viz., in the sense of proceeding only from needless usages. (1960, §53, 258-60) { §6.9 }

This brings us to the second of the five turning points, the shift from terms to sentences. The medievals had the notion of syncategorematic words, but it was a contemporary of John Horne Tooke who developed it into an explicit theory of contextual definition; namely, Jeremy Bentham. He applied contextual definition not just to grammatical particles and the like, but even to some genuine terms, categorematic ones. If he found some term convenient but ontologically embarrassing, contextual definition enabled him in some cases to continue to enjoy the services of the term while disclaiming its denotation. He could declare the term syncategorematic, despite grammatical appearances, and then could justify his continued use of it if he could show systematically how to paraphrase as wholes all sentences in which he chose to imbed it. Such was his theory of fictions: what he called paraphrasis, and what we now call contextual definition. The term, like the grammatical particles, is meaningful as a part of meaningful wholes. If every sentence in which we use a term can be paraphrased into a sentence that makes good sense, no more can be asked. (1975, 68-9) { §5.6 }

The issue is: is there such an activity as “conceptual analysis” or can philosophers do no more than describe usage and, perhaps, make recommendations for change in usage? One’s answer to this question will determine whether one thinks that Wittgenstein was wrong to give up on the idea of a systematic theory of meaning, and Quine right to suggest that the very notion of “meaning” was a hangover of Aristotelean essentialism. If they were right, it is hard to hang on to the idea that “conceptual clarity” is a goal of philosophical inquiry … Metaphilosophical issues hover in the wings of the debates over whether the content of an assertion varies from utterer to utterer and from audience to audience. If it does not, if something remains invariable – the concepts expressed by the words that make up the sentence – then perhaps there really are entities with intrinsic properties which philosophical analysis can hope to pin down. But, if content does vary in this way, then concepts are like persons - never quite the same twice, always developing, always maturing. You can change a concept by changing usage, but you cannot get a concept right, once and for all. (‘Analytic and Conversational Philosophy’, Philosophy as Cultural Politics , Cambridge: Cambridge University Press, 2007, 122-3)

Analysis, to be sure, is articulation rather than dissolution. (1980, 8) { §1.2 , §5.8 }

we must see where we are going , or what will “count” as the successful resolution to the given exercise of analysis. … Analysis is the admittedly indispensable road to our destination, but it is no more the destination than it is the intention to begin the voyage. One could perhaps say that the destination is an articulated structure. But we know that we have reached the destination only when we recognize a given articulation as the explanation of that structure. We cannot see that an analysis explains a structure by performing an additional step in the analysis. At some point we must see that we are finished. And to see an analysis is not to analyze. It is rather to see an articulated structure as a unity, whole, or synthesis. ( Ibid ., 9) { §1.2 , §5.8 }

If to understand is to possess an explanation, and if an explanation is an analysis, it remains the case that an analysis is intelligible because it is also a synthesis. Explanation may be called “recollection” in the Platonic sense because it is the process of retracing, by the method of counting and measuring, the joints of an internally articulated unity, one prefigured within the initial formulation of the entire analytical exercise. In slightly more prosaic terms, analysis is never merely the application of rules. It is also at once a seeing of which rules to apply and how to apply them. This is what it means to say that analysis is also synthesis. And this is why it is false to say, as is at least implied by so much contemporary analytical philosophy, that we begin with intuitions and then replace them with ever more sophisticated analyses. Not only is it false to say this, but strictly speaking, it is meaningless. If “to mean” is “to provide an analysis”, there is no analysis of analysis without ingredient intuition. Without intuition, there is at each stage nothing to analyze. Intuition (of syntheses or unities) without analysis is mute, but analysis without intuition is inarticulate as well as blind: the sounds it utters cannot be distinguished from noise. ( Ibid ., 9-10) { §1.2 , §5.8 }

analysis is a cognitive activity and it cannot be coherently understood except by recourse to intuition. There is a non-discursive context of analysis . ( Ibid ., 27) { §1.2 , §5.8 }

conceptual analysis is rooted in intuitions which cannot be replaced by the process of analysis but which regulate that process. ( Ibid ., 48) { §1.2 , §5.8 }

That all sound philosophy should begin with an analysis of propositions, is a truth too evident, perhaps, to demand a proof. That Leibniz’s philosophy began with such an analysis, is less evident, but seems to be no less true. ( PL , 8) { §6.3 }

It is necessary to realize that definition, in mathematics, does not mean, as in philosophy, an analysis of the idea to be defined into constituent ideas. This notion, in any case, is only applicable to concepts, whereas in mathematics it is possible to define terms which are not concepts. Thus also many notions are defined by symbolic logic which are not capable of philosophical definition, since they are simple and unanalyzable. ( POM , ch. 2, §31, 27) { §6.3 }

For the comprehension of analysis, it is necessary to investigate the notion of whole and part, a notion which has been wrapped in obscurity—though not without certain more or less valid logical reasons—by the writers who may be roughly called Hegelian. ( POM , ch. 16, §133, 137) { §6.3 }

I have already touched on a very important logical doctrine, which the theory of whole and part brings into prominence—I mean the doctrine that analysis is falsification. Whatever can be analyzed is a whole, and we have already seen that analysis of wholes is in some measure falsification. But it is important to realize the very narrow limits of this doctrine. We cannot conclude that the parts of a whole are not really its parts, nor that the parts are not presupposed in the whole in a sense in which the whole is not presupposed in the parts, nor yet that the logically prior is not usually simpler than the logically subsequent. In short, though analysis gives us the truth, and nothing but the truth, yet it can never give us the whole truth. This is the only sense in which the doctrine is to be accepted. In any wider sense, it becomes merely a cloak for laziness, by giving an excuse to those who dislike the labour of analysis. ( POM , ch. 16, §138, 141) { §6.3 }

We are sometimes told that things are organic unities, composed of many parts expressing the whole and expressed in the whole. This notion is apt to replace the older notion of substance, not, I think, to the advantage of precise thinking. The only kind of unity to which I can attach any precise sense—apart from the unity of the absolutely simple—is that of a whole composed of parts. But this form of unity cannot be what is called organic; for if the parts express the whole or the other parts, they must be complex, and therefore themselves contain parts; if the parts have been analyzed as far as possible, they must be simple terms, incapable of expressing anything except themselves. A distinction is made, in support of organic unities, between conceptual analysis and real division into parts. What is really indivisible, we are told, may be conceptually analyzable. This distinction, if the conceptual analysis be regarded as subjective, seems to me wholly inadmissible. All complexity is conceptual in the sense that it is due to a whole capable of logical analysis, but is real in the sense that it has no dependence upon the mind, but only upon the nature of the object. Where the mind can distinguish elements, there must be different elements to distinguish; though, alas! there are often different elements which the mind does not distinguish. The analysis of a finite space into points is no more objective than the analysis (say) of causality into time-sequence + ground and consequent, or of equality into sameness of relation to a given magnitude. In every case of analysis, there is a whole consisting of parts with relations; it is only the nature of the parts and the relations which distinguishes different cases. Thus the notion of an organic whole in the above sense must be attributed to defective analysis, and cannot be used to explain things.

It is also said that analysis is falsification, that the complex is not equivalent to the sum of its constituents and is changed when analyzed into these. In this doctrine, as we saw in Parts I and II, there is a measure of truth, when what is to be analyzed is a unity. A proposition has a certain indefinable unity, in virtue of which it is an assertion; and this is so completely lost by analysis that no enumeration of constituents will restore it, even though itself be mentioned as a constituent. There is, it must be confessed, a grave logical difficulty in this fact, for it is difficult not to believe that a whole must be constituted by its constituents. For us, however, it is sufficient to observe that all unities are propositions or propositional concepts, and that consequently nothing that exists is a unity. If, therefore, it is maintained that things are unities, we must reply that no things exist. ( POM , ch. 53, §439, 466-7) { §6.3 }

What we want to be clear about is the twofold method of analysis of a proposition, i.e. , first taking the proposition as it stands and analyzing it, second taking the proposition as a special case of a type of propositions. Whenever we use variables, we are already necessarily concerned with a type of propositions. E.g. “ p ⊃ q ” stands for any proposition of a certain type. When values are assigned to p and q , we reach a particular proposition by a different road from that which would have started with those values plus implication, and have so built up the particular proposition without reference to a type. This is how functions come in. (‘Fundamental Notions’, 1904, in 1994, 118) { §6.3 }

We ought to say, I think, that there are different ways of analysing complexes, and that one way of analysis is into function and argument, which is the same as type and instance. ( Ibid ., 256) { §6.3 }

The fundamental epistemological principle in the analysis of propositions containing descriptions is this: Every proposition which we can understand must be composed wholly of constituents with which we are acquainted. ( KAKD , 159) { §6.3 }

when we say ‘the author of Waverley was Scott’ we mean ‘one and only one man wrote Waverley, and he was Scott’. Here the identity is between a variable, i.e. an indeterminate subject (‘he’), and Scott; ‘the author of Waverley’ has been analysed away, and no longer appears as a constituent of the proposition. ( KAKD , 165) { §6.3 }

Analysis may be defined as the discovery of the constituents and the manner of combination of a given complex. The complex is to be one with which we are acquainted; the analysis is complete when we become acquainted with all the constituents and with their manner of combination, and know that there are no more constituents and that that is their manner of combination. We may distinguish formal analysis as the discovery of the manner of combination, and material analysis as the discovery of the constituents. Material analysis may be called descriptive when the constituents are only known by description, not by acquaintance. ( TK , 119) { §6.3 }

Philosophy, if what has been said is correct, becomes indistinguishable from logic as that word has now come to be used. The study of logic consists, broadly speaking, of two not very sharply distinguished portions. On the one hand it is concerned with those general statements which can be made concerning everything without mentioning any one thing or predicate or relation, such for example as ‘if x is a member of the class α and every member of α is a member of β , then x is a member of the class β , whatever x , α , and β may be.’. On the other hand, it is concerned with the analysis and enumeration of logical forms , i.e. with the kinds of propositions that may occur, with the various types of facts, and with the classification of the constituents of facts. In this way logic provides an inventory of possibilities, a repertory of abstractly tenable hypotheses. ( SMP , 84-5) { §6.3 }

The essence of philosophy as thus conceived is analysis, not synthesis. To build up systems of the world, like Heine’s German professor who knit together fragments of life and made an intelligible system out of them, is not, I believe, any more feasible than the discovery of the philosopher’s stone. What is feasible is the understanding of general forms, and the division of traditional problems into a number of separate and less baffling questions. ‘Divide and conquer’ is the maxim of success here as elsewhere. ( SMP , 86) { §6.3 }

Kant, under the influence of Newton, adopted, though with some vacillation, the hypothesis of absolute space, and this hypothesis, though logically unobjectionable, is removed by Occam’s razor, since absolute space is an unnecessary entity in the explanation of the physical world. Although, therefore, we cannot refute the Kantian theory of an a priori intuition, we can remove its grounds one by one through an analysis of the problem. Thus, here as in many other philosophical questions, the analytic method, while not capable of arriving at a demonstrative result, is nevertheless capable of showing that all the positive grounds in favour of a certain theory are fallacious and that a less unnatural theory is capable of accounting for the facts.

Another question by which the capacity of the analytic method can be shown is the question of realism. Both those who advocate and those who combat realism seem to me to be far from clear as to the nature of the problem which they are discussing. If we ask: ‘Are our objects of perception real and are they independent of the percipient?’ it must be supposed that we attach some meaning to the words ‘real’ and ‘independent’, and yet, if either side in the controversy of realism is asked to define these two words, their answer is pretty sure to embody confusions such as logical analysis will reveal. ( SMP , 90-1) { §6.3 }

The supreme maxim in scientific philosophizing is this:

Wherever possible, logical constructions are to be substituted for inferred entities.

Some examples of the substitution of construction for inference in the realm of mathematical philosophy may serve to elucidate the uses of this maxim. Take first the case of irrationals. In old days, irrationals were inferred as the supposed limits of series of rationals which had no rational limit; but the objection to this procedure was that it left the existence of irrationals merely optative, and for this reason the stricter methods of the present day no longer tolerate such a definition. We now define an irrational number as a certain class of ratios, thus constructing it logically by means of ratios, instead of arriving at it by a doubtful inference from them. Take again the case of cardinal numbers. Two equally numerous collections appear to have something in common: this something is supposed to be their cardinal number. But so long as the cardinal number is inferred from the collections, not constructed in terms of them, its existence must remain in doubt, unless in virtue of a metaphysical postulate ad hoc . By defining the cardinal number of a given collection as the class of all equally numerous collections, we avoid the necessity of this metaphysical postulate, and thereby remove a needless element of doubt from the philosophy of arithmetic. A similar method, as I have shown elsewhere, can be applied to classes themselves, which need not be supposed to have any metaphysical reality, but can be regarded as symbolically constructed fictions.

The method by which the construction proceeds is closely analogous in these and all similar cases. Given a set of propositions nominally dealing with the supposed inferred entities, we observe the properties which are required of the supposed entities in order to make these propositions true. By dint of a little logical ingenuity, we then construct some logical function of less hypothetical entities which has the requisite properties. The constructed function we substitute for the supposed inferred entities, and thereby obtain a new and less doubtful interpretation of the body of propositions in question. This method, so fruitful in the philosophy of mathematics, will be found equally applicable in the philosophy of physics, where, I do not doubt, it would have been applied long ago but for the fact that all who have studied this subject hitherto have been completely ignorant of mathematical logic. I myself cannot claim originality in the application of this method to physics, since I owe the suggestion and the stimulus for its application entirely to my friend and collaborator Dr Whitehead, who is engaged in applying it to the more mathematical portions of the region intermediate between sense-data and the points, instants and particles of physics.

A complete application of the method which substitutes constructions for inferences would exhibit matter wholly in terms of sense-data, and even, we may add, of the sense-data of a single person, since the sense-data of others cannot be known without some element of inference. This, however, must remain for the present an ideal, to be approached as nearly as possible, but to be reached, if at all, only after a long preliminary labour of which as yet we can only see the very beginning. ( RSDP , 115-6) { §6.3 }

In the special sciences, when they have become fully developed, the movement is forward and synthetic, from the simpler to the more complex. But in philosophy we follow the inverse direction: from the complex and relatively concrete we proceed towards the simple and abstract by means of analysis, seeking, in the process, to eliminate the particularity of the original subject-matter, and to confine our attention entirely to the logical form of the facts concerned. ( OKEW , 189-90) { §6.3 }

The nature of philosophic analysis … can now be stated in general terms. We start from a body of common knowledge, which constitutes our data. On examination, the data are found to be complex, rather vague, and largely interdependent logically. By analysis we reduce them to propositions which are as nearly as possible simple and precise, and we arrange them in deductive chains, in which a certain number of initial propositions form a logical guarantee for all the rest. ( OKEW , 214) { §6.3 }

the chief thesis that I have to maintain is the legitimacy of analysis. ( PLA , 189) { §6.3 }

it is very important to distinguish between a definition and an analysis. All analysis is only possible in regard to what is complex, and it always depends, in the last analysis, upon direct acquaintance with the objects which are the meanings of certain simple symbols. It is hardly necessary to observe that one does not define a thing but a symbol. ( PLA , 194) { §6.3 }

Analysis is not the same thing as definition. You can define a term by means of a correct description, but that does not constitute an analysis. ( PLA , 196) { §6.3 }

The business of philosophy, as I conceive it, is essentially that of logical analysis, followed by logical synthesis. ( LA , 341) { §6.3 }

Ever since I abandoned the philosophy of Kant and Hegel, I have sought solutions of philosophical problems by means of analysis; and I remain firmly persuaded, in spite of some modern tendencies to the contrary, that only by analysing is progress possible. ( MPD , 11) { §6.3 }

Philosophy must then involve the exercise of systematic restatement. But this does not mean that it is a department of philology or literary criticism.

Its restatement is not the substitution of one noun for another or one verb for another. That is what lexicographers and translators excel in. Its restatements are transmutations of syntax, and transmutations of syntax controlled not be desire for elegance or stylistic correctness but by desire to exhibit the forms of the facts into which philosophy is the enquiry.

I conclude, then, that there is, after all, a sense in which we can properly enquire and even say “what it really means to say so and so”. For we can ask what is the real form of the fact recorded when this is concealed or disguised and not duly exhibited by the expression in question. And we can often succeed in stating this fact in a new form of words which does exhibit what the other failed to exhibit. And I am for the present inclined to believe that this is what philosophical analysis is, and that this is the sole and whole function of philosophy. (1932, 100) { §6.8 }

I have no special objection to or any special liking for the fashion of describing as ‘analysis’ the sort or sorts of conceptual examination which constitute philosophizing. But the idea is totally false that this examination is a sort of garage inspection of one conceptual vehicle at a time. On the contrary, to put it dogmatically, it is always a traffic inspector’s examination of a conceptual traffic-block, involving at least two streams of vehicles hailing from the theories, or points of view or platitudes which are at cross-purposes with one another. (1953, 32) { §6.8 }

It is certain that when I wrote “Systematically Misleading Expressions” I was still under the direct influence of the notion of an “ideal language”—a doctrine according to which there were a certain number of logical forms which one could somehow dig up by scratching away at the earth which covered them. I no longer think, especially not today, that this is a good method. I do not regret having traveled that road, but I am happy to have left it behind me. (In Rorty 1967, 305) { §6.8 }

alas! intellect must first destroy the object of Inner Sense if it would make it its own. Like the analytical chemist, the philosopher can only discover how things are combined by analysing them, only lay bare the workings of spontaneous Nature by subjecting them to the torment of his own techniques. In order to lay hold of the fleeting phenomenon, he must first bind it in the fetters of rule, tear its fair body to pieces by reducing it to concepts, and preserve its living spirit in a sorry skeleton of words. Is it any wonder that natural feeling cannot find itself again in such an image, or that in the account of the analytical thinker truth should appear as paradox? ( AE , I, 4) { §5.2 }

analysis without synopsis must be blind. (‘Time and the World Order’, in Herbert Feigl and Grover Maxwell, (eds.), Minnesota Studies in the Philosophy of Science III , Minneapolis: University of Minnesota Press, 1962, 527)

[in discussing Ryle 1953 { Quotation }] Personally, I have no axe to grind about what it takes to analyze a concept. Very likely, there are different sorts of cases. It may well be that sometimes what we want from an analysis is the tracing of the sort of intricate web of conceptual relations in which Ryle delights. But there is little reason for thinking that this is always so—at least, if analysis is construed as whatever it is that philosophers do to solve their problems. What strikes me as worrisome is Ryle’ tendency to use the web metaphor as a rationale for rejecting the old, Russellian conception of analysis, with its emphasis on precisely formulated logical forms, and replacing it with methodology which, in some cases, may degenerate into a recipe for generating a conceptual fog. It is all well and good to recognize that sometimes the concepts philosophers deal with will be vague, imprecise, and open-ended, with close conceptual connections to other concepts of the same sort. We do have to be able to deal with such cases—perhaps along the lines Ryle suggests. What is not good is a prior ideological commitment to blurred edges, indirectness, and an unwillingness to separate tangential from central issues. Sometimes Ryle and other ordinary language philosophers seem to go too far in this direction; substituting one confining orthodoxy about analysis for another. When this happens, central philosophical points get missed ... (2003, II, 80-1) { §6.1 }

Philosophical analysis is a term of art. At different times in the twentieth century, different authors have used it to mean different things. What is to be analyzed (e.g., words and sentences versus concepts and propositions), what counts as a successful analysis, and what philosophical fruits come from analysis are questions that have been vigorously debated since the dawn of analysis as a self-conscious philosophical approach. Often, different views of analysis have been linked to different views of the nature of philosophy, the sources of philosophical knowledge, the role of language in thought, the relationship between language and the world, and the nature of meaning—as well to more focused questions about necessary and apriori truth. Indeed the variety of positions is so great as to make any attempt to extract a common denominator from the multiplicity of views sterile and not illuminating.

Nevertheless analytic philosophy—with its emphasis on what is called “philosophical analysis”—is a clear and recognizable tradition. Although the common core of doctrine uniting its practitioners scarcely exceeds the platitudinous, a pattern of historical influence is not hard to discern. The tradition begins with G.E. Moore, Bertrand Russell, and Ludwig Wittgenstein (as well as Gottlob Frege, whose initial influence was largely filtered through Russell and Wittgenstein). These philosophers set the agenda, first, for logical positivists such as Rudolf Carnap, Carl Hempel, and A.J. Ayer and then later for Wittgenstein, who in turn ushered in the ordinary language school led by Gilbert Ryle and J.L. Austin. More recently the second half of the twentieth century has seen a revival of Russellian and Carnapian themes in the work of W.V. Quine, Donald Davidson, and Saul Kripke. Analytic philosophy, with its changing views of philosophical analysis, is a trail of influence ... (2005, 144) { §6.1 }

In my opinion Logical Positivism fails in its treatment of analysis. Wittgenstein and the other Logical Positivists talk much about analysis, but they do not consider the various kinds of analysis, nor do they show in what sense philosophy is the analysis of facts. They make use of analytic definition of a symbolic expression, and of the analytic clarification of a concept, but they do not distinguish between them. They also employ postulational analysis. But they do not seem to understand directional analysis, and, accordingly, they fail to apprehend the need for it. In this way they depart, in my opinion, from the practice of Moore. Not only is their conception of analysis defective, but, further, their conception of the kinds of facts to be analysed is inadequate. They treat all facts as linguistic facts . Hence, they suppose that the first problem of philosophy is to determine the principles of symbolism, and from these principles to draw limits with regard to what we can think. This assumption has two important consequences. First, it leads to the view that philosophy is ‘the activity of finding meaning’, to quote Schlick’s statement. The second consequence is that they are apt to place too much reliance upon the construction of postulational systems. (1933b, 82-3) { §6.6 }

Strawson, Peter F.

An analysis, I suppose, may be thought of as a kind of breaking down or decomposing of something. So we have the picture of a kind of intellectual taking to pieces of ideas or concepts; the discovering of what elements a concept or idea is composed and how they are related. Is this the right picture or the wrong one—or is it partly right and partly wrong? That is a question which calls for a considered response … ( Analysis and Metaphysics , Oxford: Oxford University Press, 1992, 2)

If we took this notion [of analysis as decomposition] completely seriously for the case of conceptual analysis—analysis of ideas—we should conclude that our task was to find ideas that were completely simple, that were free from internal conceptual complexity; and then to demonstrate how the more or less complex ideas that are of interest to philosophers could be assembled by a kind of logical or conceptual construction out of these simple elements. The aim would be to get a clear grasp of complex meanings by reducing them, without remainder, to simple meanings. Thus baldly stated, this may seem a rather implausible project. And so it is. Nevertheless it, or some close relation of it, has been, and is, taken seriously. Even when not taken to the lengths I have just described, it continues to exercise a certain influence on the philosophical mind. ( Ibid. 18)

Among the philosophers who were most influential in England in the period between the two world wars were the analysts. Their analytic theories were sometimes associated with the metaphysical view which Russell called logical atomism, sometimes with the supposedly anti-metaphysical doctrines of logical positivism, and sometimes, as in the case of G. E. Moore, the analytic practice had no clearly defined dogmatic background at all. But they were united at least in the view that analysis was at least one of the most important tasks of the philosopher; and by analysis they meant something which, whatever precise description of it they chose, at least involved the attempt to rewrite in different and in some way more appropriate terms those statements which they found philosophically puzzling. (1956, vii) { §6.1 }

analysis is a familiar philosophical method. I shall not attempt to offer you a complete historical account of analytic philosophy. Even the minute examination of a particular analytic philosopher, or group of analytic philosophers, would not be of great interest. I propose rather to sketch, in broad strokes, four major forms of philosophical analysis which I think important to distinguish carefully from one another. I shall call the first of these: classical analysis. It corresponds, roughly, to the traditional method of analysis used by English philosophers, a method which Russell did so much to develop. I shall then examine three other, more recent forms of philosophical analysis: (1) the type of analysis which involves the construction of artificial languages; (2) the type of analysis practiced by Wittgenstein in his later period; (3) the type of analysis which characterizes present-day Oxford Philosophy.

The fundamental notion of classical analysis is that propositions couched in ordinary language are correct, in the sense that they are not objectionable in principle. They are neither logically nor metaphysically absurd. On the other hand, insofar as the form of these propositions of ordinary language hides their true meaning, they are neither metaphysically nor logically satisfactory. The task of the analyst is, therefore, to reformulate them so that this meaning will be clearly and explicitly presented, rather then to reject them. To analyze, is to reformulate,—to translate into a better wording. (1962, 294-5) { §6.1 }

The logical positivism of the Vienna Circle did not modify the methodology of classical analysis. However, because of the anti-metaphysical standpoint which was characteristic of positivism, it could not accept the notion of the goal of analysis as metaphysical discovery. For the positivists of this school, the goal of philosophical analysis is to clarify the language of science, a clarification which would result from, for example, elucidating the relationships between observation and theory, or between scientific concepts at different levels of abstraction. ( Ibid ., 296) { §6.1 }

A second school [or third school, after ‘classical analysis’ and logical positivism] was inspired (largely, but not entirely) by the thought of Wittgenstein in his later period. Wittgenstein had himself been led tothis new point of view in his criticism of his own Tractatus Logico-Philosophicus ( Logische-Philosophische Abhandlung ), a book which itself espoused implicitly a certain form of classical analysis. According to Wittgenstein, classical analysis rested upon a false conception of language and of thought. ...

... for an analyst of this sort, philosophical problems do not result from ignorance of the precise meaning of a concept, but from an entirely false conception of its function. ... Such a false conception is what Ryle calls a “category mistake”. To resolve a philosophical problem, one should exhibit the generic character of the concepts involved in it, rather than attempting to give a perfect definition or explication of these concepts. ...

This conception of philosophical analysis—of analysis as the resolution of conceptual enigmas—has sometimes been condescendingly called “therapeutic positivism”. ( Ibid ., 297-9) { §6.1 }

The fourth method of analysis ... is that of Oxford Philosophy. ...

The analytic philosophers of the Cambridge School—for example, Russell and Wittgenstein—came to philosophy after considerable work in the sciences and in mathematics. Philosophy of mathematics was the first topic to which Russell applied his classical method of analysis. But the Oxford philosophers came to their subject, almost without exception, after extensive study of classics. Thus they were naturally interested in words, in syntax, and in (idioms. They did not wish to use linguistic analysis simply to resolve philosophical problems; they were interested in the study of language for its own sake. Therefore these philosophers are, perhaps, both more given to making linguistic distinctions, and better at finding such distinctions, than most. Ibid ., 299) { §6.1 }

Many English philosophers (including many who owe allegiance to Oxford Philosophy) would place themselves at a position between that of Wittgenstein and the view I have just sketched. It may therefore be in point to indicate briefly the principal differences between the two schools:

(1) Wittgensteinian analysis has, for its sole end, the resolution of philosophical enigmas. If there were no such enigmas, there would be no need for analysis. For Oxford, on the other hand, analysis has an intrinsic value.

(2) According to Wittgenstein and his disciples, all that is necessary is to exhibit the generic character of the concepts which we analyze. For Oxford, a minute analysis is indispensable.

(3) For Wittgenstein, analysis is the only useful method in philosophy. For Oxford, it is only one among others, and no one claims that it is sufficient, by itself, to resolve all philosophical problems. ( Ibid ., 301) { §6.1 }

It is not sensible to ask for the method of making one‘s fortune (or of ruining oneself); there are many. It is no more sensible to ask “What is the analytical method?” There is not one “analytic philosophy”. There are several. ( Ibid ., 301 [closing sentences]) { §6.1 }

The primary weapon is analysis. And analysis is the evocation of insight by the hypothetical suggestions of thought, and the evocation of thought by the activities of direct insight. In this process the composite whole, the interrelations, and the things related, concurrently emerge into clarity. ( Essays in Science and Philosophy , New York: Philosophical Library, 1947, 157)

Analysis is often understood to imply a whole of which the parts are explicitly known before the analysis; but logical elements are for our ordinary consciousness only implicit: we use them without reflecting on them, just as we use grammatical distinctions long before we have any knowledge of grammar. Logic does not merely analyse: it makes explicit what was implicit. ( Statement and Inference , Oxford: Oxford University Press, 1926, 49)

The hypothetical process therefore combines in itself both the method of discovery and the proof, and is the proper scientific exposition. The non-hypothetical proof to which we are accustomed is a sort of scientific pedantry, and it is consequently a great mistake first to give what is called analysis, which corresponds to the hypothetical process, and then to follow it by a synthesis, which is the non-hypothetical part, thus putting aside analysis as if it were a sort of accident. It is an error because it conceals the true process of thinking. ( Ibid. , 560)

I have changed my views on “atomic” complexes: I now think that qualities, relations (like love) etc. are all copulae! That means I for instance analyse a subject-predicate proposition, say, “Socrates is human” into “Socrates” and “something is human”, (which I think is not complex). The reason for this is a very fundamental one. I think that there cannot be different Types of things! In other words whatever can be symbolized by a simple proper name must belong to one type. And further: every theory of types must be rendered superfluous by a proper theory of symbolism: For instance if I analyse the proposition Socrates is mortal into Socrates, mortality and (∃x,y) ∈ 1 (x,y) I want a theory of types to tell me that “mortality is Socrates” is nonsensical, because if I treat “mortality” as a proper name (as I did) there is nothing to prevent me to make the substitution the wrong way round. But if I analyse (as I do now) into Socrates and (∃x).x is mortal or generally into x and (∃x) φx it becomes impossible to substitute the wrong way round because the two symbols are now of a different kind themselves. What I am most certain of is not however the correctness of my present way of analysis, but of the fact that all theory of types must be done away with by a theory of symbolism showing that what seem to be different kinds of things are symbolized by different kinds of symbols which cannot possibly be substituted in one another’s places. I hope I have made this fairly clear!

Propositions which I formerly wrote ∈ 2 (a,R,b) I now write R(a,b) and analyse them into a,b and (∃x,y)R(x,y) [with (∃x,y)R(x,y) marked in the text as “not complex”] ( NB , 121-2) { §6.5 }

How is it reconcilable with the task of philosophy, that logic should take care of itself? If, for example, we ask: Is such and such a fact of the subject-predicate form?, we must surely know what we mean by “subject-predicate form”. We must know whether there is such a form at all. How can we know this? “From the signs”. But how? For we haven’t got any signs of this form. We may indeed say: We have signs that behave like signs of the subject-predicate form, but does that mean that there really must be facts of this form? That is, when those signs are completely analysed? And here the question arises again: Does such a complete analysis exist? And if not : then what is the task of philosophy?!!? ( NB , 2) { §6.5 }

Our difficulty now lies in the fact that to all appearances analysability, or its opposite, is not reflected in language. That is to say: We can not , as it seems, gather from language alone whether for example there are real subject-predicate facts or not. But how COULD we express this fact or its opposite? This must be shewn . ( NB , 10) { §6.5 }

The trivial fact that a completely analysed proposition contains just as many names as there are things contained in its reference [ Bedeutung ]; this fact is an example of the all-embracing representation of the world through language. ( NB , 11) { §6.5 }

The completely analysed proposition must image its reference [ Bedeutung ]. ( NB , 18) { §6.5 }

A question: can we manage without simple objects in LOGIC?

Obviously propositions are possible which contain no simple signs, i.e. no signs which have an immediate reference [ Bedeutung ]. And these are really propositions making sense, nor do the definitions of their component parts have to be attached to them.

But it is clear that components of our propositions can be analysed by means of a definition, and must be, if we want to approximate to the real structure of the proposition. At any rate, then, there is a process of analysis . And can it not now be asked whether this process comes to an end? And if so: What will the end be?

If it is true that every defined sign signifies via its definitions then presumably the chain of definitions must some time have an end. [Cf. TLP 3.261.]

The analysed proposition mentions more than the unanalysed.

Analysis makes the proposition more complicated than it was, but it cannot and must not make it more complicated than its meaning [ Bedeutung ] was from the first.

When the proposition is just as complex as its reference [ Bedeutung ], then it is completely analysed.

But the reference [ Bedeutung ] of our propositions is not infinitely complicated. ( NB , 46) { §6.5 }

But it also seems certain that we do not infer the existence of simple objects from the existence of particular simple objects, but rather know them—by description, as it were—as the end-product of analysis, by means of a process that leads to them. ( NB , 50) { §6.5 }

Let us assume that every spatial object consists of infintely many points, then it is clear that I cannot mention all these by name when I speak of that object. Here then would be a case in which I cannot arrive at the complete analysis in the old sense at all; and perhaps just this is the usual case.

But this is surely clear: the propositions which are the only ones that humanity uses will have a sense just as they are and do not wait upon a future analysis in order to acquire a sense.

Now, however, it seems to be a legitimate question: Are–e.g.–spatial objects composed of simple parts; in analysing them, does one arrive at parts that cannot be further analysed, or is this not the case?

—But what kind of question is this?—

Is it , A PRIORI, clear that in analysing we must arrive at simple components—is this, e.g., involved in the concept of analysis— , or is analysis ad infinitum possible?—Or is there in the end even a third possibility? ( NB , 62) { §6.5 }

In a proposition a thought can be expressed in such a way that elements of the propositional sign correspond to the objects of the thought.

I call such elements ‘simple signs’, and such a proposition ‘completely analysed’. ( TLP , 3.2, 3.201) { §6.5 }

A proposition has one and only one complete analysis. ( TLP , 3.25) { §6.5 }

It is obvious that the analysis of propositions must bring us to elementary propositions which consist of names in immediate combination.

This raises the question how such combination into propositions comes about. ( TLP , 4.221) { §6.5 }

If we know on purely logical grounds that there must be elementary propositions, then everyone who understands propositions in their unanalysed form must know it. ( TLP , 5.5562) { §6.5 }

A proposition is completely logically analysed if its grammar is made completely clear: no matter what idiom it may be written or expressed in. ( PR , 51; cf. BT , 308) { §6.5 }

Logical analysis is the analysis of something we have, not of something we don’t have. Therefore it is the analysis of propositions as they stand . ( PR , 52) { §6.5 }

a mathematical proof is an analysis of the mathematical proposition. ( PR , 179) { §6.5 }

Complex is not like fact. For I can, e.g., say of a complex that it moves from one place to another, but not of a fact.

But that this complex is now situated here is a fact. ...

A complex is composed of its parts, the things of a kind which go to make it up. (This is of course a grammatical proposition concerning the words ‘complex’, ‘part’ and ‘compose’.)

To say that a red circle is composed of redness and circularity, or is a complex with these component parts, is a misuse of these words and is misleading. (Frege was aware of this and told me.) It is just as misleading to say the fact that this circle is red (that I am tired) is a complex whose component parts are a circle and redness (myself and tiredness).

Neither is a house a complex of bricks and their spatial relations; i.e. that too goes against the correct use of the word. ( PR , 301-2) { §6.5 }

When I say: “My broom is in the corner”,—is this really a statement about the broomstick and the brush? Well, it could at any rate be replaced by a statement giving the position of the stick and the position of the brush. And this statement is surely a further analysed form of the first one.—But why do I call it “further analysed”?—Well, if the broom is there, that surely means that the stick and brush must be there, and in a particular relation to one another; and this was as it were hidden in the sense of the first sentence, and is expressed in the analysed sentence. Then does someone who says that the broom is in the corner really mean: the broomstick is there, and so is the brush, and the broomstick is fixed in the brush?—If we were to ask anyone if he meant this he would probably say that he had not thought specially of the broomstick or specially of the brush at all. And that would be the right answer, for he meant to speak neither of the stick nor of the brush in particular. Suppose that, instead of saying “Bring me the broom”, you said “Bring me the broomstick and the brush which is fitted on to it.”!—Isn’t the answer: “DO you want the broom? Why do you put it so oddly?”——Is he going to understand the further analysed sentence better?—This sentence, one might say, achieves the same as the ordinary one, but in a more roundabout way.— Imagine a language-game in which someone is ordered to bring certain objects which are composed of several parts, to move them about, or something else of that kind. And two ways of playing it: in one (a) the composite objects (brooms, chairs, tables, etc.) have names, as in (15); in the other (b) only the parts are given names and the wholes are described by means of them.—In what sense is an order in the second game an analysed form of an order in the first? Does the former lie concealed in the latter, and is it now brought out by analysis?—True, the broom is taken to pieces when one separates broomstick and brush; but does it follow that the order to bring the broom also consists of corresponding parts? ...

To say, however, that a sentence in (b) is an ‘analysed’ form of one in (a) readily seduces us into thinking that the former is the more fundamental form; that it alone shews what is meant by the other, and so on. For example, we think: If you have only the unanalysed form you miss the analysis; but if you know the analysed form that gives you everything.—But can I not say that an aspect of the matter is lost on you in the latter case as well as the former? ( PI , §§ 60, 63) { §6.5 }

Our investigation is therefore a grammatical one. Such an investigation sheds light on our problem by clearing misunderstandings away. Misunderstandings concerning the use of words, caused, among other things, by certain analogies between the forms of expression in different regions of language.—Some of them can be removed by substituting one form of expression for another; this may be called an “analysis” of our forms of expression, for the process is sometimes like one of taking a thing apart.

But now it may come to look as if there were something like a final analysis of our forms of language, and so a single completely resolved form of every expression. That is, as if our usual forms of expression were, essentially, unanalysed; as if there were something hidden in them that had to be brought to light. When this is done the expression is completely clarified and our problem solved.

It can also be put like this: we eliminate misunderstandings by making our expressions more exact; but now it may look as if we were moving towards a particular state, a state of complete exactness; and as if this were the real goal of our investigation. ( PI , §§ 90-1) { §6.5 }

We are not analysing a phenomenon (e.g. thought) but a concept (e.g. that of thinking), and therefore the use of a word. ( PI , §383) { §6.5 }

A list of key works on analysis (monographs and collections) can be found in the

Annotated Bibliography, §1.2 .

Copyright © 2014 by Michael Beaney < michael . beaney @ hu-berlin . de >

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Unit of Analysis: Definition, Types & Examples

The unit of analysis is the people or things whose qualities will be measured. The unit of analysis is an essential part of a research project. It’s the main thing that a researcher looks at in his research.

A unit of analysis is the object about which you hope to have something to say at the end of your analysis, perhaps the major subject of your research.

In this blog, we will define:

• Definition of “unit of analysis”

Types of “unit of analysis”

What is a unit of analysis.

A unit of analysis is the thing you want to discuss after your research, probably what you would regard to be the primary emphasis of your research.

The researcher plans to comment on the primary topic or object in the research as a unit of analysis. The research question plays a significant role in determining it. The “who” or “what” that the researcher is interested in investigating is, to put it simply, the unit of analysis.

In his book “Man, the State, and War” from 2001, author Waltz divides the world into three distinct spheres of study: the individual, the state, and war.

Understanding the reasoning behind the unit of analysis is vital. The likelihood of fruitful research increases if the rationale is understood. An individual, group, organization, nation, social phenomenon, etc., are a few examples.

LEARN ABOUT: Data Analytics Projects

In business research, there are almost unlimited types of possible analytical units. Data analytics and data analysis are closely related processes that involve extracting insights from data to make informed decisions. Even though the most typical unit of analysis is the individual, many research questions can be more precisely answered by looking at other types of units. Let’s find out, 

Individual Level

The most prevalent unit of analysis in business research is the individual. These are the primary analytical units. The researcher may be interested in looking into:

• Employee actions
• Perceptions
• Attitudes, or opinions.

Employees may come from wealthy or low-income families, as well as from rural or metropolitan areas.

A researcher might investigate if personnel from rural areas are more likely to arrive on time than those from urban areas. Additionally, he can check whether workers from rural areas who come from poorer families arrive on time compared to those from rural areas who come from wealthy families.

Each time, the individual (employee) serving as the analytical unit is discussed and explained. Employee analysis as a unit of analysis can shed light on issues in business, including customer and human resource behavior.

For example, employee work satisfaction and consumer purchasing patterns impact business, making research into these topics vital.

Psychologists typically concentrate on the research of individuals. The research of individuals may significantly aid the success of a firm. Their knowledge and experiences reveal vital information. Individuals are so heavily utilized in business research.

Aggregates Level

People are not usually the focus of social science research. By combining the reactions of individuals, social scientists frequently describe and explain social interactions, communities, and groupings. Additionally, they research the collective of individuals, including communities, groups, and countries.

Aggregate levels can be divided into two types: Groups (groups with an ad hoc structure) and Organizations (groups with a formal organization).

Groups of people make up the following levels of the unit of analysis. A group is defined as two or more individuals interacting, having common traits, and feeling connected to one another. 

Many definitions also emphasize interdependence or objective resemblance (Turner, 1982; Platow, Grace, & Smithson, 2011) and those who identify as group members (Reicher, 1982) .

As a result, society and gangs serve as examples of groups. According to Webster’s Online Dictionary (2012), they can resemble some clubs but be far less formal.

Siblings, identical twins, family, and small group functioning are examples of studies with many units of analysis.

In such circumstances, a whole group might be compared to another. Families, gender-specific groups, pals, Facebook groups, and work departments can all be groups.

By analyzing groups, researchers can learn how they form and how age, experience, class, and gender affect them. When aggregated, an individual’s data describes the group to which they belong.

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Sociologists study groups like economists. Businesspeople form teams to complete projects. They’re continually researching groups and group behavior.

Organizations

The next level of the unit of analysis is organizations, which are groups of people. Organizations are groups set up formally. It could include businesses, religious groups, parts of the military, colleges, academic departments, supermarkets, business groups, and so on.

The social organization includes things like sexual composition, styles of leadership, organizational structure, systems of communication, and so on. (Susan & Wheelan, 2005; Chapais & Berman, 2004) . (Lim, Putnam, and Robert, 2010) say that well-known social organizations and religious institutions are among them.

Moody, White, and Douglas (2003) say that social organizations are hierarchical. Hasmath, Hildebrandt, and Hsu (2016) say that social organizations can take different forms. For example, they can be made by institutions like schools or governments.

Sociology, economics, political science, psychology, management, and organizational communication (Douma & Schreuder, 2013) are some social science fields that study organizations.

Organizations are different from groups in that they are more formal and have better organization. A researcher might want to study a company to generalize its results to the whole population of companies.

One way to look at an organization is by the number of employees, the net annual revenue, the net assets, the number of projects, and so on. He might want to know if big companies hire more or fewer women than small companies.

Organization researchers might be interested in how companies like Reliance, Amazon, and HCL affect our social and economic lives. People who work in business often study business organizations.

Social Level

The social level has 2 types,

Social Artifacts Level

Things are studied alongside humans. Social artifacts are human-made objects from diverse communities. Social artifacts are items, representations, assemblages, institutions, knowledge, and conceptual frameworks used to convey, interpret, or achieve a goal (IGI Global, 2017).

Cultural artifacts are anything humans generate that reveals their culture (Watts, 1981).

Social artifacts include books, newspapers, advertising, websites, technical devices, films, photographs, paintings, clothes, poems, jokes, students’ late excuses, scientific breakthroughs, furniture, machines, structures, etc. Infinite.

Humans build social objects for social behavior. As people or groups suggest a population in business research, each social object implies a class of items.

Same-class goods include business books, magazines, articles, and case studies. A business magazine’s quantity of articles, frequency, price, content, and editor in a research study may be characterized.

Then, a linked magazine’s population might be evaluated for description and explanation. Marx W. Wartofsky (1979) defined artifacts as primary artifacts utilized in production (like a camera), secondary artifacts connected to primary artifacts (like a camera user manual), and tertiary objects related to representations of secondary artifacts (like a camera user-manual sculpture).

An artifact’s scientific study reveals its creators and users. The artifacts researcher may be interested in advertising, marketing, distribution, buying, etc.

Social Interaction Level

Social artifacts include social interaction. Such as:

• Eye contact with a coworker
• Buying something in a store
• Friendship decisions
• Road accidents
• Airline hijackings
• Professional counseling
• Whatsapp messaging

A researcher might study youthful employees’ smartphone addictions . Some addictions may involve social media, while others involve online games and movies that inhibit connection.

Smartphone addictions are examined as a societal phenomenon. Observation units are probably individuals (employees).

Anthropologists typically study social artifacts. They may be interested in the social order. A researcher who examines social interactions may be interested in how broader societal structures and factors impact daily behavior, festivals, and weddings.

LEARN ABOUT: Level of Analysis

Even though there is no perfect way to do research, it is generally agreed that researchers should try to find a unit of analysis that keeps the context needed to make sense of the data.

Researchers should consider the details of their research when deciding on the unit of analysis. 

They should keep in mind that consistent use of these units throughout the analysis process (from coding to developing categories and themes to interpreting the data) is essential to gaining insight from qualitative data and protecting the reliability of the results.

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Principles of Research Methodology pp 1–14 Cite as

Overview of the Research Process

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Research is a rigorous problem-solving process whose ultimate goal is the discovery of new knowledge. Research may include the description of a new phenomenon, definition of a new relationship, development of a new model, or application of an existing principle or procedure to a new context. Research is systematic, logical, empirical, reductive, replicable and transmittable, and generalizable. Research can be classified according to a variety of dimensions: basic, applied, or translational; hypothesis generating or hypothesis testing; retrospective or prospective; longitudinal or cross-sectional; observational or experimental; and quantitative or qualitative. The ultimate success of a research project is heavily dependent on adequate planning.

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Supino, P.G. (2012). Overview of the Research Process. In: Supino, P., Borer, J. (eds) Principles of Research Methodology. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-3360-6_1

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19 Content Analysis

Lindsay Prior, School of Sociology, Social Policy, and Social Work, Queen's University

• Published: 02 September 2020
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In this chapter, the focus is on ways in which content analysis can be used to investigate and describe interview and textual data. The chapter opens with a contextualization of the method and then proceeds to an examination of the role of content analysis in relation to both quantitative and qualitative modes of social research. Following the introductory sections, four kinds of data are subjected to content analysis. These include data derived from a sample of qualitative interviews ( N = 54), textual data derived from a sample of health policy documents ( N = 6), data derived from a single interview relating to a “case” of traumatic brain injury, and data gathered from fifty-four abstracts of academic papers on the topic of “well-being.” Using a distinctive and somewhat novel style of content analysis that calls on the notion of semantic networks, the chapter shows how the method can be used either independently or in conjunction with other forms of inquiry (including various styles of discourse analysis) to analyze data and also how it can be used to verify and underpin claims that arise from analysis. The chapter ends with an overview of the different ways in which the study of “content”—especially the study of document content—can be positioned in social scientific research projects.

What Is Content Analysis?

In his 1952 text on the subject of content analysis, Bernard Berelson traced the origins of the method to communication research and then listed what he called six distinguishing features of the approach. As one might expect, the six defining features reflect the concerns of social science as taught in the 1950s, an age in which the calls for an “objective,” “systematic,” and “quantitative” approach to the study of communication data were first heard. The reference to the field of “communication” was nothing less than a reflection of a substantive social scientific interest over the previous decades in what was called public opinion and specifically attempts to understand why and how a potential source of critical, rational judgment on political leaders (i.e., the views of the public) could be turned into something to be manipulated by dictators and demagogues. In such a context, it is perhaps not so surprising that in one of the more popular research methods texts of the decade, the terms content analysis and communication analysis are used interchangeably (see Goode & Hatt, 1952 , p. 325).

Academic fashions and interests naturally change with available technology, and these days we are more likely to focus on the individualization of communications through Twitter and the like, rather than of mass newspaper readership or mass radio audiences, yet the prevailing discourse on content analysis has remained much the same as it was in Berleson’s day. Thus, Neuendorf ( 2002 ), for example, continued to define content analysis as “the systematic, objective, quantitative analysis of message characteristics” (p. 1). Clearly, the centrality of communication as a basis for understanding and using content analysis continues to hold, but in this chapter I will try to show that, rather than locate the use of content analysis in disembodied “messages” and distantiated “media,” we would do better to focus on the fact that communication is a building block of social life itself and not merely a system of messages that are transmitted—in whatever form—from sender to receiver. To put that statement in another guise, we must note that communicative action (to use the phraseology of Habermas, 1987 ) rests at the very base of the lifeworld, and one very important way of coming to grips with that world is to study the content of what people say and write in the course of their everyday lives.

My aim is to demonstrate various ways in which content analysis (henceforth CTA) can be used and developed to analyze social scientific data as derived from interviews and documents. It is not my intention to cover the history of CTA or to venture into forms of literary analysis or to demonstrate each and every technique that has ever been deployed by content analysts. (Many of the standard textbooks deal with those kinds of issues much more fully than is possible here. See, for example, Babbie, 2013 ; Berelson, 1952 ; Bryman, 2008 , Krippendorf, 2004 ; Neuendorf, 2002 ; and Weber, 1990 ). Instead, I seek to recontextualize the use of the method in a framework of network thinking and to link the use of CTA to specific problems of data analysis. As will become evident, my exposition of the method is grounded in real-world problems. Those problems are drawn from my own research projects and tend to reflect my academic interests—which are almost entirely related to the analysis of the ways in which people talk and write about aspects of health, illness, and disease. However, lest the reader be deterred from going any further, I should emphasize that the substantive issues that I elect to examine are secondary if not tertiary to my main objective—which is to demonstrate how CTA can be integrated into a range of research designs and add depth and rigor to the analysis of interview and inscription data. To that end, in the next section I aim to clear our path to analysis by dealing with some issues that touch on the general position of CTA in the research armory, especially its location in the schism that has developed between quantitative and qualitative modes of inquiry.

The Methodological Context of Content Analysis

Content analysis is usually associated with the study of inscription contained in published reports, newspapers, adverts, books, web pages, journals, and other forms of documentation. Hence, nearly all of Berelson’s ( 1952 ) illustrations and references to the method relate to the analysis of written records of some kind, and where speech is mentioned, it is almost always in the form of broadcast and published political speeches (such as State of the Union addresses). This association of content analysis with text and documentation is further underlined in modern textbook discussions of the method. Thus, Bryman ( 2008 ), for example, defined CTA as “an approach to the analysis of documents and texts , that seek to quantify content in terms of pre-determined categories” (2008, p. 274, emphasis in original), while Babbie ( 2013 ) stated that CTA is “the study of recorded human communications” (2013, p. 295), and Weber referred to it as a method to make “valid inferences from text” (1990, p. 9). It is clear then that CTA is viewed as a text-based method of analysis, though extensions of the method to other forms of inscriptional material are also referred to in some discussions. Thus, Neuendorf ( 2002 ), for example, rightly referred to analyses of film and television images as legitimate fields for the deployment of CTA and by implication analyses of still—as well as moving—images such as photographs and billboard adverts. Oddly, in the traditional or standard paradigm of CTA, the method is solely used to capture the “message” of a text or speech; it is not used for the analysis of a recipient’s response to or understanding of the message (which is normally accessed via interview data and analyzed in other and often less rigorous ways; see, e.g., Merton, 1968 ). So, in this chapter I suggest that we can take things at least one small step further by using CTA to analyze speech (especially interview data) as well as text.

Standard textbook discussions of CTA usually refer to it as a “nonreactive” or “unobtrusive” method of investigation (see, e.g., Babbie, 2013 , p. 294), and a large part of the reason for that designation is because of its focus on already existing text (i.e., text gathered without intrusion into a research setting). More important, however (and to underline the obvious), CTA is primarily a method of analysis rather than of data collection. Its use, therefore, must be integrated into wider frames of research design that embrace systematic forms of data collection as well as forms of data analysis. Thus, routine strategies for sampling data are often required in designs that call on CTA as a method of analysis. These latter can be built around random sampling methods or even techniques of “theoretical sampling” (Glaser & Strauss, 1967 ) so as to identify a suitable range of materials for CTA. Content analysis can also be linked to styles of ethnographic inquiry and to the use of various purposive or nonrandom sampling techniques. For an example, see Altheide ( 1987 ).

The use of CTA in a research design does not preclude the use of other forms of analysis in the same study, because it is a technique that can be deployed in parallel with other methods or with other methods sequentially. For example, and as I will demonstrate in the following sections, one might use CTA as a preliminary analytical strategy to get a grip on the available data before moving into specific forms of discourse analysis. In this respect, it can be as well to think of using CTA in, say, the frame of a priority/sequence model of research design as described by Morgan ( 1998 ).

As I shall explain, there is a sense in which CTA rests at the base of all forms of qualitative data analysis, yet the paradox is that the analysis of content is usually considered a quantitative (numerically based) method. In terms of the qualitative/quantitative divide, however, it is probably best to think of CTA as a hybrid method, and some writers have in the past argued that it is necessarily so (Kracauer, 1952 ). That was probably easier to do in an age when many recognized the strictly drawn boundaries between qualitative and quantitative styles of research to be inappropriate. Thus, in their widely used text Methods in Social Research , Goode and Hatt ( 1952 ), for example, asserted that “modern research must reject as a false dichotomy the separation between ‘qualitative’ and ‘quantitative’ studies, or between the ‘statistical’ and the ‘non-statistical’ approach” (p. 313). This position was advanced on the grounds that all good research must meet adequate standards of validity and reliability, whatever its style, and the message is well worth preserving. However, there is a more fundamental reason why it is nonsensical to draw a division between the qualitative and the quantitative. It is simply this: All acts of social observation depend on the deployment of qualitative categories—whether gender, class, race, or even age; there is no descriptive category in use in the social sciences that connects to a world of “natural kinds.” In short, all categories are made, and therefore when we seek to count “things” in the world, we are dependent on the existence of socially constructed divisions. How the categories take the shape that they do—how definitions are arrived at, how inclusion and exclusion criteria are decided on, and how taxonomic principles are deployed—constitute interesting research questions in themselves. From our starting point, however, we need only note that “sorting things out” (to use a phrase from Bowker & Star, 1999 ) and acts of “counting”—whether it be of chromosomes or people (Martin & Lynch, 2009 )—are activities that connect to the social world of organized interaction rather than to unsullied observation of the external world.

Some writers deny the strict division between the qualitative and quantitative on grounds of empirical practice rather than of ontological reasoning. For example, Bryman ( 2008 ) argued that qualitative researchers also call on quantitative thinking, but tend to use somewhat vague, imprecise terms rather than numbers and percentages—referring to frequencies via the use of phrases such as “more than” and “less than.” Kracauer ( 1952 ) advanced various arguments against the view that CTA was strictly a quantitative method, suggesting that very often we wished to assess content as being negative or positive with respect to some political, social, or economic thesis and that such evaluations could never be merely statistical. He further argued that we often wished to study “underlying” messages or latent content of documentation and that, in consequence, we needed to interpret content as well as count items of content. Morgan ( 1993 ) argued that, given the emphasis that is placed on “coding” in almost all forms of qualitative data analysis, the deployment of counting techniques is essential and we ought therefore to think in terms of what he calls qualitative as well as quantitative content analysis. Naturally, some of these positions create more problems than they seemingly solve (as is the case with considerations of “latent content”), but given the 21st-century predilection for mixed methods research (Creswell, 2007 ), it is clear that CTA has a role to play in integrating quantitative and qualitative modes of analysis in a systematic rather than merely ad hoc and piecemeal fashion. In the sections that follow, I will provide some examples of the ways in which “qualitative” analysis can be combined with systematic modes of counting. First, however, we must focus on what is analyzed in CTA.

Units of Analysis

So, what is the unit of analysis in CTA? A brief answer is that analysis can be focused on words, sentences, grammatical structures, tenses, clauses, ratios (of, say, nouns to verbs), or even “themes.” Berelson ( 1952 ) gave examples of all of the above and also recommended a form of thematic analysis (cf., Braun & Clarke, 2006 ) as a viable option. Other possibilities include counting column length (of speeches and newspaper articles), amounts of (advertising) space, or frequency of images. For our purposes, however, it might be useful to consider a specific (and somewhat traditional) example. Here it is. It is an extract from what has turned out to be one of the most important political speeches of the current century.

Iraq continues to flaunt its hostility toward America and to support terror. The Iraqi regime has plotted to develop anthrax and nerve gas and nuclear weapons for over a decade. This is a regime that has already used poison gas to murder thousands of its own citizens, leaving the bodies of mothers huddled over their dead children. This is a regime that agreed to international inspections then kicked out the inspectors. This is a regime that has something to hide from the civilized world. States like these, and their terrorist allies, constitute an axis of evil, arming to threaten the peace of the world. By seeking weapons of mass destruction, these regimes pose a grave and growing danger. They could provide these arms to terrorists, giving them the means to match their hatred. They could attack our allies or attempt to blackmail the United States. In any of these cases, the price of indifference would be catastrophic. (George W. Bush, State of the Union address, January 29, 2002)

A number of possibilities arise for analyzing the content of a speech such as the one above. Clearly, words and sentences must play a part in any such analysis, but in addition to words, there are structural features of the speech that could also figure. For example, the extract takes the form of a simple narrative—pointing to a past, a present, and an ominous future (catastrophe)—and could therefore be analyzed as such. There are, in addition, several interesting oppositions in the speech (such as those between “regimes” and the “civilized” world), as well as a set of interconnected present participles such as “plotting,” “hiding,” “arming,” and “threatening” that are associated both with Iraq and with other states that “constitute an axis of evil.” Evidently, simple word counts would fail to capture the intricacies of a speech of this kind. Indeed, our example serves another purpose—to highlight the difficulty that often arises in dissociating CTA from discourse analysis (of which narrative analysis and the analysis of rhetoric and trope are subspecies). So how might we deal with these problems?

One approach that can be adopted is to focus on what is referenced in text and speech, that is, to concentrate on the characters or elements that are recruited into the text and to examine the ways in which they are connected or co-associated. I shall provide some examples of this form of analysis shortly. Let us merely note for the time being that in the previous example we have a speech in which various “characters”—including weapons in general, specific weapons (such as nerve gas), threats, plots, hatred, evil, and mass destruction—play a role. Be aware that we need not be concerned with the veracity of what is being said—whether it is true or false—but simply with what is in the speech and how what is in there is associated. (We may leave the task of assessing truth and falsity to the jurists). Be equally aware that it is a text that is before us and not an insight into the ex-president’s mind, or his thinking, or his beliefs, or any other subjective property that he may have possessed.

In the introductory paragraph, I made brief reference to some ideas of the German philosopher Jürgen Habermas ( 1987 ). It is not my intention here to expand on the detailed twists and turns of his claims with respect to the role of language in the “lifeworld” at this point. However, I do intend to borrow what I regard as some particularly useful ideas from his work. The first is his claim—influenced by a strong line of 20th-century philosophical thinking—that language and culture are constitutive of the lifeworld (Habermas, 1987 , p. 125), and in that sense we might say that things (including individuals and societies) are made in language. That is a simple justification for focusing on what people say rather than what they “think” or “believe” or “feel” or “mean” (all of which have been suggested at one time or another as points of focus for social inquiry and especially qualitative forms of inquiry). Second, Habermas argued that speakers and therefore hearers (and, one might add, writers and therefore readers), in what he calls their speech acts, necessarily adopt a pragmatic relation to one of three worlds: entities in the objective world, things in the social world, and elements of a subjective world. In practice, Habermas ( 1987 , p. 120) suggested all three worlds are implicated in any speech act, but that there will be a predominant orientation to one of them. To rephrase this in a crude form, when speakers engage in communication, they refer to things and facts and observations relating to external nature, to aspects of interpersonal relations, and to aspects of private inner subjective worlds (thoughts, feelings, beliefs, etc.). One of the problems with locating CTA in “communication research” has been that the communications referred to are but a special and limited form of action (often what Habermas called strategic acts). In other words, television, newspaper, video, and Internet communications are just particular forms (with particular features) of action in general. Again, we might note in passing that the adoption of the Habermassian perspective on speech acts implies that much of qualitative analysis in particular has tended to focus only on one dimension of communicative action—the subjective and private. In this respect, I would argue that it is much better to look at speeches such as George W Bush’s 2002 State of the Union address as an “account” and to examine what has been recruited into the account, and how what has been recruited is connected or co-associated, rather than use the data to form insights into his (or his adviser’s) thoughts, feelings, and beliefs.

In the sections that follow, and with an emphasis on the ideas that I have just expounded, I intend to demonstrate how CTA can be deployed to advantage in almost all forms of inquiry that call on either interview (or speech-based) data or textual data. In my first example, I will show how CTA can be used to analyze a group of interviews. In the second example, I will show how it can be used to analyze a group of policy documents. In the third, I shall focus on a single interview (a “case”), and in the fourth and final example, I will show how CTA can be used to track the biography of a concept. In each instance, I shall briefly introduce the context of the “problem” on which the research was based, outline the methods of data collection, discuss how the data were analyzed and presented, and underline the ways in which CTA has sharpened the analytical strategy.

Analyzing a Sample of Interviews: Looking at Concepts and Their Co-associations in a Semantic Network

My first example of using CTA is based on a research study that was initially undertaken in the early 2000s. It was a project aimed at understanding why older people might reject the offer to be immunized against influenza (at no cost to them). The ultimate objective was to improve rates of immunization in the study area. The first phase of the research was based on interviews with 54 older people in South Wales. The sample included people who had never been immunized, some who had refused immunization, and some who had accepted immunization. Within each category, respondents were randomly selected from primary care physician patient lists, and the data were initially analyzed “thematically” and published accordingly (Evans, Prout, Prior, Tapper-Jones, & Butler, 2007 ). A few years later, however, I returned to the same data set to look at a different question—how (older) lay people talked about colds and flu, especially how they distinguished between the two illnesses and how they understood the causes of the two illnesses (see Prior, Evans, & Prout, 2011 ). Fortunately, in the original interview schedule, we had asked people about how they saw the “differences between cold and flu” and what caused flu, so it was possible to reanalyze the data with such questions in mind. In that frame, the example that follows demonstrates not only how CTA might be used on interview data, but also how it might be used to undertake a secondary analysis of a preexisting data set (Bryman, 2008 ).

As with all talk about illness, talk about colds and flu is routinely set within a mesh of concerns—about causes, symptoms, and consequences. Such talk comprises the base elements of what has at times been referred to as the “explanatory model” of an illness (Kleinman, Eisenberg, & Good, 1978 ). In what follows, I shall focus almost entirely on issues of causation as understood from the viewpoint of older people; the analysis is based on the answers that respondents made in response to the question, “How do you think people catch flu?”

Semistructured interviews of the kind undertaken for a study such as this are widely used and are often characterized as akin to “a conversation with a purpose” (Kahn & Cannell, 1957 , p. 97). One of the problems of analyzing the consequent data is that, although the interviewer holds to a planned schedule, the respondents often reflect in a somewhat unstructured way about the topic of investigation, so it is not always easy to unravel the web of talk about, say, “causes” that occurs in the interview data. In this example, causal agents of flu, inhibiting agents, and means of transmission were often conflated by the respondents. Nevertheless, in their talk people did answer the questions that were posed, and in the study referred to here, that talk made reference to things such as “bugs” (and “germs”) as well as viruses, but the most commonly referred to causes were “the air” and the “atmosphere.” The interview data also pointed toward means of transmission as “cause”—so coughs and sneezes and mixing in crowds figured in the causal mix. Most interesting, perhaps, was the fact that lay people made a nascent distinction between facilitating factors (such as bugs and viruses) and inhibiting factors (such as being resistant, immune, or healthy), so that in the presence of the latter, the former are seen to have very little effect. Here are some shorter examples of typical question–response pairs from the original interview data.

(R:32): “How do you catch it [the flu]? Well, I take it its through ingesting and inhaling bugs from the atmosphere. Not from sort of contact or touching things. Sort of airborne bugs. Is that right?” (R:3): “I suppose it’s [the cause of flu] in the air. I think I get more diseases going to the surgery than if I stayed home. Sometimes the waiting room is packed and you’ve got little kids coughing and spluttering and people sneezing, and air conditioning I think is a killer by and large I think air conditioning in lots of these offices.” (R:46): “I think you catch flu from other people. You know in enclosed environments in air conditioning which in my opinion is the biggest cause of transferring diseases is air conditioning. Worse thing that was ever invented that was. I think so, you know. It happens on aircraft exactly the same you know.”

Alternatively, it was clear that for some people being cold, wet, or damp could also serve as a direct cause of flu; thus: Interviewer: “OK, good. How do you think you catch the flu?”

(R:39): “Ah. The 65 dollar question. Well, I would catch it if I was out in the rain and I got soaked through. Then I would get the flu. I mean my neighbour up here was soaked through and he got pneumonia and he died. He was younger than me: well, 70. And he stayed in his wet clothes and that’s fatal. Got pneumonia and died, but like I said, if I get wet, especially if I get my head wet, then I can get a nasty head cold and it could develop into flu later.”

As I suggested earlier, despite the presence of bugs and germs, viruses, the air, and wetness or dampness, “catching” the flu is not a matter of simple exposure to causative agents. Thus, some people hypothesized that within each person there is a measure of immunity or resistance or healthiness that comes into play and that is capable of counteracting the effects of external agents. For example, being “hardened” to germs and harsh weather can prevent a person getting colds and flu. Being “healthy” can itself negate the effects of any causative agents, and healthiness is often linked to aspects of “good” nutrition and diet and not smoking cigarettes. These mitigating and inhibiting factors can either mollify the effects of infection or prevent a person “catching” the flu entirely. Thus, (R:45) argued that it was almost impossible for him to catch flu or cold “cos I got all this resistance.” Interestingly, respondents often used possessive pronouns in their discussion of immunity and resistance (“my immunity” and “my resistance”)—and tended to view them as personal assets (or capital) that might be compromised by mixing with crowds.

By implication, having a weak immune system can heighten the risk of contracting colds and flu and might therefore spur one to take preventive measures, such as accepting a flu shot. Some people believe that the flu shot can cause the flu and other illnesses. An example of what might be called lay “epidemiology” (Davison, Davey-Smith, & Frankel, 1991 ) is evident in the following extract.

(R:4): “Well, now it’s coincidental you know that [my brother] died after the jab, but another friend of mine, about 8 years ago, the same happened to her. She had the jab and about six months later, she died, so I know they’re both coincidental, but to me there’s a pattern.”

Normally, results from studies such as this are presented in exactly the same way as has just been set out. Thus, the researcher highlights given themes that are said to have emerged from the data and then provides appropriate extracts from the interviews to illustrate and substantiate the relevant themes. However, one reasonable question that any critic might ask about the selected data extracts concerns the extent to which they are “representative” of the material in the data set as a whole. Maybe, for example, the author has been unduly selective in his or her use of both themes and quotations. Perhaps, as a consequence, the author has ignored or left out talk that does not fit the arguments or extracts that might be considered dull and uninteresting compared to more exotic material. And these kinds of issues and problems are certainly common to the reporting of almost all forms of qualitative research. However, the adoption of CTA techniques can help to mollify such problems. This is so because, by using CTA, we can indicate the extent to which we have used all or just some of the data, and we can provide a view of the content of the entire sample of interviews rather than just the content and flavor of merely one or two interviews. In this light, we must consider Figure 19.1 , which is based on counting the number of references in the 54 interviews to the various “causes” of the flu, though references to the flu shot (i.e., inoculation) as a cause of flu have been ignored for the purpose of this discussion. The node sizes reflect the relative importance of each cause as determined by the concept count (frequency of occurrence). The links between nodes reflect the degree to which causes are co-associated in interview talk and are calculated according to a co-occurrence index (see, e.g., SPSS, 2007 , p. 183).

What causes flu? A lay perspective. Factors listed as causes of colds and flu in 54 interviews. Node size is proportional to number of references “as causes.” Line thickness is proportional to co-occurrence of any two “causes” in the set of interviews.

Given this representation, we can immediately assess the relative importance of the different causes as referred to in the interview data. Thus, we can see that such things as (poor) “hygiene” and “foreigners” were mentioned as a potential cause of flu—but mention of hygiene and foreigners was nowhere near as important as references to “the air” or to “crowds” or to “coughs and sneezes.” In addition, we can also determine the strength of the connections that interviewees made between one cause and another. Thus, there are relatively strong links between “resistance” and “coughs and sneezes,” for example.

In fact, Figure 19.1 divides causes into the “external” and the “internal,” or the facilitating and the impeding (lighter and darker nodes). Among the former I have placed such things as crowds, coughs, sneezes, and the air, while among the latter I have included “resistance,” “immunity,” and “health.” That division is a product of my conceptualizing and interpreting the data, but whichever way we organize the findings, it is evident that talk about the causes of flu belongs in a web or mesh of concerns that would be difficult to represent using individual interview extracts alone. Indeed, it would be impossible to demonstrate how the semantics of causation belong to a culture (rather than to individuals) in any other way. In addition, I would argue that the counting involved in the construction of the diagram functions as a kind of check on researcher interpretations and provides a source of visual support for claims that an author might make about, say, the relative importance of “damp” and “air” as perceived causes of disease. Finally, the use of CTA techniques allied with aspects of conceptualization and interpretation has enabled us to approach the interview data as a set and to consider the respondents as belonging to a community, rather than regarding them merely as isolated and disconnected individuals, each with their own views. It has also enabled us to squeeze some new findings out of old data, and I would argue that it has done so with advantage. There are other advantages to using CTA to explore data sets, which I will highlight in the next section.

Analyzing a Sample of Documents: Using Content Analysis to Verify Claims

Policy analysis is a difficult business. To begin, it is never entirely clear where (social, health, economic, environmental) policy actually is. Is it in documents (as published by governments, think tanks, and research centers), in action (what people actually do), or in speech (what people say)? Perhaps it rests in a mixture of all three realms. Yet, wherever it may be, it is always possible, at the very least, to identify a range of policy texts and to focus on the conceptual or semantic webs in terms of which government officials and other agents (such as politicians) talk about the relevant policy issues. Furthermore, insofar as policy is recorded—in speeches, pamphlets, and reports—we may begin to speak of specific policies as having a history or a pedigree that unfolds through time (think, e.g., of U.S. or U.K. health policies during the Clinton years or the Obama years). And, insofar as we consider “policy” as having a biography or a history, we can also think of studying policy narratives.

Though firmly based in the world of literary theory, narrative method has been widely used for both the collection and the analysis of data concerning ways in which individuals come to perceive and understand various states of health, ill health, and disability (Frank, 1995 ; Hydén, 1997 ). Narrative techniques have also been adapted for use in clinical contexts and allied to concepts of healing (Charon, 2006 ). In both social scientific and clinical work, however, the focus is invariably on individuals and on how individuals “tell” stories of health and illness. Yet narratives can also belong to collectives—such as political parties and ethnic and religious groups—just as much as to individuals, and in the latter case there is a need to collect and analyze data that are dispersed across a much wider range of materials than can be obtained from the personal interview. In this context, Roe ( 1994 ) demonstrated how narrative method can be applied to an analysis of national budgets, animal rights, and environmental policies.

An extension of the concept of narrative to policy discourse is undoubtedly useful (Newman & Vidler, 2006 ), but how might such narratives be analyzed? What strategies can be used to unravel the form and content of a narrative, especially in circumstances where the narrative might be contained in multiple (policy) documents, authored by numerous individuals, and published across a span of time rather than in a single, unified text such as a novel? Roe ( 1994 ), unfortunately, was not in any way specific about analytical procedures, apart from offering the useful rule to “never stray too far from the data” (p. xii). So, in this example, I will outline a strategy for tackling such complexities. In essence, it is a strategy that combines techniques of linguistically (rule) based CTA with a theoretical and conceptual frame that enables us to unravel and identify the core features of a policy narrative. My substantive focus is on documents concerning health service delivery policies published from 2000 to 2009 in the constituent countries of the United Kingdom (that is, England, Scotland, Wales, and Northern Ireland—all of which have different political administrations).

Narratives can be described and analyzed in various ways, but for our purposes we can say that they have three key features: they point to a chronology, they have a plot, and they contain “characters.”

All narratives have beginnings; they also have middles and endings, and these three stages are often seen as comprising the fundamental structure of narrative text. Indeed, in his masterly analysis of time and narrative, Ricoeur ( 1984 ) argued that it is in the unfolding chronological structure of a narrative that one finds its explanatory (and not merely descriptive) force. By implication, one of the simplest strategies for the examination of policy narratives is to locate and then divide a narrative into its three constituent parts—beginning, middle, and end.

Unfortunately, while it can sometimes be relatively easy to locate or choose a beginning to a narrative, it can be much more difficult to locate an end point. Thus, in any illness narrative, a narrator might be quite capable of locating the start of an illness process (in an infection, accident, or other event) but unable to see how events will be resolved in an ongoing and constantly unfolding life. As a consequence, both narrators and researchers usually find themselves in the midst of an emergent present—a present without a known and determinate end (see, e.g., Frank, 1995 ). Similar considerations arise in the study of policy narratives where chronology is perhaps best approached in terms of (past) beginnings, (present) middles, and projected futures.

According to Ricoeur ( 1984 ), our basic ideas about narrative are best derived from the work and thought of Aristotle, who in his Poetics sought to establish “first principles” of composition. For Ricoeur, as for Aristotle, plot ties things together. It “brings together factors as heterogeneous as agents, goals, means, interactions, circumstances, unexpected results” (p. 65) into the narrative frame. For Aristotle, it is the ultimate untying or unraveling of the plot that releases the dramatic energy of the narrative.

Characters are most commonly thought of as individuals, but they can be considered in much broader terms. Thus, the French semiotician A. J. Greimas ( 1970 ), for example, suggested that, rather than think of characters as people, it would be better to think in terms of what he called actants and of the functions that such actants fulfill within a story. In this sense, geography, climate, and capitalism can be considered characters every bit as much as aggressive wolves and Little Red Riding Hood. Further, he argued that the same character (actant) can be considered to fulfill many functions, and the same function may be performed by many characters. Whatever else, the deployment of the term actant certainly helps us to think in terms of narratives as functioning and creative structures. It also serves to widen our understanding of the ways in which concepts, ideas, and institutions, as well “things” in the material world, can influence the direction of unfolding events every bit as much as conscious human subjects. Thus, for example, the “American people,” “the nation,” “the Constitution,” “the West,” “tradition,” and “Washington” can all serve as characters in a policy story.

As I have already suggested, narratives can unfold across many media and in numerous arenas—speech and action, as well as text. Here, however, my focus is solely on official documents—all of which are U.K. government policy statements, as listed in Table 19.1 . The question is, How might CTA help us unravel the narrative frame?

It might be argued that a simple reading of any document should familiarize the researcher with elements of all three policy narrative components (plot, chronology, and character). However, in most policy research, we are rarely concerned with a single and unified text, as is the case with a novel; rather, we have multiple documents written at distinctly different times by multiple (usually anonymous) authors that notionally can range over a wide variety of issues and themes. In the full study, some 19 separate publications were analyzed across England, Wales, Scotland, and Northern Ireland.

Naturally, listing word frequencies—still less identifying co-occurrences and semantic webs in large data sets (covering hundreds of thousands of words and footnotes)—cannot be done manually, but rather requires the deployment of complex algorithms and text-mining procedures. To this end, I analyzed the 19 documents using “Text Mining for Clementine” (SPSS, 2007 ).

Text-mining procedures begin by providing an initial list of concepts based on the lexicon of the text but that can be weighted according to word frequency and that take account of elementary word associations. For example, learning disability, mental health, and performance management indicate three concepts, not six words. Using such procedures on the aforementioned documents gives the researcher an initial grip on the most important concepts in the document set of each country. Note that this is much more than a straightforward concordance analysis of the text and is more akin to what Ryan and Bernard ( 2000 ) referred to as semantic analysis and Carley ( 1993 ) has referred to as concept and mapping analysis.

So, the first task was to identify and then extract the core concepts, thus identifying what might be called “key” characters or actants in each of the policy narratives. For example, in the Scottish documents, such actants included “Scotland” and the “Scottish people,” as well as “health” and the “National Health Service (NHS),” among others, while in the Welsh documents it was “the people of Wales” and “Wales” that figured largely—thus emphasizing how national identity can play every bit as important a role in a health policy narrative as concepts such as “health,” “hospitals,” and “well-being.”

Having identified key concepts, it was then possible to track concept clusters in which particular actants or characters are embedded. Such cluster analysis is dependent on the use of co-occurrence rules and the analysis of synonyms, whereby it is possible to get a grip on the strength of the relationships between the concepts, as well as the frequency with which the concepts appear in the collected texts. In Figure 19.2 , I provide an example of a concept cluster. The diagram indicates the nature of the conceptual and semantic web in which various actants are discussed. The diagrams further indicate strong (solid line) and weaker (dashed line) connections between the various elements in any specific mix, and the numbers indicate frequency counts for the individual concepts. Using Clementine , the researcher is unable to specify in advance which clusters will emerge from the data. One cannot, for example, choose to have an NHS cluster. In that respect, these diagrams not only provide an array in terms of which concepts are located, but also serve as a check on and to some extent validation of the interpretations of the researcher. None of this tells us what the various narratives contained within the documents might be, however. They merely point to key characters and relationships both within and between the different narratives. So, having indicated the techniques used to identify the essential parts of the four policy narratives, it is now time to sketch out their substantive form.

Concept cluster for “care” in six English policy documents, 2000–2007. Line thickness is proportional to the strength co-occurrence coefficient. Node size reflects relative frequency of concept, and (numbers) refer to the frequency of concept. Solid lines indicate relationships between terms within the same cluster, and dashed lines indicate relationships between terms in different clusters.

It may be useful to note that Aristotle recommended brevity in matters of narrative—deftly summarizing the whole of the Odyssey in just seven lines. In what follows, I attempt—albeit somewhat weakly—to emulate that example by summarizing a key narrative of English health services policy in just four paragraphs. Note how the narrative unfolds in relation to the dates of publication. In the English case (though not so much in the other U.K. countries), it is a narrative that is concerned to introduce market forces into what is and has been a state-managed health service. Market forces are justified in terms of improving opportunities for the consumer (i.e., the patients in the service), and the pivot of the newly envisaged system is something called “patient choice” or “choice.” This is how the story unfolds as told through the policy documents between 2000 and 2008 (see Table 19.1 ). The citations in the following paragraphs are to the Department of Health publications (by year) listed in Table 19.1 .

The advent of the NHS in 1948 was a “seminal event” (2000, p. 8), but under successive Conservative administrations, the NHS was seriously underfunded (2006, p. 3). The (New Labour) government will invest (2000) or already has (2003, p. 4) invested extensively in infrastructure and staff, and the NHS is now on a “journey of major improvement” (2004, p. 2). But “more money is only a starting point” (2000, p. 2), and the journey is far from finished. Continuation requires some fundamental changes of “culture” (2003, p. 6). In particular, the NHS remains unresponsive to patient need, and “all too often, the individual needs and wishes are secondary to the convenience of the services that are available. This ‘one size fits all’ approach is neither responsive, equitable nor person-centred” (2003, p. 17). In short, the NHS is a 1940s system operating in a 21st-century world (2000, p. 26). Change is therefore needed across the “whole system” (2005, p. 3) of care and treatment.

Above all, we must recognize that we “live in a consumer age” (2000, p. 26). People’s expectations have changed dramatically (2006, p. 129), and people want more choice, more independence, and more control (2003, p. 12) over their affairs. Patients are no longer, and should not be considered, “passive recipients” of care (2003, p. 62), but wish to be and should be (2006, p. 81) actively “involved” in their treatments (2003, p. 38; 2005, p. 18)—indeed, engaged in a partnership (2003, p. 22) of respect with their clinicians. Furthermore, most people want a personalized service “tailor made to their individual needs” (2000, p. 17; 2003, p. 15; 2004, p. 1; 2006, p. 83)—“a service which feels personal to each and every individual within a framework of equity and good use of public money” (2003, p. 6).

To advance the necessary changes, “patient choice” must be and “will be strengthened” (2000, p. 89). “Choice” must be made to “happen” (2003), and it must be “real” (2003, p. 3; 2004, p. 5; 2005, p. 20; 2006, p. 4). Indeed, it must be “underpinned” (2003, p. 7) and “widened and deepened” (2003, p. 6) throughout the entire system of care.

If “we” expand and underpin patient choice in appropriate ways and engage patients in their treatment systems, then levels of patient satisfaction will increase (2003, p. 39), and their choices will lead to a more “efficient” (2003, p. 5; 2004, p. 2; 2006, p. 16) and effective (2003, p. 62; 2005, p. 8) use of resources. Above all, the promotion of choice will help to drive up “standards” of care and treatment (2000, p. 4; 2003, p. 12; 2004, p. 3; 2005, p. 7; 2006, p. 3). Furthermore, the expansion of choice will serve to negate the effects of the “inverse care law,” whereby those who need services most tend to get catered to the least (2000, p. 107; 2003, p. 5; 2006, p. 63), and it will thereby help in moderating the extent of health inequalities in the society in which we live. “The overall aim of all our reforms,” therefore, “is to turn the NHS from a top down monolith into a responsive service that gives the patient the best possible experience. We need to develop an NHS that is both fair to all of us, and personal to each of us” (2003, p. 5).

We can see how most—though not all—of the elements of this story are represented in Figure 19.2. In particular, we can see strong (co-occurrence) links between care and choice and how partnership, performance, control, and improvement have a prominent profile. There are some elements of the web that have a strong profile (in terms of node size and links), but to which we have not referred; access, information, primary care, and waiting times are four. As anyone well versed in English healthcare policy would know, these elements have important roles to play in the wider, consumer-driven narrative. However, by rendering the excluded as well as included elements of that wider narrative visible, the concept web provides a degree of verification on the content of the policy story as told herein and on the scope of its “coverage.”

In following through on this example, we have moved from CTA to a form of discourse analysis (in this instance, narrative analysis). That shift underlines aspects of both the versatility of CTA and some of its weaknesses—versatility in the sense that CTA can be readily combined with other methods of analysis and in the way in which the results of the CTA help us to check and verify the claims of the researcher. The weakness of the diagram compared to the narrative is that CTA on its own is a somewhat one-dimensional and static form of analysis, and while it is possible to introduce time and chronology into the diagrams, the diagrams themselves remain lifeless in the absence of some form of discursive overview. (For a fuller analysis of these data, see Prior, Hughes, & Peckham, 2012 ).

Analyzing a Single Interview: The Role of Content Analysis in a Case Study

So far, I have focused on using CTA on a sample of interviews and a sample of documents. In the first instance, I recommended CTA for its capacity to tell us something about what is seemingly central to interviewees and for demonstrating how what is said is linked (in terms of a concept network). In the second instance, I reaffirmed the virtues of co-occurrence and network relations, but this time in the context of a form of discourse analysis. I also suggested that CTA can serve an important role in the process of verification of a narrative and its academic interpretation. In this section, however, I am going to link the use of CTA to another style of research—case study—to show how CTA might be used to analyze a single “case.”

Case study is a term used in multiple and often ambiguous ways. However, Gerring ( 2004 ) defined it as “an intensive study of a single unit for the purpose of understanding a larger class of (similar) units” (p. 342). As Gerring pointed out, case study does not necessarily imply a focus on N = 1, although that is indeed the most logical number for case study research (Ragin & Becker, 1992 ). Naturally, an N of 1 can be immensely informative, and whether we like it or not, we often have only one N to study (think, e.g., of the 1986 Challenger shuttle disaster or of the 9/11 attack on the World Trade Center). In the clinical sciences, case studies are widely used to represent the “typical” features of a wider class of phenomena and often used to define a kind or syndrome (as in the field of clinical genetics). Indeed, at the risk of mouthing a tautology, one can say that the distinctive feature of case study is its focus on a case in all of its complexity—rather than on individual variables and their interrelationships, which tends to be a point of focus for large N research.

There was a time when case study was central to the science of psychology. Breuer and Freud’s (2001) famous studies of “hysteria” (originally published in 1895) provide an early and outstanding example of the genre in this respect, but as with many of the other styles of social science research, the influence of case studies waned with the rise of much more powerful investigative techniques—including experimental methods—driven by the deployment of new statistical technologies. Ideographic studies consequently gave way to the current fashion for statistically driven forms of analysis that focus on causes and cross-sectional associations between variables rather than ideographic complexity.

In the example that follows, we will look at the consequences of a traumatic brain injury (TBI) on just one individual. The analysis is based on an interview with a person suffering from such an injury, and it was one of 32 interviews carried out with people who had experienced a TBI. The objective of the original research was to develop an outcome measure for TBI that was sensitive to the sufferer’s (rather than the health professional’s) point of view. In our original study (see Morris et al., 2005 ), interviews were also undertaken with 27 carers of the injured with the intention of comparing their perceptions of TBI to those of the people for whom they cared. A sample survey was also undertaken to elicit views about TBI from a much wider population of patients than was studied via interview.

In the introduction, I referred to Habermas and the concept of the lifeworld. Lifeworld ( Lebenswelt ) is a concept that first arose from 20th-century German philosophy. It constituted a specific focus for the work of Alfred Schutz (see, e.g., Schutz & Luckman, 1974 ). Schutz ( 1974 ) described the lifeworld as “that province of reality which the wide-awake and normal adult simply takes-for-granted in an attitude of common sense” (p. 3). Indeed, it was the routine and taken-for-granted quality of such a world that fascinated Schutz. As applied to the worlds of those with head injuries, the concept has particular resonance because head injuries often result in that taken-for-granted quality being disrupted and fragmented, ending in what Russian neuropsychologist A. R. Luria ( 1975 ) once described as “shattered” worlds. As well as providing another excellent example of a case study, Luria’s work is also pertinent because he sometimes argued for a “romantic science” of brain injury—that is, a science that sought to grasp the worldview of the injured patient by paying attention to an unfolding and detailed personal “story” of the individual with the head injury as well as to the neurological changes and deficits associated with the injury itself. In what follows, I shall attempt to demonstrate how CTA might be used to underpin such an approach.

In the original research, we began analysis by a straightforward reading of the interview transcripts. Unfortunately, a simple reading of a text or an interview can, strangely, mislead the reader into thinking that some issues or themes are more important than is warranted by the contents of the text. How that comes about is not always clear, but it probably has something to do with a desire to develop “findings” and our natural capacity to overlook the familiar in favor of the unusual. For that reason alone, it is always useful to subject any text to some kind of concordance analysis—that is, generating a simple frequency list of words used in an interview or text. Given the current state of technology, one might even speak these days of using text-mining procedures such as the aforementioned Clementine to undertake such a task. By using Clementine , and as we have seen, it is also possible to measure the strength of co-occurrence links between elements (i.e., words and concepts) in the entire data set (in this example, 32 interviews), though for a single interview these aims can just as easily be achieved using much simpler, low-tech strategies.

By putting all 32 interviews into the database, several common themes emerged. For example, it was clear that “time” entered into the semantic web in a prominent manner, and it was clearly linked to such things as “change,” “injury,” “the body,” and what can only be called the “I was.” Indeed, time runs through the 32 stories in many guises, and the centrality of time is a reflection of storytelling and narrative recounting in general—chronology, as we have noted, being a defining feature of all storytelling (Ricoeur, 1984 ). Thus, sufferers both recounted the events surrounding their injury and provided accounts as to how the injuries affected their current life and future hopes. As to time present, much of the patient story circled around activities of daily living—walking, working, talking, looking, feeling, remembering, and so forth.

Understandably, the word and the concept of “injury” featured largely in the interviews, though it was a word most commonly associated with discussions of physical consequences of injury. There were many references in that respect to injured arms, legs, hands, and eyes. There were also references to “mind”—though with far less frequency than with references to the body and to body parts. Perhaps none of this is surprising. However, one of the most frequent concepts in the semantic mix was the “I was” (716 references). The statement “I was,” or “I used to” was, in turn, strongly connected to terms such as “the accident” and “change.” Interestingly, the “I was” overwhelmingly eclipsed the “I am” in the interview data (the latter with just 63 references). This focus on the “I was” appears in many guises. For example, it is often associated with the use of the passive voice: “I was struck by a car,” “I was put on the toilet,” “I was shipped from there then, transferred to [Cityville],” “I got told that I would never be able …,” “I was sat in a room,” and so forth. In short, the “I was” is often associated with things, people, and events acting on the injured person. More important, however, the appearance of the “I was” is often used to preface statements signifying a state of loss or change in the person’s course of life—that is, as an indicator for talk about the patient’s shattered world. For example, Patient 7122 stated,

The main (effect) at the moment is I’m not actually with my children, I can’t really be their mum at the moment. I was a caring Mum, but I can’t sort of do the things that I want to be able to do like take them to school. I can’t really do a lot on my own. Like crossing the roads.

Another patient stated,

Everything is completely changed. The way I was … I can’t really do anything at the moment. I mean my German, my English, everything’s gone. Job possibilities is out the window. Everything is just out of the window … I just think about it all the time actually every day you know. You know it has destroyed me anyway, but if I really think about what has happened I would just destroy myself.

Each of these quotations, in its own way, serves to emphasize how life has changed and how the patient’s world has changed. In that respect, we can say that one of the major outcomes arising from TBI may be substantial “biographical disruption” (Bury, 1982 ), whereupon key features of an individual’s life course are radically altered forever. Indeed, as Becker ( 1997 , p. 37) argued in relation to a wide array of life events, “When their health is suddenly disrupted, people are thrown into chaos. Illness challenges one’s knowledge of one’s body. It defies orderliness. People experience the time before their illness and its aftermath as two separate entities.” Indeed, this notion of a cusp in personal biography is particularly well illustrated by Luria’s patient Zasetsky; the latter often refers to being a “newborn creature” (Luria, 1975 , pp. 24, 88), a shadow of a former self (p. 25), and as having his past “wiped out” (p. 116).

However, none of this tells us about how these factors come together in the life and experience of one individual. When we focus on an entire set of interviews, we necessarily lose the rich detail of personal experience and tend instead to rely on a conceptual rather than a graphic description of effects and consequences (to focus on, say, “memory loss,” rather than loss of memory about family life). The contents of Figure 19.3 attempt to correct that vision. Figure 19.3 records all the things that a particular respondent (Patient 7011) used to do and liked doing. It records all the things that he says he can no longer do (at 1 year after injury), and it records all the consequences that he suffered from his head injury at the time of the interview. Thus, we see references to epilepsy (his “fits”), paranoia (the patient spoke of his suspicions concerning other people, people scheming behind his back, and his inability to trust others), deafness, depression, and so forth. Note that, although I have inserted a future tense into the web (“I will”), such a statement never appeared in the transcript. I have set it there for emphasis and to show how, for this person, the future fails to connect to any of the other features of his world except in a negative way. Thus, he states at one point that he cannot think of the future because it makes him feel depressed (see Figure 19.3 ). The line thickness of the arcs reflects the emphasis that the subject placed on the relevant “outcomes” in relation to the “I was” and the “now” during the interview. Thus, we see that factors affecting his concentration and balance loom large, but that he is also concerned about his being dependent on others, his epileptic fits, and his being unable to work and drive a vehicle. The schism in his life between what he used to do, what he cannot now do, and his current state of being is nicely represented in the CTA diagram.

The shattered world of Patient 7011. Thickness of lines (arcs) is proportional to the frequency of reference to the “outcome” by the patient during the interview.

What have we gained from executing this kind of analysis? For a start, we have moved away from a focus on variables, frequencies, and causal connections (e.g., a focus on the proportion of people with TBI who suffer from memory problems or memory problems and speech problems) and refocused on how the multiple consequences of a TBI link together in one person. In short, instead of developing a narrative of acting variables, we have emphasized a narrative of an acting individual (Abbott, 1992 , p. 62). Second, it has enabled us to see how the consequences of a TBI connect to an actual lifeworld (and not simply an injured body). So the patient is not viewed just as having a series of discrete problems such as balancing, or staying awake, which is the usual way of assessing outcomes, but as someone struggling to come to terms with an objective world of changed things, people, and activities (missing work is not, for example, routinely considered an outcome of head injury). Third, by focusing on what the patient was saying, we gain insight into something that is simply not visible by concentrating on single outcomes or symptoms alone—namely, the void that rests at the center of the interview, what I have called the “I was.” Fourth, we have contributed to understanding a type, because the case that we have read about is not simply a case of “John” or “Jane” but a case of TBI, and in that respect it can add to many other accounts of what it is like to experience head injury—including one of the most well documented of all TBI cases, that of Zatetsky. Finally, we have opened up the possibility of developing and comparing cognitive maps (Carley, 1993 ) for different individuals and thereby gained insight into how alternative cognitive frames of the world arise and operate.

Tracing the Biography of a Concept

In the previous sections, I emphasized the virtues of CTA for its capacity to link into a data set in its entirety—and how the use of CTA can counter any tendency of a researcher to be selective and partial in the presentation and interpretation of information contained in interviews and documents. However, that does not mean that we always must take an entire document or interview as the data source. Indeed, it is possible to select (on rational and explicit grounds) sections of documentation and to conduct the CTA on the chosen portions. In the example that follows, I do just that. The sections that I chose to concentrate on are titles and abstracts of academic papers—rather than the full texts. The research on which the following is based is concerned with a biography of a concept and is being conducted in conjunction with a Ph.D. student of mine, Joanne Wilson. Joanne thinks of this component of the study more in terms of a “scoping study” than of a biographical study, and that, too, is a useful framework for structuring the context in which CTA can be used. Scoping studies (Arksey & O’Malley, 2005 ) are increasingly used in health-related research to “map the field” and to get a sense of the range of work that has been conducted on a given topic. Such studies can also be used to refine research questions and research designs. In our investigation, the scoping study was centered on the concept of well-being. Since 2010, well-being has emerged as an important research target for governments and corporations as well as for academics, yet it is far from clear to what the term refers. Given the ambiguity of meaning, it is clear that a scoping review, rather than either a systematic review or a narrative review of available literature, would be best suited to our goals.

The origins of the concept of well-being can be traced at least as far back as the 4th century bc , when philosophers produced normative explanations of the good life (e.g., eudaimonia, hedonia, and harmony). However, contemporary interest in the concept seemed to have been regenerated by the concerns of economists and, most recently, psychologists. These days, governments are equally concerned with measuring well-being to inform policy and conduct surveys of well-being to assess that state of the nation (see, e.g., Office for National Statistics, 2012 )—but what are they assessing?

We adopted a two-step process to address the research question, “What is the meaning of ‘well-being’ in the context of public policy?” First, we explored the existing thesauri of eight databases to establish those higher order headings (if any) under which articles with relevance to well-being might be cataloged. Thus, we searched the following databases: Cumulative Index of Nursing and Allied Health Literature, EconLit, Health Management Information Consortium, Medline, Philosopher’s Index, PsycINFO, Sociological Abstracts, and Worldwide Political Science Abstracts. Each of these databases adopts keyword-controlled vocabularies. In other words, they use inbuilt statistical procedures to link core terms to a set lexis of phrases that depict the concepts contained in the database. Table 19.2 shows each database and its associated taxonomy. The contents of Table 19.2 point toward a linguistic infrastructure in terms of which academic discourse is conducted, and our task was to extract from this infrastructure the semantic web wherein the concept of well-being is situated. We limited the thesaurus terms to well-being and its variants (i.e., wellbeing or well being). If the term was returned, it was then exploded to identify any associated terms.

To develop the conceptual map, we conducted a free-text search for well-being and its variants within the context of public policy across the same databases. We orchestrated these searches across five time frames: January 1990 to December 1994, January 1995 to December 1999, January 2000 to December 2004, January 2005 to December 2009, and January 2010 to October 2011. Naturally, different disciplines use different words to refer to well-being, each of which may wax and wane in usage over time. The searches thus sought to quantitatively capture any changes in the use and subsequent prevalence of well-being and any referenced terms (i.e., to trace a biography).

It is important to note that we did not intend to provide an exhaustive, systematic search of all the relevant literature. Rather, we wanted to establish the prevalence of well-being and any referenced (i.e., allied) terms within the context of public policy. This has the advantage of ensuring that any identified words are grounded in the literature (i.e., they represent words actually used by researchers to talk and write about well-being in policy settings). The searches were limited to abstracts to increase the specificity, albeit at some expense to sensitivity, with which we could identify relevant articles.

We also employed inclusion/exclusion criteria to facilitate the process by which we selected articles, thereby minimizing any potential bias arising from our subjective interpretations. We included independent, stand-alone investigations relevant to the study’s objectives (i.e., concerned with well-being in the context of public policy), which focused on well-being as a central outcome or process and which made explicit reference to “well-being” and “public policy” in either the title or the abstract. We excluded articles that were irrelevant to the study’s objectives, those that used noun adjuncts to focus on the well-being of specific populations (i.e., children, elderly, women) and contexts (e.g., retirement village), and those that focused on deprivation or poverty unless poverty indices were used to understand well-being as opposed to social exclusion. We also excluded book reviews and abstracts describing a compendium of studies.

Using these criteria, Joanne Wilson conducted the review and recorded the results on a template developed specifically for the project, organized chronologically across each database and timeframe. Results were scrutinized by two other colleagues to ensure the validity of the search strategy and the findings. Any concerns regarding the eligibility of studies for inclusion were discussed among the research team. I then analyzed the co-occurrence of the key terms in the database. The resultant conceptual map is shown in Figure 19.4.

The position of a concept in a network—a study of “well-being.” Node size is proportional to the frequency of terms in 54 selected abstracts. Line thickness is proportional to the co-occurrence of two terms in any phrase of three words (e.g., subjective well-being, economics of well-being, well-being and development).

The diagram can be interpreted as a visualization of a conceptual space. So, when academics write about well-being in the context of public policy, they tend to connect the discussion to the other terms in the matrix. “Happiness,” “health,” “economic,” and “subjective,” for example, are relatively dominant terms in the matrix. The node size of these words suggests that references to such entities is only slightly less than references to well-being itself. However, when we come to analyze how well-being is talked about in detail, we see specific connections come to the fore. Thus, the data imply that talk of “subjective well-being” far outweighs discussion of “social well-being” or “economic well-being.” Happiness tends to act as an independent node (there is only one occurrence of happiness and well-being), probably suggesting that “happiness” is acting as a synonym for well-being. Quality of life is poorly represented in the abstracts, and its connection to most of the other concepts in the space is very weak—confirming, perhaps, that quality of life is unrelated to contemporary discussions of well-being and happiness. The existence of “measures” points to a distinct concern to assess and to quantify expressions of happiness, well-being, economic growth, and gross domestic product. More important and underlying this detail, there are grounds for suggesting that there are in fact a number of tensions in the literature on well-being.

On the one hand, the results point toward an understanding of well-being as a property of individuals—as something that they feel or experience. Such a discourse is reflected through the use of words like happiness, subjective , and individual . This individualistic and subjective frame has grown in influence over the past decade in particular, and one of the problems with it is that it tends toward a somewhat content-free conceptualization of well-being. To feel a sense of well-being, one merely states that one is in a state of well-being; to be happy, one merely proclaims that one is happy (cf., Office for National Statistics, 2012 ). It is reminiscent of the conditions portrayed in Aldous Huxley’s Brave New World , wherein the rulers of a closely managed society gave their priority to maintaining order and ensuring the happiness of the greatest number—in the absence of attention to justice or freedom of thought or any sense of duty and obligation to others, many of whom were systematically bred in “the hatchery” as slaves.

On the other hand, there is some intimation in our web that the notion of well-being cannot be captured entirely by reference to individuals alone and that there are other dimensions to the concept—that well-being is the outcome or product of, say, access to reasonable incomes, to safe environments, to “development,” and to health and welfare. It is a vision hinted at by the inclusion of those very terms in the network. These different concepts necessarily give rise to important differences concerning how well-being is identified and measured and therefore what policies are most likely to advance well-being. In the first kind of conceptualization, we might improve well-being merely by dispensing what Huxley referred to as “soma” (a superdrug that ensured feelings of happiness and elation); in the other case, however, we would need to invest in economic, human, and social capital as the infrastructure for well-being. In any event and even at this nascent level, we can see how CTA can begin to tease out conceptual complexities and theoretical positions in what is otherwise routine textual data.

Putting the Content of Documents in Their Place

I suggested in my introduction that CTA was a method of analysis—not a method of data collection or a form of research design. As such, it does not necessarily inveigle us into any specific forms of either design or data collection, though designs and methods that rely on quantification are dominant. In this closing section, however, I want to raise the issue as to how we should position a study of content in our research strategies as a whole. We must keep in mind that documents and records always exist in a context and that while what is “in” the document may be considered central, a good research plan can often encompass a variety of ways of looking at how content links to context. Hence, in what follows, I intend to outline how an analysis of content might be combined with other ways of looking at a record or text and even how the analysis of content might be positioned as secondary to an examination of a document or record. The discussion calls on a much broader analysis, as presented in Prior ( 2011 ).

I have already stated that basic forms of CTA can serve as an important point of departure for many types of data analysis—for example, as discourse analysis. Naturally, whenever “discourse” is invoked, there is at least some recognition of the notion that words might play a part in structuring the world rather than merely reporting on it or describing it (as is the case with the 2002 State of the Nation address that was quoted in the section “Units of Analysis”). Thus, for example, there is a considerable tradition within social studies of science and technology for examining the place of scientific rhetoric in structuring notions of “nature” and the position of human beings (especially as scientists) within nature (see, e.g., work by Bazerman, 1988 ; Gilbert & Mulkay, 1984 ; and Kay, 2000 ). Nevertheless, little, if any, of that scholarship situates documents as anything other than inert objects, either constructed by or waiting patiently to be activated by scientists.

However, in the tradition of the ethnomethodologists (Heritage, 1991 ) and some adherents of discourse analysis, it is also possible to argue that documents might be more fruitfully approached as a “topic” (Zimmerman & Pollner, 1971 ) rather than a “resource” (to be scanned for content), in which case the focus would be on the ways in which any given document came to assume its present content and structure. In the field of documentation, these latter approaches are akin to what Foucault ( 1970 ) might have called an “archaeology of documentation” and are well represented in studies of such things as how crime, suicide, and other statistics and associated official reports and policy documents are routinely generated. That, too, is a legitimate point of research focus, and it can often be worth examining the genesis of, say, suicide statistics or statistics about the prevalence of mental disorder in a community as well as using such statistics as a basis for statistical modeling.

Unfortunately, the distinction between topic and resource is not always easy to maintain—especially in the hurly-burly of doing empirical research (see, e.g., Prior, 2003 ). Putting an emphasis on “topic,” however, can open a further dimension of research that concerns the ways in which documents function in the everyday world. And, as I have already hinted, when we focus on function, it becomes apparent that documents serve not merely as containers of content but also very often as active agents in episodes of interaction and schemes of social organization. In this vein, one can begin to think of an ethnography of documentation. Therein, the key research questions revolve around the ways in which documents are used and integrated into specific kinds of organizational settings, as well as with how documents are exchanged and how they circulate within such settings. Clearly, documents carry content—words, images, plans, ideas, patterns, and so forth—but the manner in which such material is called on and manipulated, and the way in which it functions, cannot be determined (though it may be constrained) by an analysis of content. Thus, Harper’s ( 1998 ) study of the use of economic reports inside the International Monetary Fund provides various examples of how “reports” can function to both differentiate and cohere work groups. In the same way. Henderson ( 1995 ) illustrated how engineering sketches and drawings can serve as what she calls conscription devices on the workshop floor.

Documents constitute a form of what Latour ( 1986 ) would refer to as “immutable mobiles,” and with an eye on the mobility of documents, it is worth noting an emerging interest in histories of knowledge that seek to examine how the same documents have been received and absorbed quite differently by different cultural networks (see, e.g., Burke, 2000 ). A parallel concern has arisen with regard to the newly emergent “geographies of knowledge” (see, e.g., Livingstone, 2005 ). In the history of science, there has also been an expressed interest in the biography of scientific objects (Latour, 1987 , p. 262) or of “epistemic things” (Rheinberger, 2000 )—tracing the history of objects independent of the “inventors” and “discoverers” to which such objects are conventionally attached. It is an approach that could be easily extended to the study of documents and is partly reflected in the earlier discussion concerning the meaning of the concept of well-being. Note how in all these cases a key consideration is how words and documents as “things” circulate and translate from one culture to another; issues of content are secondary.

Studying how documents are used and how they circulate can constitute an important area of research in its own right. Yet even those who focus on document use can be overly anthropocentric and subsequently overemphasize the potency of human action in relation to written text. In that light, it is interesting to consider ways in which we might reverse that emphasis and instead to study the potency of text and the manner in which documents can influence organizational activities as well as reflect them. Thus, Dorothy Winsor ( 1999 ), for example, examined the ways in which work orders drafted by engineers not only shape and fashion the practices and activities of engineering technicians but also construct “two different worlds” on the workshop floor.

In light of this, I will suggest a typology (Table 19.3 ) of the ways in which documents have come to be and can be considered in social research.

While accepting that no form of categorical classification can capture the inherent fluidity of the world, its actors, and its objects, Table 19.3 aims to offer some understanding of the various ways in which documents have been dealt with by social researchers. Thus, approaches that fit into Cell 1 have been dominant in the history of social science generally. Therein, documents (especially as text) have been analyzed and coded for what they contain in the way of descriptions, reports, images, representations, and accounts. In short, they have been scoured for evidence. Data analysis strategies concentrate almost entirely on what is in the “text” (via various forms of CTA). This emphasis on content is carried over into Cell 2–type approaches, with the key differences being that analysis is concerned with how document content comes into being. The attention here is usually on the conceptual architecture and sociotechnical procedures by means of which written reports, descriptions, statistical data, and so forth are generated. Various kinds of discourse analysis have been used to unravel the conceptual issues, while a focus on sociotechnical and rule-based procedures by means of which clinical, police, social work, and other forms of records and reports are constructed has been well represented in the work of ethnomethodologists (see Prior, 2011 ). In contrast, and in Cell 3, the research focus is on the ways in which documents are called on as a resource by various and different kinds of “user.” Here, concerns with document content or how a document has come into being are marginal, and the analysis concentrates on the relationship between specific documents and their use or recruitment by identifiable human actors for purposeful ends. I have pointed to some studies of the latter kind in earlier paragraphs (e.g., Henderson, 1995 ). Finally, the approaches that fit into Cell 4 also position content as secondary. The emphasis here is on how documents as “things” function in schemes of social activity and with how such things can drive, rather than be driven by, human actors. In short, the spotlight is on the vita activa of documentation, and I have provided numerous example of documents as actors in other publications (see Prior, 2003 , 2008 , 2011 ).

Content analysis was a method originally developed to analyze mass media “messages” in an age of radio and newspaper print, well before the digital age. Unfortunately, CTA struggles to break free of its origins and continues to be associated with the quantitative analysis of “communication.” Yet, as I have argued, there is no rational reason why its use must be restricted to such a narrow field, because it can be used to analyze printed text and interview data (as well as other forms of inscription) in various settings. What it cannot overcome is the fact that it is a method of analysis and not a method of data collection. However, as I have shown, it is an analytical strategy that can be integrated into a variety of research designs and approaches—cross-sectional and longitudinal survey designs, ethnography and other forms of qualitative design, and secondary analysis of preexisting data sets. Even as a method of analysis, it is flexible and can be used either independent of other methods or in conjunction with them. As we have seen, it is easily merged with various forms of discourse analysis and can be used as an exploratory method or as a means of verification. Above all, perhaps, it crosses the divide between “quantitative” and “qualitative” modes of inquiry in social research and offers a new dimension to the meaning of mixed methods research. I recommend it.

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Home » Quantitative Research – Methods, Types and Analysis

Quantitative Research – Methods, Types and Analysis

Table of Contents

Quantitative Research

Quantitative research is a type of research that collects and analyzes numerical data to test hypotheses and answer research questions . This research typically involves a large sample size and uses statistical analysis to make inferences about a population based on the data collected. It often involves the use of surveys, experiments, or other structured data collection methods to gather quantitative data.

Quantitative Research Methods

Quantitative Research Methods are as follows:

Descriptive Research Design

Descriptive research design is used to describe the characteristics of a population or phenomenon being studied. This research method is used to answer the questions of what, where, when, and how. Descriptive research designs use a variety of methods such as observation, case studies, and surveys to collect data. The data is then analyzed using statistical tools to identify patterns and relationships.

Correlational Research Design

Correlational research design is used to investigate the relationship between two or more variables. Researchers use correlational research to determine whether a relationship exists between variables and to what extent they are related. This research method involves collecting data from a sample and analyzing it using statistical tools such as correlation coefficients.

Quasi-experimental Research Design

Quasi-experimental research design is used to investigate cause-and-effect relationships between variables. This research method is similar to experimental research design, but it lacks full control over the independent variable. Researchers use quasi-experimental research designs when it is not feasible or ethical to manipulate the independent variable.

Experimental Research Design

Experimental research design is used to investigate cause-and-effect relationships between variables. This research method involves manipulating the independent variable and observing the effects on the dependent variable. Researchers use experimental research designs to test hypotheses and establish cause-and-effect relationships.

Survey Research

Survey research involves collecting data from a sample of individuals using a standardized questionnaire. This research method is used to gather information on attitudes, beliefs, and behaviors of individuals. Researchers use survey research to collect data quickly and efficiently from a large sample size. Survey research can be conducted through various methods such as online, phone, mail, or in-person interviews.

Quantitative Research Analysis Methods

Here are some commonly used quantitative research analysis methods:

Statistical Analysis

Statistical analysis is the most common quantitative research analysis method. It involves using statistical tools and techniques to analyze the numerical data collected during the research process. Statistical analysis can be used to identify patterns, trends, and relationships between variables, and to test hypotheses and theories.

Regression Analysis

Regression analysis is a statistical technique used to analyze the relationship between one dependent variable and one or more independent variables. Researchers use regression analysis to identify and quantify the impact of independent variables on the dependent variable.

Factor Analysis

Factor analysis is a statistical technique used to identify underlying factors that explain the correlations among a set of variables. Researchers use factor analysis to reduce a large number of variables to a smaller set of factors that capture the most important information.

Structural Equation Modeling

Structural equation modeling is a statistical technique used to test complex relationships between variables. It involves specifying a model that includes both observed and unobserved variables, and then using statistical methods to test the fit of the model to the data.

Time Series Analysis

Time series analysis is a statistical technique used to analyze data that is collected over time. It involves identifying patterns and trends in the data, as well as any seasonal or cyclical variations.

Multilevel Modeling

Multilevel modeling is a statistical technique used to analyze data that is nested within multiple levels. For example, researchers might use multilevel modeling to analyze data that is collected from individuals who are nested within groups, such as students nested within schools.

Applications of Quantitative Research

Quantitative research has many applications across a wide range of fields. Here are some common examples:

• Market Research : Quantitative research is used extensively in market research to understand consumer behavior, preferences, and trends. Researchers use surveys, experiments, and other quantitative methods to collect data that can inform marketing strategies, product development, and pricing decisions.
• Health Research: Quantitative research is used in health research to study the effectiveness of medical treatments, identify risk factors for diseases, and track health outcomes over time. Researchers use statistical methods to analyze data from clinical trials, surveys, and other sources to inform medical practice and policy.
• Social Science Research: Quantitative research is used in social science research to study human behavior, attitudes, and social structures. Researchers use surveys, experiments, and other quantitative methods to collect data that can inform social policies, educational programs, and community interventions.
• Education Research: Quantitative research is used in education research to study the effectiveness of teaching methods, assess student learning outcomes, and identify factors that influence student success. Researchers use experimental and quasi-experimental designs, as well as surveys and other quantitative methods, to collect and analyze data.
• Environmental Research: Quantitative research is used in environmental research to study the impact of human activities on the environment, assess the effectiveness of conservation strategies, and identify ways to reduce environmental risks. Researchers use statistical methods to analyze data from field studies, experiments, and other sources.

Characteristics of Quantitative Research

Here are some key characteristics of quantitative research:

• Numerical data : Quantitative research involves collecting numerical data through standardized methods such as surveys, experiments, and observational studies. This data is analyzed using statistical methods to identify patterns and relationships.
• Large sample size: Quantitative research often involves collecting data from a large sample of individuals or groups in order to increase the reliability and generalizability of the findings.
• Objective approach: Quantitative research aims to be objective and impartial in its approach, focusing on the collection and analysis of data rather than personal beliefs, opinions, or experiences.
• Control over variables: Quantitative research often involves manipulating variables to test hypotheses and establish cause-and-effect relationships. Researchers aim to control for extraneous variables that may impact the results.
• Replicable : Quantitative research aims to be replicable, meaning that other researchers should be able to conduct similar studies and obtain similar results using the same methods.
• Statistical analysis: Quantitative research involves using statistical tools and techniques to analyze the numerical data collected during the research process. Statistical analysis allows researchers to identify patterns, trends, and relationships between variables, and to test hypotheses and theories.
• Generalizability: Quantitative research aims to produce findings that can be generalized to larger populations beyond the specific sample studied. This is achieved through the use of random sampling methods and statistical inference.

Examples of Quantitative Research

Here are some examples of quantitative research in different fields:

• Market Research: A company conducts a survey of 1000 consumers to determine their brand awareness and preferences. The data is analyzed using statistical methods to identify trends and patterns that can inform marketing strategies.
• Health Research : A researcher conducts a randomized controlled trial to test the effectiveness of a new drug for treating a particular medical condition. The study involves collecting data from a large sample of patients and analyzing the results using statistical methods.
• Social Science Research : A sociologist conducts a survey of 500 people to study attitudes toward immigration in a particular country. The data is analyzed using statistical methods to identify factors that influence these attitudes.
• Education Research: A researcher conducts an experiment to compare the effectiveness of two different teaching methods for improving student learning outcomes. The study involves randomly assigning students to different groups and collecting data on their performance on standardized tests.
• Environmental Research : A team of researchers conduct a study to investigate the impact of climate change on the distribution and abundance of a particular species of plant or animal. The study involves collecting data on environmental factors and population sizes over time and analyzing the results using statistical methods.
• Psychology : A researcher conducts a survey of 500 college students to investigate the relationship between social media use and mental health. The data is analyzed using statistical methods to identify correlations and potential causal relationships.
• Political Science: A team of researchers conducts a study to investigate voter behavior during an election. They use survey methods to collect data on voting patterns, demographics, and political attitudes, and analyze the results using statistical methods.

How to Conduct Quantitative Research

Here is a general overview of how to conduct quantitative research:

• Develop a research question: The first step in conducting quantitative research is to develop a clear and specific research question. This question should be based on a gap in existing knowledge, and should be answerable using quantitative methods.
• Develop a research design: Once you have a research question, you will need to develop a research design. This involves deciding on the appropriate methods to collect data, such as surveys, experiments, or observational studies. You will also need to determine the appropriate sample size, data collection instruments, and data analysis techniques.
• Collect data: The next step is to collect data. This may involve administering surveys or questionnaires, conducting experiments, or gathering data from existing sources. It is important to use standardized methods to ensure that the data is reliable and valid.
• Analyze data : Once the data has been collected, it is time to analyze it. This involves using statistical methods to identify patterns, trends, and relationships between variables. Common statistical techniques include correlation analysis, regression analysis, and hypothesis testing.
• Interpret results: After analyzing the data, you will need to interpret the results. This involves identifying the key findings, determining their significance, and drawing conclusions based on the data.
• Communicate findings: Finally, you will need to communicate your findings. This may involve writing a research report, presenting at a conference, or publishing in a peer-reviewed journal. It is important to clearly communicate the research question, methods, results, and conclusions to ensure that others can understand and replicate your research.

When to use Quantitative Research

Here are some situations when quantitative research can be appropriate:

• To test a hypothesis: Quantitative research is often used to test a hypothesis or a theory. It involves collecting numerical data and using statistical analysis to determine if the data supports or refutes the hypothesis.
• To generalize findings: If you want to generalize the findings of your study to a larger population, quantitative research can be useful. This is because it allows you to collect numerical data from a representative sample of the population and use statistical analysis to make inferences about the population as a whole.
• To measure relationships between variables: If you want to measure the relationship between two or more variables, such as the relationship between age and income, or between education level and job satisfaction, quantitative research can be useful. It allows you to collect numerical data on both variables and use statistical analysis to determine the strength and direction of the relationship.
• To identify patterns or trends: Quantitative research can be useful for identifying patterns or trends in data. For example, you can use quantitative research to identify trends in consumer behavior or to identify patterns in stock market data.
• To quantify attitudes or opinions : If you want to measure attitudes or opinions on a particular topic, quantitative research can be useful. It allows you to collect numerical data using surveys or questionnaires and analyze the data using statistical methods to determine the prevalence of certain attitudes or opinions.

Purpose of Quantitative Research

The purpose of quantitative research is to systematically investigate and measure the relationships between variables or phenomena using numerical data and statistical analysis. The main objectives of quantitative research include:

• Description : To provide a detailed and accurate description of a particular phenomenon or population.
• Explanation : To explain the reasons for the occurrence of a particular phenomenon, such as identifying the factors that influence a behavior or attitude.
• Prediction : To predict future trends or behaviors based on past patterns and relationships between variables.
• Control : To identify the best strategies for controlling or influencing a particular outcome or behavior.

Quantitative research is used in many different fields, including social sciences, business, engineering, and health sciences. It can be used to investigate a wide range of phenomena, from human behavior and attitudes to physical and biological processes. The purpose of quantitative research is to provide reliable and valid data that can be used to inform decision-making and improve understanding of the world around us.

Advantages of Quantitative Research

There are several advantages of quantitative research, including:

• Objectivity : Quantitative research is based on objective data and statistical analysis, which reduces the potential for bias or subjectivity in the research process.
• Reproducibility : Because quantitative research involves standardized methods and measurements, it is more likely to be reproducible and reliable.
• Generalizability : Quantitative research allows for generalizations to be made about a population based on a representative sample, which can inform decision-making and policy development.
• Precision : Quantitative research allows for precise measurement and analysis of data, which can provide a more accurate understanding of phenomena and relationships between variables.
• Efficiency : Quantitative research can be conducted relatively quickly and efficiently, especially when compared to qualitative research, which may involve lengthy data collection and analysis.
• Large sample sizes : Quantitative research can accommodate large sample sizes, which can increase the representativeness and generalizability of the results.

Limitations of Quantitative Research

There are several limitations of quantitative research, including:

• Limited understanding of context: Quantitative research typically focuses on numerical data and statistical analysis, which may not provide a comprehensive understanding of the context or underlying factors that influence a phenomenon.
• Simplification of complex phenomena: Quantitative research often involves simplifying complex phenomena into measurable variables, which may not capture the full complexity of the phenomenon being studied.
• Potential for researcher bias: Although quantitative research aims to be objective, there is still the potential for researcher bias in areas such as sampling, data collection, and data analysis.
• Limited ability to explore new ideas: Quantitative research is often based on pre-determined research questions and hypotheses, which may limit the ability to explore new ideas or unexpected findings.
• Limited ability to capture subjective experiences : Quantitative research is typically focused on objective data and may not capture the subjective experiences of individuals or groups being studied.
• Ethical concerns : Quantitative research may raise ethical concerns, such as invasion of privacy or the potential for harm to participants.

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Methodology

• What Is Qualitative Research? | Methods & Examples

What Is Qualitative Research? | Methods & Examples

Published on June 19, 2020 by Pritha Bhandari . Revised on June 22, 2023.

Qualitative research involves collecting and analyzing non-numerical data (e.g., text, video, or audio) to understand concepts, opinions, or experiences. It can be used to gather in-depth insights into a problem or generate new ideas for research.

Qualitative research is the opposite of quantitative research , which involves collecting and analyzing numerical data for statistical analysis.

Qualitative research is commonly used in the humanities and social sciences, in subjects such as anthropology, sociology, education, health sciences, history, etc.

• How does social media shape body image in teenagers?
• How do children and adults interpret healthy eating in the UK?
• What factors influence employee retention in a large organization?
• How is anxiety experienced around the world?
• How can teachers integrate social issues into science curriculums?

Table of contents

Approaches to qualitative research, qualitative research methods, qualitative data analysis, advantages of qualitative research, disadvantages of qualitative research, other interesting articles, frequently asked questions about qualitative research.

Qualitative research is used to understand how people experience the world. While there are many approaches to qualitative research, they tend to be flexible and focus on retaining rich meaning when interpreting data.

Common approaches include grounded theory, ethnography , action research , phenomenological research, and narrative research. They share some similarities, but emphasize different aims and perspectives.

Note that qualitative research is at risk for certain research biases including the Hawthorne effect , observer bias , recall bias , and social desirability bias . While not always totally avoidable, awareness of potential biases as you collect and analyze your data can prevent them from impacting your work too much.

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Each of the research approaches involve using one or more data collection methods . These are some of the most common qualitative methods:

• Observations: recording what you have seen, heard, or encountered in detailed field notes.
• Interviews:  personally asking people questions in one-on-one conversations.
• Focus groups: asking questions and generating discussion among a group of people.
• Surveys : distributing questionnaires with open-ended questions.
• Secondary research: collecting existing data in the form of texts, images, audio or video recordings, etc.
• You take field notes with observations and reflect on your own experiences of the company culture.
• You distribute open-ended surveys to employees across all the company’s offices by email to find out if the culture varies across locations.
• You conduct in-depth interviews with employees in your office to learn about their experiences and perspectives in greater detail.

Qualitative researchers often consider themselves “instruments” in research because all observations, interpretations and analyses are filtered through their own personal lens.

For this reason, when writing up your methodology for qualitative research, it’s important to reflect on your approach and to thoroughly explain the choices you made in collecting and analyzing the data.

Qualitative data can take the form of texts, photos, videos and audio. For example, you might be working with interview transcripts, survey responses, fieldnotes, or recordings from natural settings.

Most types of qualitative data analysis share the same five steps:

• Prepare and organize your data. This may mean transcribing interviews or typing up fieldnotes.
• Review and explore your data. Examine the data for patterns or repeated ideas that emerge.
• Develop a data coding system. Based on your initial ideas, establish a set of codes that you can apply to categorize your data.
• Assign codes to the data. For example, in qualitative survey analysis, this may mean going through each participant’s responses and tagging them with codes in a spreadsheet. As you go through your data, you can create new codes to add to your system if necessary.
• Identify recurring themes. Link codes together into cohesive, overarching themes.

There are several specific approaches to analyzing qualitative data. Although these methods share similar processes, they emphasize different concepts.

Qualitative research often tries to preserve the voice and perspective of participants and can be adjusted as new research questions arise. Qualitative research is good for:

• Flexibility

The data collection and analysis process can be adapted as new ideas or patterns emerge. They are not rigidly decided beforehand.

• Natural settings

Data collection occurs in real-world contexts or in naturalistic ways.

• Meaningful insights

Detailed descriptions of people’s experiences, feelings and perceptions can be used in designing, testing or improving systems or products.

• Generation of new ideas

Open-ended responses mean that researchers can uncover novel problems or opportunities that they wouldn’t have thought of otherwise.

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Researchers must consider practical and theoretical limitations in analyzing and interpreting their data. Qualitative research suffers from:

• Unreliability

The real-world setting often makes qualitative research unreliable because of uncontrolled factors that affect the data.

• Subjectivity

Due to the researcher’s primary role in analyzing and interpreting data, qualitative research cannot be replicated . The researcher decides what is important and what is irrelevant in data analysis, so interpretations of the same data can vary greatly.

• Limited generalizability

Small samples are often used to gather detailed data about specific contexts. Despite rigorous analysis procedures, it is difficult to draw generalizable conclusions because the data may be biased and unrepresentative of the wider population .

• Labor-intensive

Although software can be used to manage and record large amounts of text, data analysis often has to be checked or performed manually.

If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

• Chi square goodness of fit test
• Degrees of freedom
• Null hypothesis
• Discourse analysis
• Control groups
• Mixed methods research
• Non-probability sampling
• Quantitative research
• Inclusion and exclusion criteria

Research bias

• Rosenthal effect
• Implicit bias
• Cognitive bias
• Selection bias
• Negativity bias
• Status quo bias

Quantitative research deals with numbers and statistics, while qualitative research deals with words and meanings.

Quantitative methods allow you to systematically measure variables and test hypotheses . Qualitative methods allow you to explore concepts and experiences in more detail.

There are five common approaches to qualitative research :

• Grounded theory involves collecting data in order to develop new theories.
• Ethnography involves immersing yourself in a group or organization to understand its culture.
• Narrative research involves interpreting stories to understand how people make sense of their experiences and perceptions.
• Phenomenological research involves investigating phenomena through people’s lived experiences.
• Action research links theory and practice in several cycles to drive innovative changes.

Data collection is the systematic process by which observations or measurements are gathered in research. It is used in many different contexts by academics, governments, businesses, and other organizations.

There are various approaches to qualitative data analysis , but they all share five steps in common:

• Prepare and organize your data.
• Review and explore your data.
• Develop a data coding system.
• Assign codes to the data.
• Identify recurring themes.

The specifics of each step depend on the focus of the analysis. Some common approaches include textual analysis , thematic analysis , and discourse analysis .

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Ratio Data: Definition, Examples, and Analysis

Published by Owen Ingram at September 2nd, 2021 , Revised On July 20, 2023

There are a total of four types of data in statistics primarily. They are nominal data, ordinal data, ratio data, and interval data.

Ordinal Data : This type of data is classified into categories. However, the distance between these categories is unknown.

Nominal Data : Nominal data is used to label variables without assigning any quantitative value to them.

Ratio Data: This is a kind of qualitative data that measures variables on a continuous scale.

Interval Data : This data type is measured along a scale and has an equal distance between its values.

If you’re looking to learn everything there is to know about the ratio data, then you’re at the right place. Let’s take a look into the definition, examples, and analysis of ratio data.

What is a Ratio Data?

A Ratio scale is the fourth type of measurement scale and is quantitative in nature. It is similar to interval data , where each value is placed at an equal distance from its subsequent value. However, it has a ‘true zero,’ which means that zero possesses a meaning.

The ratio scale contains the characteristics of nominal, ordinal, and interval scales and is, therefore, used widely in market research.

Examples of Ratio Data

Here are some of the common examples of ratio data:

• Mass and Weight

In Market Research, it is used to evaluate:

• Number of customers

Ratio Data vs. Interval Data – The Difference

Both interval and ratio data have equal values placed between two variables . However, one significant difference between the two is the presence of the ‘true zero.’ The ratio data has a true zero, which denotes an absence of a variable. For example, in interval data, you can measure temperature beyond 0 degrees because zero, in this case, holds a value. However, in ratio data, the variables never fall beneath zero.

An example of this is body mass. We know mass is measured from 0 as a starting point and goes above. It does not fall beneath zero.

Characteristics of Ratio Data

Here are some of the characteristics of the ratio data:

• Absolute zero: As explained earlier, ratio scales have an absolute zero. Although they are not categorical, they have a specific order and have equal distance between their values. We can use multiplication or division to describe them because of the absolute zero characteristics in the ratio scales. For example, 40kg is twice more than 20kg, or the distance from point A to B is 50km which is twice less than the distance from point B to C, i.e., 150km.
• No negative number: Because ratio scales have an absolute zero, they do not have significant negative numbers. Unlike interval scales where -10 would hold a meaningful, ratio scales begin from a certain point as a way of measurement.
• Possibilities for statistical measurement: Since ratio scales have an absolute zero, variables in this type of data can be added, subtracted, multiplied, or divided. Furthermore, all measures of central tendency can be performed with ratio scales. These include the mean , mode , and median .

Not sure which statistical tests to use for your data?

Let the experts at researchprospect do the daunting work for you. 📊📈.

Using our approach, we illustrate how to collect data, sample sizes, validity, reliability, credibility, and ethics, so you won’t have to do it all by yourself!

How is Ratio Data Collected?

There are several ways to collect ratio data. Your method solely depends on the type of research you’re doing. Common ways to collect data are surveys, questionnaires, and interviews.

• Interviews: In this method, participants are interviewed ad data is collected from there. Such discussions are often structured, semi-structured, or unstructured. They can be either face-to-face, telephonic, panel or group, and computer-assisted.
• Questionnaires and Surveys: This is a standard data collection method for qualitative data. A survey or a questionnaire is handed out to participants, and they are asked to answer a series of questions. Their answers are then recorded for qualitative analysis.
• Direct Observation: Ratio data can also be collected through direct observation. For example, if you were to measure the height of some athletes, there will be a point zero. A measurement of 0 would indicate an absence of the athlete.
• Automated Data Collectors: Some roads have automated speed calculators, which are an efficient and practical way to collect data.

Here’s an example,

Question: How much is your family’s monthly income?

Possible answers: $0-$5000, $5000-$10,000, $10,000-$15,000, $15,000 or more.

Note: The distance between the intervals is equal, i.e., $5000.There is also a true zero. Also, the answer can not be negative, i.e., $ -20

Analyzing Ratio Data

Ratio Data can be analyzed and interpreted in precisely the same way as the interval way. These include the following methods:

• Mean : This is the average of the interval data set. Mean can be calculated by adding the numbers in the interval data set and dividing this total by the number of values in the set.
• Median : Median is used to determine the middle value in the data set. Since all values in the interval data are equal distance apart, the median is easy to calculate.
• Mode : This is the value that is the most occurring in the data set.
• Standard Deviation: This measures the dispersion of a data set relative to its mean.
• Percentiles: This is the percentage of values that fall below a specific number from the data set. For example, let’s suppose the 75th percentile of an IELTS test is 6.0 overall. If you scored an overall 6.0, this would mean that your score was better than 75% of the IELTS test takers.
• Range : This is the difference between the highest and the lowest value in the data set.

What Statistical Tests can you do with Ratio Data?

You can perform several statistical tests with ratio scales, mainly,

• Pearson Correlation
• Simple Linear Regression

And that’s a wrap! That’s all you need to know about ratio data, its definition, examples, and analysis.

FAQs About Ratio Data

What are the main differences between interval and ratio scales.

• Interval scales do not have a true zero, whereas ratio scales do.
• Negative numbers have meaning in interval scales, whereas negative numbers do not hold any meaningful value in ratio scales.
• Interval data can only be expressed using addition or subtraction, whereas ratio data can be expressed using addition, subtraction, multiplication, and division.

What are the examples of Ratio Scales?

Some common examples of ratio scales are age, distance, speed, and mass. What are the four levels of measurement of data? The four levels of measurement of data are nominal , ordinals , interval , and ratio data.

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Chaichana U , Man KKC , Chen A, et al. Definition of Post–COVID-19 Condition Among Published Research Studies. JAMA Netw Open. 2023;6(4):e235856. doi:10.1001/jamanetworkopen.2023.5856

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Definition of Post–COVID-19 Condition Among Published Research Studies

• 1 UCL School of Pharmacy, London, United Kingdom
• 2 Laboratory of Data Discovery for Health (D24H), Hong Kong Science Park, Hong Kong Special Administrative Region, China
• 3 Centre for Medicines Optimisation Research and Education, University College London Hospitals National Health Service (NHS) Foundation Trust, London, United Kingdom
• 4 Centre for Safe Medication Practice and Research, Department of Pharmacology and Pharmacy, Li Ka Shing Faculty of Medicine, The University of Hong Kong, Hong Kong Special Administrative Region, China
• 5 Ninewells Hospital, University of Dundee Medical School, Dundee, United Kingdom
• 6 University College London Hospitals NHS Foundation Trust, London, United Kingdom
• Invited Commentary Toward a Universal Definition of Post–COVID-19 Condition Daniel Pan, MRCP; Manish Pareek, PhD, MRCP JAMA Network Open

As of February 2023, there have been approximately 759 million confirmed cases of COVID-19 infections globally 1 and some individuals have experienced persistent symptoms, such as fatigue and shortness of breath, after recovering from the initial illness from COVID-19. The UK National Institute for Health and Care Excellence (NICE), 2 the World Health Organization (WHO), 3 and the US Centers for Disease Control and Prevention (CDC) 4 have published their definitions of post–COVID-19 condition (PCC) between December 2020 and October 2021, with some discrepancies between them. Despite the growing volume of research on lasting symptoms of COVID-19, the definition has not been universally agreed on. This study aimed to describe how post–COVID-19 condition has been defined to date in studies on this topic.

We conducted a descriptive study on PCC definition following the STROBE reporting guideline and performed the literature search using the PRISMA checklist in PubMed on October 26, 2022. A total of 7087 studies containing information on PCC were identified from February 1, 2020, to October 26, 2022. Definition of PCC (eAppendix in Supplement 1 ), study type, country where the study was conducted, and manuscript submission date were extracted from the publications and are presented chronologically (eAppendix in Supplement 1 ).

Two investigators (U.C. and A.C.) reviewed the studies and screened titles and abstracts independently and cross-checked a 10% sample of the data collected from the studies. When submission dates were not available, the publication dates were used to determine the study time. Exemption from ethical approval was indicated by the University College of London Ethics Committee. SPSS Statistics for Windows, version 28 (IBM Corp) was used for data analysis.

Among 7087 studies, we excluded 6792 that were not relevant to PCC (eg, SARS-CoV-2 vaccines, commentary, systematic review, and full articles in languages other than English). The remaining 295 studies were included, consisting of 2 randomized clinical trials (0.7%), 134 cohort studies (45.4%), 66 cross-sectional studies (22.4%), 13 case-control studies (4.4%), 45 case reports or case series (15.3%), and 35 studies using other designs (11.9%) ( Figure 1 ). Of these, 167 studies (56.6%) were conducted in European countries. We found that only 102 studies (34.6%) used 1 of the 3 organizational definitions for their studies (NICE: 56, WHO: 31, and CDC: 15). A total of 193 studies (65.4%) did not follow any of the 3 definitions for PCC and 6 studies were submitted for publication before NICE released their PCC definition (ie, before December 18, 2020) ( Figure 2 ).

Of 193 studies that did not follow any of 3 definitions, 129 studies (66.8%) used their own definitions for PCC (eg, presence of chronic symptoms that last >5 months or after 2 weeks of SARS-CoV-2 infection), while 64 studies (33.2%) did not define PCC.

We found substantial heterogeneity in defining PCC in the published studies, with almost two-thirds (65.4%) not complying with the definitions from the NICE, CDC, or WHO. This study highlights major issues in comparing interventions and outcomes between these reported studies in PCC due to differences in definition. The differences also result in considerable variation when translating findings into clinical management and cost-effectiveness assessments of interventions in patients with PCC. The clinical management of PCC must be evidence-based and include a personalized approach. A clearer definition of PCC is timely so that clinical trial evidence can reliably be applied to clinical management and the well-being of patients with PCC can be improved.

Our study has some limitations. We conducted the literature search only in PubMed. Furthermore, the NICE updated their PCC definition in November 2022 after we finished the study screening. However, the updated definition would not affect our study and would only apply to studies conducted after November 2022.

Accepted for Publication: February 8, 2023.

Published: April 5, 2023. doi:10.1001/jamanetworkopen.2023.5856

Open Access: This is an open access article distributed under the terms of the CC-BY License . © 2023 Chaichana U et al. JAMA Network Open .

Corresponding Author: Li Wei, PhD, UCL School of Pharmacy, 29-39 Brunswick Square, London WC1N 1AX, United Kingdom ( [email protected] ).

Author Contributions: Ms Chaichana and Dr Wei had full access to all of the data in the study and take responsibility for the integrity of the data and the accuracy of the data analysis.

Concept and design: Chaichana, Man, Wong, Wei.

Acquisition, analysis, or interpretation of data: Chaichana, Man, Chen, George, Wilson, Wei.

Drafting of the manuscript: Chaichana, Chen.

Critical revision of the manuscript for important intellectual content: All authors.

Statistical analysis: Chaichana, Chen.

Obtained funding: Wong.

Administrative, technical, or material support: Chen.

Supervision: Man, Wilson, Wei.

Conflict of Interest Disclosures: Ms Chaichana reported receiving a scholarship from the Royal Thai Government outside the submitted work. Dr Man reported receiving grants from the Hong Kong Research Grant Council during the conduct of the study; grants from CW Maplethorpe Fellowship, European Commission Horizon 2020, and the National Institute for Health and Care Research; and personal fees from IQVIA Ltd outside the submitted work. Dr Wong reported receiving grants from the Hong Kong Health and Medical Research Fund, Amgen, Bristol-Myers Squibb, Pfizer, Janssen, Bayer, GSK, Novartis, the Food and Health Bureau of the Government of the Hong Kong Special Administrative Region, the UK National Institute for Health and Care Research, the European Commission, and the National Health and Medical Research Council in Australia outside the submitted work; receiving consulting fees from IQVIA outside the submitted work; and serving as a paid nonexecutive director of Jacobson Medical in Hong Kong and a paid consultant to the World Health Organization. Dr Wilson reported receiving personal fees from the Pfizer Advisory Board and the Roche Drug Safety Monitoring Board outside the submitted work. Dr Wei reported receiving grants from the National Institute Health Research Health Technology Assessment, Hong Kong Innovation and Technology Commission, Diabetes UK, The Cure Parkinson’s Trust, and BOPA-PRUK outside the submitted work. No other disclosures were reported.

Funding/Support: This work was partially supported by grant C7154-20G from the Research Grants Council of Hong Kong under the Collaborative Research Fund Scheme.

Role of the Funder/Sponsor: The funding organization had no role in the design and conduct of the study; collection, management, analysis, and interpretation of the data; preparation, review, or approval of the manuscript; and decision to submit the manuscript for publication.

Data Sharing Statement: See Supplement 2 .

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