quantitative analysis hypothesis

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A Practical Guide to Writing Quantitative and Qualitative Research Questions and Hypotheses in Scholarly Articles

Edward barroga.

1 Department of General Education, Graduate School of Nursing Science, St. Luke’s International University, Tokyo, Japan.

Glafera Janet Matanguihan

2 Department of Biological Sciences, Messiah University, Mechanicsburg, PA, USA.

The development of research questions and the subsequent hypotheses are prerequisites to defining the main research purpose and specific objectives of a study. Consequently, these objectives determine the study design and research outcome. The development of research questions is a process based on knowledge of current trends, cutting-edge studies, and technological advances in the research field. Excellent research questions are focused and require a comprehensive literature search and in-depth understanding of the problem being investigated. Initially, research questions may be written as descriptive questions which could be developed into inferential questions. These questions must be specific and concise to provide a clear foundation for developing hypotheses. Hypotheses are more formal predictions about the research outcomes. These specify the possible results that may or may not be expected regarding the relationship between groups. Thus, research questions and hypotheses clarify the main purpose and specific objectives of the study, which in turn dictate the design of the study, its direction, and outcome. Studies developed from good research questions and hypotheses will have trustworthy outcomes with wide-ranging social and health implications.

INTRODUCTION

Scientific research is usually initiated by posing evidenced-based research questions which are then explicitly restated as hypotheses. 1 , 2 The hypotheses provide directions to guide the study, solutions, explanations, and expected results. 3 , 4 Both research questions and hypotheses are essentially formulated based on conventional theories and real-world processes, which allow the inception of novel studies and the ethical testing of ideas. 5 , 6

It is crucial to have knowledge of both quantitative and qualitative research 2 as both types of research involve writing research questions and hypotheses. 7 However, these crucial elements of research are sometimes overlooked; if not overlooked, then framed without the forethought and meticulous attention it needs. Planning and careful consideration are needed when developing quantitative or qualitative research, particularly when conceptualizing research questions and hypotheses. 4

There is a continuing need to support researchers in the creation of innovative research questions and hypotheses, as well as for journal articles that carefully review these elements. 1 When research questions and hypotheses are not carefully thought of, unethical studies and poor outcomes usually ensue. Carefully formulated research questions and hypotheses define well-founded objectives, which in turn determine the appropriate design, course, and outcome of the study. This article then aims to discuss in detail the various aspects of crafting research questions and hypotheses, with the goal of guiding researchers as they develop their own. Examples from the authors and peer-reviewed scientific articles in the healthcare field are provided to illustrate key points.

DEFINITIONS AND RELATIONSHIP OF RESEARCH QUESTIONS AND HYPOTHESES

A research question is what a study aims to answer after data analysis and interpretation. The answer is written in length in the discussion section of the paper. Thus, the research question gives a preview of the different parts and variables of the study meant to address the problem posed in the research question. 1 An excellent research question clarifies the research writing while facilitating understanding of the research topic, objective, scope, and limitations of the study. 5

On the other hand, a research hypothesis is an educated statement of an expected outcome. This statement is based on background research and current knowledge. 8 , 9 The research hypothesis makes a specific prediction about a new phenomenon 10 or a formal statement on the expected relationship between an independent variable and a dependent variable. 3 , 11 It provides a tentative answer to the research question to be tested or explored. 4

Hypotheses employ reasoning to predict a theory-based outcome. 10 These can also be developed from theories by focusing on components of theories that have not yet been observed. 10 The validity of hypotheses is often based on the testability of the prediction made in a reproducible experiment. 8

Conversely, hypotheses can also be rephrased as research questions. Several hypotheses based on existing theories and knowledge may be needed to answer a research question. Developing ethical research questions and hypotheses creates a research design that has logical relationships among variables. These relationships serve as a solid foundation for the conduct of the study. 4 , 11 Haphazardly constructed research questions can result in poorly formulated hypotheses and improper study designs, leading to unreliable results. Thus, the formulations of relevant research questions and verifiable hypotheses are crucial when beginning research. 12

CHARACTERISTICS OF GOOD RESEARCH QUESTIONS AND HYPOTHESES

Excellent research questions are specific and focused. These integrate collective data and observations to confirm or refute the subsequent hypotheses. Well-constructed hypotheses are based on previous reports and verify the research context. These are realistic, in-depth, sufficiently complex, and reproducible. More importantly, these hypotheses can be addressed and tested. 13

There are several characteristics of well-developed hypotheses. Good hypotheses are 1) empirically testable 7 , 10 , 11 , 13 ; 2) backed by preliminary evidence 9 ; 3) testable by ethical research 7 , 9 ; 4) based on original ideas 9 ; 5) have evidenced-based logical reasoning 10 ; and 6) can be predicted. 11 Good hypotheses can infer ethical and positive implications, indicating the presence of a relationship or effect relevant to the research theme. 7 , 11 These are initially developed from a general theory and branch into specific hypotheses by deductive reasoning. In the absence of a theory to base the hypotheses, inductive reasoning based on specific observations or findings form more general hypotheses. 10

TYPES OF RESEARCH QUESTIONS AND HYPOTHESES

Research questions and hypotheses are developed according to the type of research, which can be broadly classified into quantitative and qualitative research. We provide a summary of the types of research questions and hypotheses under quantitative and qualitative research categories in Table 1 .

Research questions in quantitative research

In quantitative research, research questions inquire about the relationships among variables being investigated and are usually framed at the start of the study. These are precise and typically linked to the subject population, dependent and independent variables, and research design. 1 Research questions may also attempt to describe the behavior of a population in relation to one or more variables, or describe the characteristics of variables to be measured ( descriptive research questions ). 1 , 5 , 14 These questions may also aim to discover differences between groups within the context of an outcome variable ( comparative research questions ), 1 , 5 , 14 or elucidate trends and interactions among variables ( relationship research questions ). 1 , 5 We provide examples of descriptive, comparative, and relationship research questions in quantitative research in Table 2 .

Hypotheses in quantitative research

In quantitative research, hypotheses predict the expected relationships among variables. 15 Relationships among variables that can be predicted include 1) between a single dependent variable and a single independent variable ( simple hypothesis ) or 2) between two or more independent and dependent variables ( complex hypothesis ). 4 , 11 Hypotheses may also specify the expected direction to be followed and imply an intellectual commitment to a particular outcome ( directional hypothesis ) 4 . On the other hand, hypotheses may not predict the exact direction and are used in the absence of a theory, or when findings contradict previous studies ( non-directional hypothesis ). 4 In addition, hypotheses can 1) define interdependency between variables ( associative hypothesis ), 4 2) propose an effect on the dependent variable from manipulation of the independent variable ( causal hypothesis ), 4 3) state a negative relationship between two variables ( null hypothesis ), 4 , 11 , 15 4) replace the working hypothesis if rejected ( alternative hypothesis ), 15 explain the relationship of phenomena to possibly generate a theory ( working hypothesis ), 11 5) involve quantifiable variables that can be tested statistically ( statistical hypothesis ), 11 6) or express a relationship whose interlinks can be verified logically ( logical hypothesis ). 11 We provide examples of simple, complex, directional, non-directional, associative, causal, null, alternative, working, statistical, and logical hypotheses in quantitative research, as well as the definition of quantitative hypothesis-testing research in Table 3 .

Research questions in qualitative research

Unlike research questions in quantitative research, research questions in qualitative research are usually continuously reviewed and reformulated. The central question and associated subquestions are stated more than the hypotheses. 15 The central question broadly explores a complex set of factors surrounding the central phenomenon, aiming to present the varied perspectives of participants. 15

There are varied goals for which qualitative research questions are developed. These questions can function in several ways, such as to 1) identify and describe existing conditions ( contextual research question s); 2) describe a phenomenon ( descriptive research questions ); 3) assess the effectiveness of existing methods, protocols, theories, or procedures ( evaluation research questions ); 4) examine a phenomenon or analyze the reasons or relationships between subjects or phenomena ( explanatory research questions ); or 5) focus on unknown aspects of a particular topic ( exploratory research questions ). 5 In addition, some qualitative research questions provide new ideas for the development of theories and actions ( generative research questions ) or advance specific ideologies of a position ( ideological research questions ). 1 Other qualitative research questions may build on a body of existing literature and become working guidelines ( ethnographic research questions ). Research questions may also be broadly stated without specific reference to the existing literature or a typology of questions ( phenomenological research questions ), may be directed towards generating a theory of some process ( grounded theory questions ), or may address a description of the case and the emerging themes ( qualitative case study questions ). 15 We provide examples of contextual, descriptive, evaluation, explanatory, exploratory, generative, ideological, ethnographic, phenomenological, grounded theory, and qualitative case study research questions in qualitative research in Table 4 , and the definition of qualitative hypothesis-generating research in Table 5 .

Qualitative studies usually pose at least one central research question and several subquestions starting with How or What . These research questions use exploratory verbs such as explore or describe . These also focus on one central phenomenon of interest, and may mention the participants and research site. 15

Hypotheses in qualitative research

Hypotheses in qualitative research are stated in the form of a clear statement concerning the problem to be investigated. Unlike in quantitative research where hypotheses are usually developed to be tested, qualitative research can lead to both hypothesis-testing and hypothesis-generating outcomes. 2 When studies require both quantitative and qualitative research questions, this suggests an integrative process between both research methods wherein a single mixed-methods research question can be developed. 1

FRAMEWORKS FOR DEVELOPING RESEARCH QUESTIONS AND HYPOTHESES

Research questions followed by hypotheses should be developed before the start of the study. 1 , 12 , 14 It is crucial to develop feasible research questions on a topic that is interesting to both the researcher and the scientific community. This can be achieved by a meticulous review of previous and current studies to establish a novel topic. Specific areas are subsequently focused on to generate ethical research questions. The relevance of the research questions is evaluated in terms of clarity of the resulting data, specificity of the methodology, objectivity of the outcome, depth of the research, and impact of the study. 1 , 5 These aspects constitute the FINER criteria (i.e., Feasible, Interesting, Novel, Ethical, and Relevant). 1 Clarity and effectiveness are achieved if research questions meet the FINER criteria. In addition to the FINER criteria, Ratan et al. described focus, complexity, novelty, feasibility, and measurability for evaluating the effectiveness of research questions. 14

The PICOT and PEO frameworks are also used when developing research questions. 1 The following elements are addressed in these frameworks, PICOT: P-population/patients/problem, I-intervention or indicator being studied, C-comparison group, O-outcome of interest, and T-timeframe of the study; PEO: P-population being studied, E-exposure to preexisting conditions, and O-outcome of interest. 1 Research questions are also considered good if these meet the “FINERMAPS” framework: Feasible, Interesting, Novel, Ethical, Relevant, Manageable, Appropriate, Potential value/publishable, and Systematic. 14

As we indicated earlier, research questions and hypotheses that are not carefully formulated result in unethical studies or poor outcomes. To illustrate this, we provide some examples of ambiguous research question and hypotheses that result in unclear and weak research objectives in quantitative research ( Table 6 ) 16 and qualitative research ( Table 7 ) 17 , and how to transform these ambiguous research question(s) and hypothesis(es) into clear and good statements.

a These statements were composed for comparison and illustrative purposes only.

b These statements are direct quotes from Higashihara and Horiuchi. 16

a This statement is a direct quote from Shimoda et al. 17

The other statements were composed for comparison and illustrative purposes only.

CONSTRUCTING RESEARCH QUESTIONS AND HYPOTHESES

To construct effective research questions and hypotheses, it is very important to 1) clarify the background and 2) identify the research problem at the outset of the research, within a specific timeframe. 9 Then, 3) review or conduct preliminary research to collect all available knowledge about the possible research questions by studying theories and previous studies. 18 Afterwards, 4) construct research questions to investigate the research problem. Identify variables to be accessed from the research questions 4 and make operational definitions of constructs from the research problem and questions. Thereafter, 5) construct specific deductive or inductive predictions in the form of hypotheses. 4 Finally, 6) state the study aims . This general flow for constructing effective research questions and hypotheses prior to conducting research is shown in Fig. 1 .

Research questions are used more frequently in qualitative research than objectives or hypotheses. 3 These questions seek to discover, understand, explore or describe experiences by asking “What” or “How.” The questions are open-ended to elicit a description rather than to relate variables or compare groups. The questions are continually reviewed, reformulated, and changed during the qualitative study. 3 Research questions are also used more frequently in survey projects than hypotheses in experiments in quantitative research to compare variables and their relationships.

Hypotheses are constructed based on the variables identified and as an if-then statement, following the template, ‘If a specific action is taken, then a certain outcome is expected.’ At this stage, some ideas regarding expectations from the research to be conducted must be drawn. 18 Then, the variables to be manipulated (independent) and influenced (dependent) are defined. 4 Thereafter, the hypothesis is stated and refined, and reproducible data tailored to the hypothesis are identified, collected, and analyzed. 4 The hypotheses must be testable and specific, 18 and should describe the variables and their relationships, the specific group being studied, and the predicted research outcome. 18 Hypotheses construction involves a testable proposition to be deduced from theory, and independent and dependent variables to be separated and measured separately. 3 Therefore, good hypotheses must be based on good research questions constructed at the start of a study or trial. 12

In summary, research questions are constructed after establishing the background of the study. Hypotheses are then developed based on the research questions. Thus, it is crucial to have excellent research questions to generate superior hypotheses. In turn, these would determine the research objectives and the design of the study, and ultimately, the outcome of the research. 12 Algorithms for building research questions and hypotheses are shown in Fig. 2 for quantitative research and in Fig. 3 for qualitative research.

EXAMPLES OF RESEARCH QUESTIONS FROM PUBLISHED ARTICLES

• EXAMPLE 1. Descriptive research question (quantitative research)
• - Presents research variables to be assessed (distinct phenotypes and subphenotypes)
• “BACKGROUND: Since COVID-19 was identified, its clinical and biological heterogeneity has been recognized. Identifying COVID-19 phenotypes might help guide basic, clinical, and translational research efforts.
• RESEARCH QUESTION: Does the clinical spectrum of patients with COVID-19 contain distinct phenotypes and subphenotypes? ” 19
• EXAMPLE 2. Relationship research question (quantitative research)
• - Shows interactions between dependent variable (static postural control) and independent variable (peripheral visual field loss)
• “Background: Integration of visual, vestibular, and proprioceptive sensations contributes to postural control. People with peripheral visual field loss have serious postural instability. However, the directional specificity of postural stability and sensory reweighting caused by gradual peripheral visual field loss remain unclear.
• Research question: What are the effects of peripheral visual field loss on static postural control ?” 20
• EXAMPLE 3. Comparative research question (quantitative research)
• - Clarifies the difference among groups with an outcome variable (patients enrolled in COMPERA with moderate PH or severe PH in COPD) and another group without the outcome variable (patients with idiopathic pulmonary arterial hypertension (IPAH))
• “BACKGROUND: Pulmonary hypertension (PH) in COPD is a poorly investigated clinical condition.
• RESEARCH QUESTION: Which factors determine the outcome of PH in COPD?
• STUDY DESIGN AND METHODS: We analyzed the characteristics and outcome of patients enrolled in the Comparative, Prospective Registry of Newly Initiated Therapies for Pulmonary Hypertension (COMPERA) with moderate or severe PH in COPD as defined during the 6th PH World Symposium who received medical therapy for PH and compared them with patients with idiopathic pulmonary arterial hypertension (IPAH) .” 21
• EXAMPLE 4. Exploratory research question (qualitative research)
• - Explores areas that have not been fully investigated (perspectives of families and children who receive care in clinic-based child obesity treatment) to have a deeper understanding of the research problem
• “Problem: Interventions for children with obesity lead to only modest improvements in BMI and long-term outcomes, and data are limited on the perspectives of families of children with obesity in clinic-based treatment. This scoping review seeks to answer the question: What is known about the perspectives of families and children who receive care in clinic-based child obesity treatment? This review aims to explore the scope of perspectives reported by families of children with obesity who have received individualized outpatient clinic-based obesity treatment.” 22
• EXAMPLE 5. Relationship research question (quantitative research)
• - Defines interactions between dependent variable (use of ankle strategies) and independent variable (changes in muscle tone)
• “Background: To maintain an upright standing posture against external disturbances, the human body mainly employs two types of postural control strategies: “ankle strategy” and “hip strategy.” While it has been reported that the magnitude of the disturbance alters the use of postural control strategies, it has not been elucidated how the level of muscle tone, one of the crucial parameters of bodily function, determines the use of each strategy. We have previously confirmed using forward dynamics simulations of human musculoskeletal models that an increased muscle tone promotes the use of ankle strategies. The objective of the present study was to experimentally evaluate a hypothesis: an increased muscle tone promotes the use of ankle strategies. Research question: Do changes in the muscle tone affect the use of ankle strategies ?” 23

EXAMPLES OF HYPOTHESES IN PUBLISHED ARTICLES

• EXAMPLE 1. Working hypothesis (quantitative research)
• - A hypothesis that is initially accepted for further research to produce a feasible theory
• “As fever may have benefit in shortening the duration of viral illness, it is plausible to hypothesize that the antipyretic efficacy of ibuprofen may be hindering the benefits of a fever response when taken during the early stages of COVID-19 illness .” 24
• “In conclusion, it is plausible to hypothesize that the antipyretic efficacy of ibuprofen may be hindering the benefits of a fever response . The difference in perceived safety of these agents in COVID-19 illness could be related to the more potent efficacy to reduce fever with ibuprofen compared to acetaminophen. Compelling data on the benefit of fever warrant further research and review to determine when to treat or withhold ibuprofen for early stage fever for COVID-19 and other related viral illnesses .” 24
• EXAMPLE 2. Exploratory hypothesis (qualitative research)
• - Explores particular areas deeper to clarify subjective experience and develop a formal hypothesis potentially testable in a future quantitative approach
• “We hypothesized that when thinking about a past experience of help-seeking, a self distancing prompt would cause increased help-seeking intentions and more favorable help-seeking outcome expectations .” 25
• “Conclusion
• Although a priori hypotheses were not supported, further research is warranted as results indicate the potential for using self-distancing approaches to increasing help-seeking among some people with depressive symptomatology.” 25
• EXAMPLE 3. Hypothesis-generating research to establish a framework for hypothesis testing (qualitative research)
• “We hypothesize that compassionate care is beneficial for patients (better outcomes), healthcare systems and payers (lower costs), and healthcare providers (lower burnout). ” 26
• Compassionomics is the branch of knowledge and scientific study of the effects of compassionate healthcare. Our main hypotheses are that compassionate healthcare is beneficial for (1) patients, by improving clinical outcomes, (2) healthcare systems and payers, by supporting financial sustainability, and (3) HCPs, by lowering burnout and promoting resilience and well-being. The purpose of this paper is to establish a scientific framework for testing the hypotheses above . If these hypotheses are confirmed through rigorous research, compassionomics will belong in the science of evidence-based medicine, with major implications for all healthcare domains.” 26
• EXAMPLE 4. Statistical hypothesis (quantitative research)
• - An assumption is made about the relationship among several population characteristics ( gender differences in sociodemographic and clinical characteristics of adults with ADHD ). Validity is tested by statistical experiment or analysis ( chi-square test, Students t-test, and logistic regression analysis)
• “Our research investigated gender differences in sociodemographic and clinical characteristics of adults with ADHD in a Japanese clinical sample. Due to unique Japanese cultural ideals and expectations of women's behavior that are in opposition to ADHD symptoms, we hypothesized that women with ADHD experience more difficulties and present more dysfunctions than men . We tested the following hypotheses: first, women with ADHD have more comorbidities than men with ADHD; second, women with ADHD experience more social hardships than men, such as having less full-time employment and being more likely to be divorced.” 27
• “Statistical Analysis
• ( text omitted ) Between-gender comparisons were made using the chi-squared test for categorical variables and Students t-test for continuous variables…( text omitted ). A logistic regression analysis was performed for employment status, marital status, and comorbidity to evaluate the independent effects of gender on these dependent variables.” 27

EXAMPLES OF HYPOTHESIS AS WRITTEN IN PUBLISHED ARTICLES IN RELATION TO OTHER PARTS

• EXAMPLE 1. Background, hypotheses, and aims are provided
• “Pregnant women need skilled care during pregnancy and childbirth, but that skilled care is often delayed in some countries …( text omitted ). The focused antenatal care (FANC) model of WHO recommends that nurses provide information or counseling to all pregnant women …( text omitted ). Job aids are visual support materials that provide the right kind of information using graphics and words in a simple and yet effective manner. When nurses are not highly trained or have many work details to attend to, these job aids can serve as a content reminder for the nurses and can be used for educating their patients (Jennings, Yebadokpo, Affo, & Agbogbe, 2010) ( text omitted ). Importantly, additional evidence is needed to confirm how job aids can further improve the quality of ANC counseling by health workers in maternal care …( text omitted )” 28
• “ This has led us to hypothesize that the quality of ANC counseling would be better if supported by job aids. Consequently, a better quality of ANC counseling is expected to produce higher levels of awareness concerning the danger signs of pregnancy and a more favorable impression of the caring behavior of nurses .” 28
• “This study aimed to examine the differences in the responses of pregnant women to a job aid-supported intervention during ANC visit in terms of 1) their understanding of the danger signs of pregnancy and 2) their impression of the caring behaviors of nurses to pregnant women in rural Tanzania.” 28
• EXAMPLE 2. Background, hypotheses, and aims are provided
• “We conducted a two-arm randomized controlled trial (RCT) to evaluate and compare changes in salivary cortisol and oxytocin levels of first-time pregnant women between experimental and control groups. The women in the experimental group touched and held an infant for 30 min (experimental intervention protocol), whereas those in the control group watched a DVD movie of an infant (control intervention protocol). The primary outcome was salivary cortisol level and the secondary outcome was salivary oxytocin level.” 29
• “ We hypothesize that at 30 min after touching and holding an infant, the salivary cortisol level will significantly decrease and the salivary oxytocin level will increase in the experimental group compared with the control group .” 29
• EXAMPLE 3. Background, aim, and hypothesis are provided
• “In countries where the maternal mortality ratio remains high, antenatal education to increase Birth Preparedness and Complication Readiness (BPCR) is considered one of the top priorities [1]. BPCR includes birth plans during the antenatal period, such as the birthplace, birth attendant, transportation, health facility for complications, expenses, and birth materials, as well as family coordination to achieve such birth plans. In Tanzania, although increasing, only about half of all pregnant women attend an antenatal clinic more than four times [4]. Moreover, the information provided during antenatal care (ANC) is insufficient. In the resource-poor settings, antenatal group education is a potential approach because of the limited time for individual counseling at antenatal clinics.” 30
• “This study aimed to evaluate an antenatal group education program among pregnant women and their families with respect to birth-preparedness and maternal and infant outcomes in rural villages of Tanzania.” 30
• “ The study hypothesis was if Tanzanian pregnant women and their families received a family-oriented antenatal group education, they would (1) have a higher level of BPCR, (2) attend antenatal clinic four or more times, (3) give birth in a health facility, (4) have less complications of women at birth, and (5) have less complications and deaths of infants than those who did not receive the education .” 30

Research questions and hypotheses are crucial components to any type of research, whether quantitative or qualitative. These questions should be developed at the very beginning of the study. Excellent research questions lead to superior hypotheses, which, like a compass, set the direction of research, and can often determine the successful conduct of the study. Many research studies have floundered because the development of research questions and subsequent hypotheses was not given the thought and meticulous attention needed. The development of research questions and hypotheses is an iterative process based on extensive knowledge of the literature and insightful grasp of the knowledge gap. Focused, concise, and specific research questions provide a strong foundation for constructing hypotheses which serve as formal predictions about the research outcomes. Research questions and hypotheses are crucial elements of research that should not be overlooked. They should be carefully thought of and constructed when planning research. This avoids unethical studies and poor outcomes by defining well-founded objectives that determine the design, course, and outcome of the study.

Disclosure: The authors have no potential conflicts of interest to disclose.

Author Contributions:

• Conceptualization: Barroga E, Matanguihan GJ.
• Methodology: Barroga E, Matanguihan GJ.
• Writing - original draft: Barroga E, Matanguihan GJ.
• Writing - review & editing: Barroga E, Matanguihan GJ.

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Methodology

• What Is Quantitative Research? | Definition, Uses & Methods

What Is Quantitative Research? | Definition, Uses & Methods

Published on June 12, 2020 by Pritha Bhandari . Revised on June 22, 2023.

Quantitative research is the process of collecting and analyzing numerical data. It can be used to find patterns and averages, make predictions, test causal relationships, and generalize results to wider populations.

Quantitative research is the opposite of qualitative research , which involves collecting and analyzing non-numerical data (e.g., text, video, or audio).

Quantitative research is widely used in the natural and social sciences: biology, chemistry, psychology, economics, sociology, marketing, etc.

• What is the demographic makeup of Singapore in 2020?
• How has the average temperature changed globally over the last century?
• Does environmental pollution affect the prevalence of honey bees?
• Does working from home increase productivity for people with long commutes?

Table of contents

Quantitative research methods, quantitative data analysis, advantages of quantitative research, disadvantages of quantitative research, other interesting articles, frequently asked questions about quantitative research.

You can use quantitative research methods for descriptive, correlational or experimental research.

• In descriptive research , you simply seek an overall summary of your study variables.
• In correlational research , you investigate relationships between your study variables.
• In experimental research , you systematically examine whether there is a cause-and-effect relationship between variables.

Correlational and experimental research can both be used to formally test hypotheses , or predictions, using statistics. The results may be generalized to broader populations based on the sampling method used.

To collect quantitative data, you will often need to use operational definitions that translate abstract concepts (e.g., mood) into observable and quantifiable measures (e.g., self-ratings of feelings and energy levels).

Note that quantitative research is at risk for certain research biases , including information bias , omitted variable bias , sampling bias , or selection bias . Be sure that you’re aware of potential biases as you collect and analyze your data to prevent them from impacting your work too much.

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Once data is collected, you may need to process it before it can be analyzed. For example, survey and test data may need to be transformed from words to numbers. Then, you can use statistical analysis to answer your research questions .

Descriptive statistics will give you a summary of your data and include measures of averages and variability. You can also use graphs, scatter plots and frequency tables to visualize your data and check for any trends or outliers.

Using inferential statistics , you can make predictions or generalizations based on your data. You can test your hypothesis or use your sample data to estimate the population parameter .

First, you use descriptive statistics to get a summary of the data. You find the mean (average) and the mode (most frequent rating) of procrastination of the two groups, and plot the data to see if there are any outliers.

You can also assess the reliability and validity of your data collection methods to indicate how consistently and accurately your methods actually measured what you wanted them to.

Quantitative research is often used to standardize data collection and generalize findings . Strengths of this approach include:

• Replication

Repeating the study is possible because of standardized data collection protocols and tangible definitions of abstract concepts.

• Direct comparisons of results

The study can be reproduced in other cultural settings, times or with different groups of participants. Results can be compared statistically.

• Large samples

Data from large samples can be processed and analyzed using reliable and consistent procedures through quantitative data analysis.

• Hypothesis testing

Using formalized and established hypothesis testing procedures means that you have to carefully consider and report your research variables, predictions, data collection and testing methods before coming to a conclusion.

Despite the benefits of quantitative research, it is sometimes inadequate in explaining complex research topics. Its limitations include:

• Superficiality

Using precise and restrictive operational definitions may inadequately represent complex concepts. For example, the concept of mood may be represented with just a number in quantitative research, but explained with elaboration in qualitative research.

• Narrow focus

Predetermined variables and measurement procedures can mean that you ignore other relevant observations.

• Structural bias

Despite standardized procedures, structural biases can still affect quantitative research. Missing data , imprecise measurements or inappropriate sampling methods are biases that can lead to the wrong conclusions.

• Lack of context

Quantitative research often uses unnatural settings like laboratories or fails to consider historical and cultural contexts that may affect data collection and results.

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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
• 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.

In mixed methods research , you use both qualitative and quantitative data collection and analysis methods to answer your research question .

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.

Operationalization means turning abstract conceptual ideas into measurable observations.

For example, the concept of social anxiety isn’t directly observable, but it can be operationally defined in terms of self-rating scores, behavioral avoidance of crowded places, or physical anxiety symptoms in social situations.

Before collecting data , it’s important to consider how you will operationalize the variables that you want to measure.

Reliability and validity are both about how well a method measures something:

• Reliability refers to the  consistency of a measure (whether the results can be reproduced under the same conditions).
• Validity   refers to the  accuracy of a measure (whether the results really do represent what they are supposed to measure).

If you are doing experimental research, you also have to consider the internal and external validity of your experiment.

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.

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Research Questions & Hypotheses

Generally, in quantitative studies, reviewers expect hypotheses rather than research questions. However, both research questions and hypotheses serve different purposes and can be beneficial when used together.

Research Questions

Clarify the research’s aim (farrugia et al., 2010).

• Research often begins with an interest in a topic, but a deep understanding of the subject is crucial to formulate an appropriate research question.
• Descriptive: “What factors most influence the academic achievement of senior high school students?”
• Comparative: “What is the performance difference between teaching methods A and B?”
• Relationship-based: “What is the relationship between self-efficacy and academic achievement?”
• Increasing knowledge about a subject can be achieved through systematic literature reviews, in-depth interviews with patients (and proxies), focus groups, and consultations with field experts.
• Some funding bodies, like the Canadian Institute for Health Research, recommend conducting a systematic review or a pilot study before seeking grants for full trials.
• The presence of multiple research questions in a study can complicate the design, statistical analysis, and feasibility.
• It’s advisable to focus on a single primary research question for the study.
• The primary question, clearly stated at the end of a grant proposal’s introduction, usually specifies the study population, intervention, and other relevant factors.
• The FINER criteria underscore aspects that can enhance the chances of a successful research project, including specifying the population of interest, aligning with scientific and public interest, clinical relevance, and contribution to the field, while complying with ethical and national research standards.

• The P ICOT approach is crucial in developing the study’s framework and protocol, influencing inclusion and exclusion criteria and identifying patient groups for inclusion.

• Defining the specific population, intervention, comparator, and outcome helps in selecting the right outcome measurement tool.
• The more precise the population definition and stricter the inclusion and exclusion criteria, the more significant the impact on the interpretation, applicability, and generalizability of the research findings.
• A restricted study population enhances internal validity but may limit the study’s external validity and generalizability to clinical practice.
• A broadly defined study population may better reflect clinical practice but could increase bias and reduce internal validity.
• An inadequately formulated research question can negatively impact study design, potentially leading to ineffective outcomes and affecting publication prospects.

Checklist: Good research questions for social science projects (Panke, 2018)

Research Hypotheses

Present the researcher’s predictions based on specific statements.

• These statements define the research problem or issue and indicate the direction of the researcher’s predictions.
• Formulating the research question and hypothesis from existing data (e.g., a database) can lead to multiple statistical comparisons and potentially spurious findings due to chance.
• The research or clinical hypothesis, derived from the research question, shapes the study’s key elements: sampling strategy, intervention, comparison, and outcome variables.
• Hypotheses can express a single outcome or multiple outcomes.
• After statistical testing, the null hypothesis is either rejected or not rejected based on whether the study’s findings are statistically significant.
• Hypothesis testing helps determine if observed findings are due to true differences and not chance.
• Hypotheses can be 1-sided (specific direction of difference) or 2-sided (presence of a difference without specifying direction).
• 2-sided hypotheses are generally preferred unless there’s a strong justification for a 1-sided hypothesis.
• A solid research hypothesis, informed by a good research question, influences the research design and paves the way for defining clear research objectives.

Types of Research Hypothesis

• In a Y-centered research design, the focus is on the dependent variable (DV) which is specified in the research question. Theories are then used to identify independent variables (IV) and explain their causal relationship with the DV.
• Example: “An increase in teacher-led instructional time (IV) is likely to improve student reading comprehension scores (DV), because extensive guided practice under expert supervision enhances learning retention and skill mastery.”
• Hypothesis Explanation: The dependent variable (student reading comprehension scores) is the focus, and the hypothesis explores how changes in the independent variable (teacher-led instructional time) affect it.
• In X-centered research designs, the independent variable is specified in the research question. Theories are used to determine potential dependent variables and the causal mechanisms at play.
• Example: “Implementing technology-based learning tools (IV) is likely to enhance student engagement in the classroom (DV), because interactive and multimedia content increases student interest and participation.”
• Hypothesis Explanation: The independent variable (technology-based learning tools) is the focus, with the hypothesis exploring its impact on a potential dependent variable (student engagement).
• Probabilistic hypotheses suggest that changes in the independent variable are likely to lead to changes in the dependent variable in a predictable manner, but not with absolute certainty.
• Example: “The more teachers engage in professional development programs (IV), the more their teaching effectiveness (DV) is likely to improve, because continuous training updates pedagogical skills and knowledge.”
• Hypothesis Explanation: This hypothesis implies a probable relationship between the extent of professional development (IV) and teaching effectiveness (DV).
• Deterministic hypotheses state that a specific change in the independent variable will lead to a specific change in the dependent variable, implying a more direct and certain relationship.
• Example: “If the school curriculum changes from traditional lecture-based methods to project-based learning (IV), then student collaboration skills (DV) are expected to improve because project-based learning inherently requires teamwork and peer interaction.”
• Hypothesis Explanation: This hypothesis presumes a direct and definite outcome (improvement in collaboration skills) resulting from a specific change in the teaching method.
• Example : “Students who identify as visual learners will score higher on tests that are presented in a visually rich format compared to tests presented in a text-only format.”
• Explanation : This hypothesis aims to describe the potential difference in test scores between visual learners taking visually rich tests and text-only tests, without implying a direct cause-and-effect relationship.
• Example : “Teaching method A will improve student performance more than method B.”
• Explanation : This hypothesis compares the effectiveness of two different teaching methods, suggesting that one will lead to better student performance than the other. It implies a direct comparison but does not necessarily establish a causal mechanism.
• Example : “Students with higher self-efficacy will show higher levels of academic achievement.”
• Explanation : This hypothesis predicts a relationship between the variable of self-efficacy and academic achievement. Unlike a causal hypothesis, it does not necessarily suggest that one variable causes changes in the other, but rather that they are related in some way.

Tips for developing research questions and hypotheses for research studies

• Perform a systematic literature review (if one has not been done) to increase knowledge and familiarity with the topic and to assist with research development.
• Learn about current trends and technological advances on the topic.
• Seek careful input from experts, mentors, colleagues, and collaborators to refine your research question as this will aid in developing the research question and guide the research study.
• Use the FINER criteria in the development of the research question.
• Ensure that the research question follows PICOT format.
• Develop a research hypothesis from the research question.
• Ensure that the research question and objectives are answerable, feasible, and clinically relevant.

If your research hypotheses are derived from your research questions, particularly when multiple hypotheses address a single question, it’s recommended to use both research questions and hypotheses. However, if this isn’t the case, using hypotheses over research questions is advised. It’s important to note these are general guidelines, not strict rules. If you opt not to use hypotheses, consult with your supervisor for the best approach.

Farrugia, P., Petrisor, B. A., Farrokhyar, F., & Bhandari, M. (2010). Practical tips for surgical research: Research questions, hypotheses and objectives.  Canadian journal of surgery. Journal canadien de chirurgie ,  53 (4), 278–281.

Hulley, S. B., Cummings, S. R., Browner, W. S., Grady, D., & Newman, T. B. (2007). Designing clinical research. Philadelphia.

Panke, D. (2018). Research design & method selection: Making good choices in the social sciences.  Research Design & Method Selection , 1-368.

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How to Write a Strong Hypothesis | Guide & Examples

Published on 6 May 2022 by Shona McCombes .

A hypothesis is a statement that can be tested by scientific research. If you want to test a relationship between two or more variables, you need to write hypotheses before you start your experiment or data collection.

Table of contents

What is a hypothesis, developing a hypothesis (with example), hypothesis examples, frequently asked questions about writing hypotheses.

A hypothesis states your predictions about what your research will find. It is a tentative answer to your research question that has not yet been tested. For some research projects, you might have to write several hypotheses that address different aspects of your research question.

A hypothesis is not just a guess – it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations, and statistical analysis of data).

Variables in hypotheses

Hypotheses propose a relationship between two or more variables . An independent variable is something the researcher changes or controls. A dependent variable is something the researcher observes and measures.

In this example, the independent variable is exposure to the sun – the assumed cause . The dependent variable is the level of happiness – the assumed effect .

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Step 1: ask a question.

Writing a hypothesis begins with a research question that you want to answer. The question should be focused, specific, and researchable within the constraints of your project.

Step 2: Do some preliminary research

Your initial answer to the question should be based on what is already known about the topic. Look for theories and previous studies to help you form educated assumptions about what your research will find.

At this stage, you might construct a conceptual framework to identify which variables you will study and what you think the relationships are between them. Sometimes, you’ll have to operationalise more complex constructs.

Step 3: Formulate your hypothesis

Now you should have some idea of what you expect to find. Write your initial answer to the question in a clear, concise sentence.

Step 4: Refine your hypothesis

You need to make sure your hypothesis is specific and testable. There are various ways of phrasing a hypothesis, but all the terms you use should have clear definitions, and the hypothesis should contain:

• The relevant variables
• The specific group being studied
• The predicted outcome of the experiment or analysis

Step 5: Phrase your hypothesis in three ways

To identify the variables, you can write a simple prediction in if … then form. The first part of the sentence states the independent variable and the second part states the dependent variable.

In academic research, hypotheses are more commonly phrased in terms of correlations or effects, where you directly state the predicted relationship between variables.

If you are comparing two groups, the hypothesis can state what difference you expect to find between them.

Step 6. Write a null hypothesis

If your research involves statistical hypothesis testing , you will also have to write a null hypothesis. The null hypothesis is the default position that there is no association between the variables. The null hypothesis is written as H 0 , while the alternative hypothesis is H 1 or H a .

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.

A hypothesis is not just a guess. It should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations, and statistical analysis of data).

A research hypothesis is your proposed answer to your research question. The research hypothesis usually includes an explanation (‘ x affects y because …’).

A statistical hypothesis, on the other hand, is a mathematical statement about a population parameter. Statistical hypotheses always come in pairs: the null and alternative hypotheses. In a well-designed study , the statistical hypotheses correspond logically to the research hypothesis.

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Quantitative Data Analysis

5 Hypothesis Testing in Quantitative Research

Mikaila Mariel Lemonik Arthur

Statistical reasoning is built on the assumption that data are normally distributed , meaning that they will be distributed in the shape of a bell curve as discussed in the chapter on Univariate Analysis . While real life often—perhaps even usually—does not resemble a bell curve, basic statistical analysis assumes that if all possible random samples from a population were drawn and the mean taken from each sample, the distribution of sample means, when plotted on a graph, would be normally distributed (this assumption is called the Central Limit Theorem ). Given this assumption, we can use the mathematical techniques developed for the study of probability to determine the likelihood that the relationships or patterns we observe in our data occurred due to random chance rather than due some actual real-world connection, which we call statistical significance.

Statistical significance is not the same as practical significance. The fact that we have determined that a given result is unlikely to have occurred due to random chance does not mean that this given result is important, that it matters, or that it is useful. Similarly, we might observe a relationship or result that is very important in practical terms, but that we cannot claim is statistically significant—perhaps because our sample size is too small, for instance. Such a result might have occurred by chance, but ignoring it might still be a mistake. Let’s consider some examples to make this a bit clearer. Assume we were interested in the impacts of diet on health outcomes and found the statistically significant result that people who eat a lot of citrus fruit end up having pinky fingernails that are, on average, 1.5 millimeters longer than those who tend not to eat any citrus fruit. Should anyone change their diet due to this finding? Probably not, even those it is statistically significant. On the other hand, if we found that the people who ate the diets highest in processed sugar died on average five years sooner than those who ate the least processed sugar, even in the absence of a statistically significant result we might want to advise that people consider limiting sugar in their diet. This latter result has more practical significance (lifespan matters more than the length of your pinky fingernail) as well as a larger effect size or association (5 years of life as opposed to 1.5 millimeters of length), a factor that will be discussed in the chapter on association .

While people generally use the shorthand of “the likelihood that the results occurred by chance” when talking about statistical significance, it is actually a bit more complicated than that. What statistical significance is really telling us is the likelihood (or probability ) that a result equal to or more “extreme [1] ” is true in the real world, rather than our results having occurred due to random chance or sampling error . Testing for statistical significance, then, requires us to understand something about probability.

A Brief Review of Probability

You might remember having studied probability in a math class, with questions about coin flips or drawing marbles out of a jar. Such exercises can make probability seem very abstract. But in reality, computations of probability are deeply important for a wide variety of activities, ranging from gambling and stock trading to weather forecasts and, yes, statistical significance.

Probability is represented as a proportion (or decimal number) somewhere between 0 and 1. At 0, there is absolutely no likelihood that the event or pattern of interest would occur; at 1, it is absolutely certain that the event or pattern of interest will occur. We indicate that we are talking about probability by using the symbol [latex]p[/latex]. For example, if something has a 50% chance of occurring, we would write [latex]p=0.5[/latex] or [latex]\frac {1}{2}[/latex]. If we want to represent the likelihood of something not occurring, we can write [latex]1-p[/latex].

Check your thinking: Assume you were flipping coins, and you called heads. The probability of getting heads on a coin flip using a fair coin (in other words, a normal coin that has not been weighted to bias the result) is 0.5. Thus, in 50% of coin flips you should get heads. Consider the following probability questions and write down your answers so you can check them against the discussion below.

• Imagine you have flipped the coin 29 times and you have gotten heads each time. What is the probability you will get heads on flip 30?
• What is the probability that you will get heads on all of the first five coin flips?
• What is the probability that you will get heads on at least one of the first five coin flips?

There are a few basic concepts from the mathematical study of probability that are important for beginner data analysts to know, and we will review them here.

Probability over Repeated Trials : The probability of the outcome of interest is the same in each trial or test, regardless of the results of the prior test. So, if we flip a coin 29 times and get heads each time, what happens when we flip it the 29th time? The probability of heads is still 0.5! The belief that “this time it must be tails because it has been heads so many times” or “this coin just wants to come up heads” is simply superstition, and—assuming a fair coin—the results of prior trials do not influence the results of this one.

Probability of Multiple Events : The probability that the outcome of interest will occur repeatedly across multiple trials is the product [2] of the probability of the outcome on each individual trial. This is called the multiplication theorem . Thinking about the multiplication theorem requires that we keep in mind the fact that when we multiply decimal numbers together, those numbers get smaller— thus, the probability that a series of outcomes will occur is smaller than the probability of any one of those outcomes occurring on its own. So, what is the probability that we will get heads on all five of our coin flips? Well, to figure that out, we need to multiply the probability of getting heads on each of our coin flips together. The math looks like this (and produces a very small probability indeed):

[latex]\frac {1}{2} \cdot \frac {1}{2} \cdot \frac {1}{2} \cdot \frac {1}{2} \cdot \frac {1}{2} = 0.03125[/latex]

Probability of One of Many Events : Determining the probability that the outcome of interest will occur on at least one out of a series of events or repeated trials is a little bit more complicated. Mathematicians use the addition theorem to refer to this, because the basic way to calculate it is to calculate the probability of each sequence of events (say, heads-heads-heads, heads-heads-tails, heads-tails-heads, and so on) and add them together. But the greater the number of repeated trials, the more complicated that gets, so there is a simpler way to do it. Consider that the probability of getting  no heads is the same as the probability of getting all tails (which would be the same as the probability of getting all heads that we calculated above). And the only circumstance in which we would not have at least one flip resulting in heads would be a circumstance in which all flips had resulted in tails. Therefore, what we need to do in order to calculate the probability that we get at least one heads is to subtract the probability that we get no heads from 1—and as you can imagine, this procedure shows us that the probability of the outcome of interest occurring at least once over repeated trials is higher than the probability of the occurrence on any given trial. The math would look like this:

[latex]1- (\frac{1}{2})^5=0.9688[/latex]

So why is this digression into the math of probability important? Well, when we test for statistical significance, what we are really doing is determining the probability that the outcome we observed—or one that is more extreme than that which we observed—occurred by chance. We perform this analysis via a procedure called Null Hypothesis Significance Testing.

Null Hypothesis Significance Testing

Null hypothesis significance testing , or NHST , is a method of testing for statistical significance by comparing observed data to the data we would expect to see if there were no relationship between the variables or phenomena in question. NHST can take a little while to wrap one’s head around, especially because it relies on a logic of double negatives: first, we state a hypothesis we believe not to be true (there is no relationship between the variables in question) and then, we look for evidence that disconfirms this hypothesis. In other words, we are assuming that there is no relationship between the variables—even though our research hypothesis states that we think there is a relationship—and then looking to see if there is any evidence to suggest there is not no relationship. Confusing, right?

So why do we use the null hypothesis significance testing approach?

• The null hypothesis—that there is no relationship between the variables we are exploring—would be what we would generally accept as true in the absence of other information,
• It means we are assuming that differences or patterns occur due to chance unless there is strong evidence to suggest otherwise,
• It provides a benchmark for comparing observed outcomes, and
• It means we are searching for evidence that disconforms our hypothesis, making it less likely that we will accept a conclusion that turns out to be untrue.

Thus, NHST helps us avoid making errors in our interpretation of the result. In particular, it helps us avoid Type 2 error , as discussed in the chapter on Bivariate Analyses . As a reminder, Type 2 error is error where you accept a hypothesis as true when in fact it was false (while Type 1 error is error where you reject the hypothesis when in fact it was true). For example, you are making a Type 1 error if you decide not to study for a test because you assume you are so bad at the subject that studying simply cannot help you, when in fact we know from research that studying does lead to higher grades. And you are making a Type 2 error if your boss tells you that she is going to promote you if you do enough overtime and you then work lots of overtime in response, when actually your boss is just trying to make you work more hours and already had someone else in mind to promote.

We can never remove all sources of error from our analyses, though larger sample sizes help reduce error. Looking at the formula for computing standard error , we can see that the standard error ([latex]SE[/latex]) would get smaller as the sample size ([latex]N[/latex]) gets larger. Note: σ is the symbol we use to represent standard deviation.

[latex]SE = \frac{\sigma}{\sqrt N}[/latex]

Besides making our samples larger, another thing that we can do is that we can choose whether we are more willing to accept Type 1 error or Type 2 error and adjust our strategies accordingly. In most research, we would prefer to accept more Type 1 error, because we are more willing to miss out on a finding than we are to make a finding that turns out later to be inaccurate (though, of course, lots of research does eventually turn out to be inaccurate).

Performing NHST

Performing NHST requires that our data meet several assumptions:

• Our sample must be a random sample—statistical significance testing and other inferential and explanatory statistical methods are generally not appropriate for non-random samples [3] —as well as representative and of a sufficient size (see the Central Limit Theorem above).
• Observations must be independent of other observations, or else additional statistical manipulation must be performed. For instance, a dataset of data about siblings would need to be handled differently due to the fact that siblings affect one another, so data on each person in the dataset is not truly independent.
• You must determine the rules for your significance test, including the level of uncertainty you are willing to accept (significance level) and whether or not you are interested in the direction of the result (one-tailed versus two-tailed tests, to be discussed below), in advance of performing any analysis.
• The number of significance tests you run should be limited, because the more tests you run, the greater the likelihood that one of your tests will result in an error. To make this more clear, if you are willing to accept a 5% probability that you will make the error of accepting a hypothesis as true when it is really false, and you run 20 tests, one of those tests (5% of them!) is pretty likely to have produced an incorrect result.

If our data has met these assumptions, we can move forward with the process of conducting an NHST. This requires us to make three decisions: determining our null hypothesis , our confidence level (or acceptable significance level), and whether we will conduct a one-tailed or a two-tailed test. In keeping with Assumption 3 above, we must make these decisions before performing our analysis. The null hypothesis is the hypothesis that there is no relationship between the variables in question. So, for example, if our research hypothesis was that people who spend more time with their friends are happier, our null hypothesis would be that there is no relationship between how much time people spend with their friends and their happiness.

Our confidence level is the level of risk we are willing to accept that our results could have occurred by chance. Typically, in social science research, researchers use p<0.05 (we are willing to accept up to a 5% risk that our results occurred by chance), p<0.01 (we are willing to accept up to a 1% risk that our results occurred by chance), and/or p<0.001 (we are willing to accept up to a 0.1% risk that our results occurred by chance). P, as was noted above, is the mathematical notation for probability, and that’s why we use a p-value to indicate the probability that our results may have occurred by chance. A higher p-value increases the likelihood that we will accept as accurate a result that really occurred by chance; a lower p-value increases the likelihood that we will assume a result occurred by chance when actually it was real. Remember, what the p-value tells us is not the probability that our own research hypothesis is true, but rather this: assuming that the null hypothesis is correct, what is the probability that the data we observed—or data more extreme than the data we observed—would have occurred by chance.

Whether we choose a one-tailed or a two-tailed test tells us what we mean when we say “data more extreme than.” Remember that normal curve? A two-tailed test is agnostic as to the direction of our results—and many of the most common tests for statistical significance that we perform, like the Chi square, are two-tailed by default. However, if you are only interested in a result that occurs in a particular direction, you might choose a one-tailed test. For instance, if you were testing a new blood pressure medication, you might only care if the blood pressure of those taking the medication is significantly lower than those not taking the medication—having blood pressure significantly higher would not be a good or helpful result, so you might not want to test for that.

Having determined the parameters for our analysis, we then compute our test of statistical significance. There are different tests of statistical significance for different variables (for example, the Chi square discussed in the chapter on bivariate analyses ), as you will see in other chapters of this text, but all of them produce results in a similar format. We then compare this result to the p value we already selected. If the p value produced by our analysis is lower than the confidence level we selected, we can reject the null hypothesis, as the probability that our result occurred by chance is very low. If, on the other hand, the p value produced by our analysis is higher than the confidence level we selected, we fail to reject the null hypothesis, as the probability that our result occurred by chance is too high to accept. Keep in mind this is what we do even when the p value produced by our analysis is quite close to the threshold we have selected. So, for instance, if we have selected the confidence level of p<0.05 and the p value produced by our analysis is p=0.0501, we still fail to reject the null hypothesis and proceed as if there is not any support for our research hypothesis.

Thus, the process of null hypothesis significance testing proceeds according to the following steps:

• Determine the null hypothesis
• Set the confidence level and whether this will be a one-tailed or two-tailed test
• Compute the test value for the appropriate significance test
• Compare the test value to the critical value of that test statistic for the confidence level you selected
• Determine whether or not to reject the null hypothesis

Your statistical analysis software will perform steps 3 and 4 for you (before there was computer software to do this, researchers had to do the calculations by hand and compare their results to figures on published tables of critical values). But you as the researcher must perform steps 1, 2, and 5 yourself.

Confidence Intervals & Margins of Error

When talking about statistical significance, some researchers also use the terms confidence intervals and margins of error . Confidence intervals are ranges of probabilities within which we can assume the true population parameter lies. Most typically, analysts aim for 95% confidence intervals, meaning that in 95 out of 100 cases, the population parameter will lie within the upper and lower levels specified by your confidence interval. These are calculated by your statistics software as well. The margin of error, then, is the range of values within the confidence interval. So, for instance, a 2021 survey of Americans conducted by the Robert Wood Johnson Foundation and the Harvard T.H. Chan School of Public Health found that 71% of respondents favor substantially increasing federal spending on public health programs. This poll had a 95% confidence interval with a +/- 3.6 margin of error. What this tells us is that there is a 95% probability (19 in 20) that between 67.4% (71-3.6) and 74.6% (71+3.6) of Americans favored increasing federal public health spending at the time the poll was conducted. When a figure reflects an overwhelming majority, such as this one, the margin of error may seem of little relevance. But consider a similar poll with the same margin of error that sought to predict support for a political candidate and found that 51.5% of people said they would vote for that candidate. In that case, we would have found that there was a 95% probability that between 47.9% and 55.1% of people intended to vote for the candidate—which means the race is total tossup and we really would have no idea what to expect. For some people, thinking in terms of confidence intervals and margins of error is easier to understand than thinking in terms of p values; confidence intervals and margins of error are more frequently used in analyses of polls while p values are found more often in academic research. But basically, both approaches are doing the same fundamental analysis—they are determining the likelihood that the results we observed or a similarly-meaningful result would have occurred by chance.

What Does Significance Testing Tell Us?

One of the most important things to remember about significance testing is that, while the word “significance” is used in ordinary speech to mean importance, significance testing does not tell us whether our results are important—or even whether they are interesting. A full understanding of the relationship between a given set of variables requires looking at statistical significance as well as association and the theoretical importance of the findings. Table 1 provides a perspective on using the combination of significance and association to determine how important the results of statistical analysis are—but even using Table 1 as a guide, evaluating findings based on theoretical importance remains key. So: make sure that when you are conducting analyses, you avoid being misled into assuming that significant results are sufficient for making broad claims about the importance and meaning of results. And remember as well that significance only tells us the likelihood that the pattern of relationships we observe occurred by chance—not whether that pattern is causal. For, after all, quantitative research can never eliminate all plausible alternative explanations for the phenomenon in question (one of the three elements of causation, along with association and temporal order).

• Getting 7 heads on 7 coin flips
• Getting 5 heads on 7 coin flips
• Getting 1 head on 10 coin flips

Then check your work using the Coin Flip Probability Calculator .

• As the advertised hourly pay for a job goes up, the number of job applicants increases.
• Teenagers who watch more hours of makeup tutorial videos on TikTok have, on average, lower self-esteem.
• Couples who share hobbies in common are less likely to get divorced.
• Assume a research conducted a study that found that people wearing green socks type on average one word per minute faster than people who are not wearing green socks, and that this study found a p value of p<0.01. Is this result statistically significant? Is this result practically significant? Explain your answers.
• If we conduct a political poll and have a 95% confidence interval and a margin of error of +/- 2.3%, what can we conclude about support for Candidate X if 49.3% of respondents tell us they will vote for Candidate X? If 24.7% do? If 52.1% do? If 83.7% do?
• One way to think about this is to imagine that your result has been plotted on a bell curve. Statistical significance tells us the probability that the "real" result—the thing that is true in the real world and not due to random chance—is at the same point as or further along the skinny tails of the bell curve than the result we have plotted. ↵
• In other words, what you get when you multiply. ↵
• They also are not appropriate for censuses—but you do not need inferential statistics in a census because you are looking at the entire population rather than a sample, so you can simply describe the relationships that do exist. ↵

A distribution of values that is symmetrical and bell-shaped.

A graph showing a normal distribution—one that is symmetrical with a rounded top that then falls away towards the extremes in the shape of a bell

The sum of all the values in a list divided by the number of such values.

The theorem that states that if you take a series of sufficiently large random samples from the population (replacing people back into the population so they can be reselected each time you draw a new sample), the distribution of the sample means will be approximately normally distributed.

A statistical measure that suggests that sample results can be generalized to the larger population, based on a low probability of having made a Type 1 error.

How likely something is to happen; also, a branch of mathematics concerned with investigating the likelihood of occurrences.

Measurement error created due to the fact that even properly-constructed random samples are do not have precisely the same characteristics as the larger population from which they were drawn.

The theorem in probability about the likelihood of a given outcome occurring repeatedly over multiple trials; this is determined by multiplying the probabilities together.

The theorem addressing the determination of the probability of a given outcome occurring at least once across a series of trials; it is determined by adding the probability of each possible series of outcomes together.

A method of testing for statistical significance in which an observed relationship, pattern, or figure is tested against a hypothesis that there is no relationship or pattern among the variables being tested

Null hypothesis significance testing.

The error you make when you do not infer a relationship exists in the larger population when it actually does exist; in other words, a false negative conclusion.

The error made if one infers that a relationship exists in a larger population when it does not really exist; in other words, a false positive error.

A measure of accuracy of sample statistics computed using the standard deviation of the sampling distribution.

The hypothesis that there is no relationship between the variables in question.

The probability that the sample statistics we observe holds true for the larger population.

A measure of statistical significance used in crosstabulation to determine the generalizability of results.

A range of estimates into which it is highly probable that an unknown population parameter falls.

A suggestion of how far away from the actual population parameter a sample statistic is likely to be.

Social Data Analysis Copyright © 2021 by Mikaila Mariel Lemonik Arthur is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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• One-tailed or two-tailed?
• Degrees of freedom

A hypothesis is a statement that we are trying to prove or disprove. It is used to express the relationship between variables  and whether this relationship is significant. It is specific and offers a prediction on the results of your research question.

Your research question  will lead you to developing a hypothesis, this is why your research question needs to be specific and clear.

The hypothesis will then guide you to the most appropriate techniques you should use to answer the question. They reflect the literature and theories on which you basing them. They need to be testable (i.e. measurable and practical).

Null hypothesis  (H 0 ) is the proposition that there will not be a relationship between the variables you are looking at. i.e. any differences are due to chance). They always refer to the population. (Usually we don't believe this to be true.)

e.g. There is  no difference in instances of illegal drug use by teenagers who are members of a gang and those who are not..

Alternative hypothesis  (H A ) or ( H 1 ):  this is sometimes called the research hypothesis or experimental hypothesis. It is the proposition that there will be a relationship. It is a statement of inequality between the variables you are interested in. They always refer to the sample. It is usually a declaration rather than a question and is clear, to the point and specific.

e.g. The instances of illegal drug use of teenagers who are members of a gang  is different than the instances of illegal drug use of teenagers who are not gang members.

A non-directional research hypothesis - reflects an expected difference between groups but does not specify the direction of this difference (see two-tailed test).

A directional research hypothesis - reflects an expected difference between groups but does specify the direction of this difference. (see one-tailed test)

e.g. The instances of illegal drug use by teenagers who are members of a gang will be higher t han the instances of illegal drug use of teenagers who are not gang members.

Then the process of testing is to ascertain which hypothesis to believe. 

It is usually easier to prove something as untrue rather than true, so looking at the null hypothesis is the usual starting point.

The process of examining the null hypothesis in light of evidence from the sample is called significance testing . It is a way of establishing a range of values in which we can establish whether the null hypothesis is true or false.

The debate over hypothesis testing

There has been discussion over whether the scientific method employed in traditional hypothesis testing is appropriate.  

See below for some articles that discuss this:

• Gill, J. (1999) 'The insignificance of null hypothesis testing',  Politics Research Quarterly , 52(3), pp. 647-674.
• Wainer, H. and Robinson, D.H. (2003) 'Shaping up the practice of null hypothesis significance testing',  Educational Researcher, 32(7), pp.22-30.
• Ferguson, C.J. and Heener, M. (2012) ' A vast graveyard of undead theories: publication bias and psychological science's aversion to the null' , Perspectives on Psychological Science , 7(6), pp.555-561.

Taken from: Salkind, N.J. (2017)  Statistics for people who (think they) hate statistics. 6th edn. London: SAGE pp. 144-145.

• Null hypothesis - a simple introduction (SPSS)

A significance level defines the level when your sample evidence contradicts your null hypothesis so that your can then reject it. It is the probability of rejecting the null hypothesis when it is really true.

e.g. a significance level of 0.05 indicates that there is a 5% (or 1 in 20) risk of deciding that there is an effect when in fact there is none.

The lower the significance level that you set,  then the evidence from the sample has to be stronger to be able to reject the null hypothesis.

N.B.  - it is important that you set the significance level before you carry out your study and analysis.

Using Confidence Intervals

I t is possible to test the significance of your null hypothesis using Confidence Interval (see under samples and populations tab).

- if the range lies outside our predicted null hypothesis value we can reject it and accept the alternative hypothesis  

The test statistic

This is another commonly used statistic

• Write down your null and alternative hypothesis
• Find the sample statistic (e.g.the mean of your sample)
• Calculate the test statistic Z score (see under Measures of spread or dispersion and Statistical tests - parametric). In this case the sample mean is compared to the population mean (assumed from the null hypothesis) and the standard error (see under Samples and population) is used rather than the standard deviation.
• Compare the test statistic with the critical values (e.g. plus or minus 1.96 for 5% significance)
• Draw a conclusion about the hypotheses - does the calculated z value lies in this critical range i.e. above 1.96 or below -1.96? If it does we can reject the null hypothesis. This would indicate that the results are significant (or an effect has been detected) - which means that if there were no difference in the population then getting a result that you have observed would be highly unlikely therefore you can reject the null hypothesis.

Type I error  - this is the chance of wrongly rejecting the null hypothesis even though it is actually true, e.g. by using a 5% p  level you would expect the null hypothesis to be rejected about 5% of the time when the null hypothesis is true. You could set a more stringent p  level such as 1% (or 1 in 100) to be more certain of not seeing a Type I error. This, however, makes more likely another type of error (Type II) occurring.

Type II error  - this is where there is an effect, but the  p  value you obtain is non-significant hence you don’t detect this effect.

• Statistical significance - what does it really mean?
• Statistical tables

One-tailed tests - where we know in which direction (e.g. larger or smaller) the difference between sample and population will be. It is a directional hypothesis.

Two-tailed tests - where we are looking at whether there is a difference between sample and population. This difference could be larger or smaller. This is a non-directional hypothesis.

If the difference is in the direction you have predicted (i.e. a one-tailed test) it is easier to get a significant result. Though there are arguments against using a one-tailed test (Wright and London, 2009, p. 98-99)*

*Wright, D. B. & London, K. (2009)  First (and second) steps in statistics . 2nd edn. London: SAGE.

N.B. - think of the ‘tails’ as the regions at the far-end of a normal distribution. For a two-tailed test with significance level of 0.05% then 0.025% of the values would be at one end of the distribution and the other 0.025% would be at the other end of the distribution. It is the values in these ‘critical’ extreme regions where we can think about rejecting the null hypothesis and claim that there has been an effect.

Degrees of freedom ( df)  is a rather difficult mathematical concept, but is needed to calculate the signifcance of certain statistical tests, such as the t-test, ANOVA and Chi-squared test.

It is broadly defined as the number of "observations" (pieces of information) in the data that are free to vary when estimating statistical parameters. (Taken from Minitab Blog ).

The higher the degrees of freedom are the more powerful and precise your estimates of the parameter (population) will be.

Typically, for a 1-sample t-test it is considered as the number of values in your sample minus 1.

For chi-squared tests with a table of rows and columns the rule is:

(Number of rows minus 1) times (number of columns minus 1)

Any accessible example to illustrate the principle of degrees of freedom using chocolates.

• You have seven chocolates in a box, each being a different type, e.g. truffle, coffee cream, caramel cluster, fudge, strawberry dream, hazelnut whirl, toffee. 
• You are being good and intend to eat only one chocolate each day of the week.
• On the first day, you can choose to eat any one of the 7 chocolate types  - you have a choice from all 7.
• On the second day, you can choose from the 6 remaining chocolates, on day 3 you can choose from 5 chocolates, and so on.
• On the sixth day you have a choice of the remaining 2 chocolates you haven't ate that week.
• However on the seventh day - you haven't really got any choice of chocolate - it has got to be the one you have left in your box.
• You had 7-1 = 6 days of “chocolate” freedom—in which the chocolate you ate could vary!
• << Previous: Samples and population
• Next: Statistical tests - parametric >>
• Last Updated: Aug 1, 2024 3:26 PM
• URL: https://libguides.tees.ac.uk/quantitative

Quantitative Research

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• Leigh A. Wilson 2 , 3  

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Quantitative research methods are concerned with the planning, design, and implementation of strategies to collect and analyze data. Descartes, the seventeenth-century philosopher, suggested that how the results are achieved is often more important than the results themselves, as the journey taken along the research path is a journey of discovery. High-quality quantitative research is characterized by the attention given to the methods and the reliability of the tools used to collect the data. The ability to critique research in a systematic way is an essential component of a health professional’s role in order to deliver high quality, evidence-based healthcare. This chapter is intended to provide a simple overview of the way new researchers and health practitioners can understand and employ quantitative methods. The chapter offers practical, realistic guidance in a learner-friendly way and uses a logical sequence to understand the process of hypothesis development, study design, data collection and handling, and finally data analysis and interpretation.

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Wilson, L.A. (2019). Quantitative Research. In: Liamputtong, P. (eds) Handbook of Research Methods in Health Social Sciences. Springer, Singapore. https://doi.org/10.1007/978-981-10-5251-4_54

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