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• How to Write a Strong Hypothesis | Steps & Examples

How to Write a Strong Hypothesis | Steps & Examples

Published on May 6, 2022 by Shona McCombes . Revised on November 20, 2023.

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 .

Example: Hypothesis

Daily apple consumption leads to fewer doctor’s visits.

Table of contents

What is a hypothesis, developing a hypothesis (with example), hypothesis examples, other interesting articles, 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 types of variables .

• An independent variable is something the researcher changes or controls.
• A dependent variable is something the researcher observes and measures.

If there are any control variables , extraneous variables , or confounding variables , be sure to jot those down as you go to minimize the chances that research bias  will affect your results.

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 ensure that you’re embarking on a relevant topic . This can also help you identify which variables you will study and what you think the relationships are between them. Sometimes, you’ll have to operationalize 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.

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

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.

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 .

• H 0 : The number of lectures attended by first-year students has no effect on their final exam scores.
• H 1 : The number of lectures attended by first-year students has a positive effect on their final exam scores.

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

• Sampling methods
• Simple random sampling
• Stratified sampling
• Cluster sampling
• Likert scales
• Reproducibility

 Statistics

• Null hypothesis
• Statistical power
• Probability distribution
• Effect size
• Poisson distribution

Research bias

• Optimism bias
• Cognitive bias
• Implicit bias
• Hawthorne effect
• Anchoring bias
• Explicit bias

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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).

Null and alternative hypotheses are used in statistical hypothesis testing . The null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship.

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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The Craft of Writing a Strong Hypothesis

Table of Contents

Writing a hypothesis is one of the essential elements of a scientific research paper. It needs to be to the point, clearly communicating what your research is trying to accomplish. A blurry, drawn-out, or complexly-structured hypothesis can confuse your readers. Or worse, the editor and peer reviewers.

A captivating hypothesis is not too intricate. This blog will take you through the process so that, by the end of it, you have a better idea of how to convey your research paper's intent in just one sentence.

What is a Hypothesis?

The first step in your scientific endeavor, a hypothesis, is a strong, concise statement that forms the basis of your research. It is not the same as a thesis statement , which is a brief summary of your research paper .

The sole purpose of a hypothesis is to predict your paper's findings, data, and conclusion. It comes from a place of curiosity and intuition . When you write a hypothesis, you're essentially making an educated guess based on scientific prejudices and evidence, which is further proven or disproven through the scientific method.

The reason for undertaking research is to observe a specific phenomenon. A hypothesis, therefore, lays out what the said phenomenon is. And it does so through two variables, an independent and dependent variable.

The independent variable is the cause behind the observation, while the dependent variable is the effect of the cause. A good example of this is “mixing red and blue forms purple.” In this hypothesis, mixing red and blue is the independent variable as you're combining the two colors at your own will. The formation of purple is the dependent variable as, in this case, it is conditional to the independent variable.

Different Types of Hypotheses‌

Types of hypotheses

Some would stand by the notion that there are only two types of hypotheses: a Null hypothesis and an Alternative hypothesis. While that may have some truth to it, it would be better to fully distinguish the most common forms as these terms come up so often, which might leave you out of context.

Apart from Null and Alternative, there are Complex, Simple, Directional, Non-Directional, Statistical, and Associative and casual hypotheses. They don't necessarily have to be exclusive, as one hypothesis can tick many boxes, but knowing the distinctions between them will make it easier for you to construct your own.

1. Null hypothesis

A null hypothesis proposes no relationship between two variables. Denoted by H 0 , it is a negative statement like “Attending physiotherapy sessions does not affect athletes' on-field performance.” Here, the author claims physiotherapy sessions have no effect on on-field performances. Even if there is, it's only a coincidence.

2. Alternative hypothesis

Considered to be the opposite of a null hypothesis, an alternative hypothesis is donated as H1 or Ha. It explicitly states that the dependent variable affects the independent variable. A good  alternative hypothesis example is “Attending physiotherapy sessions improves athletes' on-field performance.” or “Water evaporates at 100 °C. ” The alternative hypothesis further branches into directional and non-directional.

• Directional hypothesis: A hypothesis that states the result would be either positive or negative is called directional hypothesis. It accompanies H1 with either the ‘<' or ‘>' sign.
• Non-directional hypothesis: A non-directional hypothesis only claims an effect on the dependent variable. It does not clarify whether the result would be positive or negative. The sign for a non-directional hypothesis is ‘≠.'

3. Simple hypothesis

A simple hypothesis is a statement made to reflect the relation between exactly two variables. One independent and one dependent. Consider the example, “Smoking is a prominent cause of lung cancer." The dependent variable, lung cancer, is dependent on the independent variable, smoking.

4. Complex hypothesis

In contrast to a simple hypothesis, a complex hypothesis implies the relationship between multiple independent and dependent variables. For instance, “Individuals who eat more fruits tend to have higher immunity, lesser cholesterol, and high metabolism.” The independent variable is eating more fruits, while the dependent variables are higher immunity, lesser cholesterol, and high metabolism.

5. Associative and casual hypothesis

Associative and casual hypotheses don't exhibit how many variables there will be. They define the relationship between the variables. In an associative hypothesis, changing any one variable, dependent or independent, affects others. In a casual hypothesis, the independent variable directly affects the dependent.

6. Empirical hypothesis

Also referred to as the working hypothesis, an empirical hypothesis claims a theory's validation via experiments and observation. This way, the statement appears justifiable and different from a wild guess.

Say, the hypothesis is “Women who take iron tablets face a lesser risk of anemia than those who take vitamin B12.” This is an example of an empirical hypothesis where the researcher  the statement after assessing a group of women who take iron tablets and charting the findings.

7. Statistical hypothesis

The point of a statistical hypothesis is to test an already existing hypothesis by studying a population sample. Hypothesis like “44% of the Indian population belong in the age group of 22-27.” leverage evidence to prove or disprove a particular statement.

Characteristics of a Good Hypothesis

Writing a hypothesis is essential as it can make or break your research for you. That includes your chances of getting published in a journal. So when you're designing one, keep an eye out for these pointers:

• A research hypothesis has to be simple yet clear to look justifiable enough.
• It has to be testable — your research would be rendered pointless if too far-fetched into reality or limited by technology.
• It has to be precise about the results —what you are trying to do and achieve through it should come out in your hypothesis.
• A research hypothesis should be self-explanatory, leaving no doubt in the reader's mind.
• If you are developing a relational hypothesis, you need to include the variables and establish an appropriate relationship among them.
• A hypothesis must keep and reflect the scope for further investigations and experiments.

Separating a Hypothesis from a Prediction

Outside of academia, hypothesis and prediction are often used interchangeably. In research writing, this is not only confusing but also incorrect. And although a hypothesis and prediction are guesses at their core, there are many differences between them.

A hypothesis is an educated guess or even a testable prediction validated through research. It aims to analyze the gathered evidence and facts to define a relationship between variables and put forth a logical explanation behind the nature of events.

Predictions are assumptions or expected outcomes made without any backing evidence. They are more fictionally inclined regardless of where they originate from.

For this reason, a hypothesis holds much more weight than a prediction. It sticks to the scientific method rather than pure guesswork. "Planets revolve around the Sun." is an example of a hypothesis as it is previous knowledge and observed trends. Additionally, we can test it through the scientific method.

Whereas "COVID-19 will be eradicated by 2030." is a prediction. Even though it results from past trends, we can't prove or disprove it. So, the only way this gets validated is to wait and watch if COVID-19 cases end by 2030.

Finally, How to Write a Hypothesis

Quick tips on writing a hypothesis

1.  Be clear about your research question

A hypothesis should instantly address the research question or the problem statement. To do so, you need to ask a question. Understand the constraints of your undertaken research topic and then formulate a simple and topic-centric problem. Only after that can you develop a hypothesis and further test for evidence.

2. Carry out a recce

Once you have your research's foundation laid out, it would be best to conduct preliminary research. Go through previous theories, academic papers, data, and experiments before you start curating your research hypothesis. It will give you an idea of your hypothesis's viability or originality.

Making use of references from relevant research papers helps draft a good research hypothesis. SciSpace Discover offers a repository of over 270 million research papers to browse through and gain a deeper understanding of related studies on a particular topic. Additionally, you can use SciSpace Copilot , your AI research assistant, for reading any lengthy research paper and getting a more summarized context of it. A hypothesis can be formed after evaluating many such summarized research papers. Copilot also offers explanations for theories and equations, explains paper in simplified version, allows you to highlight any text in the paper or clip math equations and tables and provides a deeper, clear understanding of what is being said. This can improve the hypothesis by helping you identify potential research gaps.

3. Create a 3-dimensional hypothesis

Variables are an essential part of any reasonable hypothesis. So, identify your independent and dependent variable(s) and form a correlation between them. The ideal way to do this is to write the hypothetical assumption in the ‘if-then' form. If you use this form, make sure that you state the predefined relationship between the variables.

In another way, you can choose to present your hypothesis as a comparison between two variables. Here, you must specify the difference you expect to observe in the results.

4. Write the first draft

Now that everything is in place, it's time to write your hypothesis. For starters, create the first draft. In this version, write what you expect to find from your research.

Clearly separate your independent and dependent variables and the link between them. Don't fixate on syntax at this stage. The goal is to ensure your hypothesis addresses the issue.

5. Proof your hypothesis

After preparing the first draft of your hypothesis, you need to inspect it thoroughly. It should tick all the boxes, like being concise, straightforward, relevant, and accurate. Your final hypothesis has to be well-structured as well.

Research projects are an exciting and crucial part of being a scholar. And once you have your research question, you need a great hypothesis to begin conducting research. Thus, knowing how to write a hypothesis is very important.

Now that you have a firmer grasp on what a good hypothesis constitutes, the different kinds there are, and what process to follow, you will find it much easier to write your hypothesis, which ultimately helps your research.

Now it's easier than ever to streamline your research workflow with SciSpace Discover . Its integrated, comprehensive end-to-end platform for research allows scholars to easily discover, write and publish their research and fosters collaboration.

It includes everything you need, including a repository of over 270 million research papers across disciplines, SEO-optimized summaries and public profiles to show your expertise and experience.

If you found these tips on writing a research hypothesis useful, head over to our blog on Statistical Hypothesis Testing to learn about the top researchers, papers, and institutions in this domain.

Frequently Asked Questions (FAQs)

1. what is the definition of hypothesis.

According to the Oxford dictionary, a hypothesis is defined as “An idea or explanation of something that is based on a few known facts, but that has not yet been proved to be true or correct”.

2. What is an example of hypothesis?

The hypothesis is a statement that proposes a relationship between two or more variables. An example: "If we increase the number of new users who join our platform by 25%, then we will see an increase in revenue."

3. What is an example of null hypothesis?

A null hypothesis is a statement that there is no relationship between two variables. The null hypothesis is written as H0. The null hypothesis states that there is no effect. For example, if you're studying whether or not a particular type of exercise increases strength, your null hypothesis will be "there is no difference in strength between people who exercise and people who don't."

4. What are the types of research?

• Fundamental research

• Applied research

• Qualitative research

• Quantitative research

• Mixed research

• Exploratory research

• Longitudinal research

• Cross-sectional research

• Field research

• Laboratory research

• Fixed research

• Flexible research

• Action research

• Policy research

• Classification research

• Comparative research

• Causal research

• Inductive research

• Deductive research

5. How to write a hypothesis?

• Your hypothesis should be able to predict the relationship and outcome.

• Avoid wordiness by keeping it simple and brief.

• Your hypothesis should contain observable and testable outcomes.

• Your hypothesis should be relevant to the research question.

6. What are the 2 types of hypothesis?

• Null hypotheses are used to test the claim that "there is no difference between two groups of data".

• Alternative hypotheses test the claim that "there is a difference between two data groups".

7. Difference between research question and research hypothesis?

A research question is a broad, open-ended question you will try to answer through your research. A hypothesis is a statement based on prior research or theory that you expect to be true due to your study. Example - Research question: What are the factors that influence the adoption of the new technology? Research hypothesis: There is a positive relationship between age, education and income level with the adoption of the new technology.

8. What is plural for hypothesis?

The plural of hypothesis is hypotheses. Here's an example of how it would be used in a statement, "Numerous well-considered hypotheses are presented in this part, and they are supported by tables and figures that are well-illustrated."

9. What is the red queen hypothesis?

The red queen hypothesis in evolutionary biology states that species must constantly evolve to avoid extinction because if they don't, they will be outcompeted by other species that are evolving. Leigh Van Valen first proposed it in 1973; since then, it has been tested and substantiated many times.

10. Who is known as the father of null hypothesis?

The father of the null hypothesis is Sir Ronald Fisher. He published a paper in 1925 that introduced the concept of null hypothesis testing, and he was also the first to use the term itself.

11. When to reject null hypothesis?

You need to find a significant difference between your two populations to reject the null hypothesis. You can determine that by running statistical tests such as an independent sample t-test or a dependent sample t-test. You should reject the null hypothesis if the p-value is less than 0.05.

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A case study research paper examines a person, place, event, condition, phenomenon, or other type of subject of analysis in order to extrapolate  key themes and results that help predict future trends, illuminate previously hidden issues that can be applied to practice, and/or provide a means for understanding an important research problem with greater clarity. A case study research paper usually examines a single subject of analysis, but case study papers can also be designed as a comparative investigation that shows relationships between two or more subjects. The methods used to study a case can rest within a quantitative, qualitative, or mixed-method investigative paradigm.

Case Studies. Writing@CSU. Colorado State University; Mills, Albert J. , Gabrielle Durepos, and Eiden Wiebe, editors. Encyclopedia of Case Study Research . Thousand Oaks, CA: SAGE Publications, 2010 ; “What is a Case Study?” In Swanborn, Peter G. Case Study Research: What, Why and How? London: SAGE, 2010.

How to Approach Writing a Case Study Research Paper

General information about how to choose a topic to investigate can be found under the " Choosing a Research Problem " tab in the Organizing Your Social Sciences Research Paper writing guide. Review this page because it may help you identify a subject of analysis that can be investigated using a case study design.

However, identifying a case to investigate involves more than choosing the research problem . A case study encompasses a problem contextualized around the application of in-depth analysis, interpretation, and discussion, often resulting in specific recommendations for action or for improving existing conditions. As Seawright and Gerring note, practical considerations such as time and access to information can influence case selection, but these issues should not be the sole factors used in describing the methodological justification for identifying a particular case to study. Given this, selecting a case includes considering the following:

• The case represents an unusual or atypical example of a research problem that requires more in-depth analysis? Cases often represent a topic that rests on the fringes of prior investigations because the case may provide new ways of understanding the research problem. For example, if the research problem is to identify strategies to improve policies that support girl's access to secondary education in predominantly Muslim nations, you could consider using Azerbaijan as a case study rather than selecting a more obvious nation in the Middle East. Doing so may reveal important new insights into recommending how governments in other predominantly Muslim nations can formulate policies that support improved access to education for girls.
• The case provides important insight or illuminate a previously hidden problem? In-depth analysis of a case can be based on the hypothesis that the case study will reveal trends or issues that have not been exposed in prior research or will reveal new and important implications for practice. For example, anecdotal evidence may suggest drug use among homeless veterans is related to their patterns of travel throughout the day. Assuming prior studies have not looked at individual travel choices as a way to study access to illicit drug use, a case study that observes a homeless veteran could reveal how issues of personal mobility choices facilitate regular access to illicit drugs. Note that it is important to conduct a thorough literature review to ensure that your assumption about the need to reveal new insights or previously hidden problems is valid and evidence-based.
• The case challenges and offers a counter-point to prevailing assumptions? Over time, research on any given topic can fall into a trap of developing assumptions based on outdated studies that are still applied to new or changing conditions or the idea that something should simply be accepted as "common sense," even though the issue has not been thoroughly tested in current practice. A case study analysis may offer an opportunity to gather evidence that challenges prevailing assumptions about a research problem and provide a new set of recommendations applied to practice that have not been tested previously. For example, perhaps there has been a long practice among scholars to apply a particular theory in explaining the relationship between two subjects of analysis. Your case could challenge this assumption by applying an innovative theoretical framework [perhaps borrowed from another discipline] to explore whether this approach offers new ways of understanding the research problem. Taking a contrarian stance is one of the most important ways that new knowledge and understanding develops from existing literature.
• The case provides an opportunity to pursue action leading to the resolution of a problem? Another way to think about choosing a case to study is to consider how the results from investigating a particular case may result in findings that reveal ways in which to resolve an existing or emerging problem. For example, studying the case of an unforeseen incident, such as a fatal accident at a railroad crossing, can reveal hidden issues that could be applied to preventative measures that contribute to reducing the chance of accidents in the future. In this example, a case study investigating the accident could lead to a better understanding of where to strategically locate additional signals at other railroad crossings so as to better warn drivers of an approaching train, particularly when visibility is hindered by heavy rain, fog, or at night.
• The case offers a new direction in future research? A case study can be used as a tool for an exploratory investigation that highlights the need for further research about the problem. A case can be used when there are few studies that help predict an outcome or that establish a clear understanding about how best to proceed in addressing a problem. For example, after conducting a thorough literature review [very important!], you discover that little research exists showing the ways in which women contribute to promoting water conservation in rural communities of east central Africa. A case study of how women contribute to saving water in a rural village of Uganda can lay the foundation for understanding the need for more thorough research that documents how women in their roles as cooks and family caregivers think about water as a valuable resource within their community. This example of a case study could also point to the need for scholars to build new theoretical frameworks around the topic [e.g., applying feminist theories of work and family to the issue of water conservation].

Eisenhardt, Kathleen M. “Building Theories from Case Study Research.” Academy of Management Review 14 (October 1989): 532-550; Emmel, Nick. Sampling and Choosing Cases in Qualitative Research: A Realist Approach . Thousand Oaks, CA: SAGE Publications, 2013; Gerring, John. “What Is a Case Study and What Is It Good for?” American Political Science Review 98 (May 2004): 341-354; Mills, Albert J. , Gabrielle Durepos, and Eiden Wiebe, editors. Encyclopedia of Case Study Research . Thousand Oaks, CA: SAGE Publications, 2010; Seawright, Jason and John Gerring. "Case Selection Techniques in Case Study Research." Political Research Quarterly 61 (June 2008): 294-308.

Structure and Writing Style

The purpose of a paper in the social sciences designed around a case study is to thoroughly investigate a subject of analysis in order to reveal a new understanding about the research problem and, in so doing, contributing new knowledge to what is already known from previous studies. In applied social sciences disciplines [e.g., education, social work, public administration, etc.], case studies may also be used to reveal best practices, highlight key programs, or investigate interesting aspects of professional work.

In general, the structure of a case study research paper is not all that different from a standard college-level research paper. However, there are subtle differences you should be aware of. Here are the key elements to organizing and writing a case study research paper.

I.  Introduction

As with any research paper, your introduction should serve as a roadmap for your readers to ascertain the scope and purpose of your study . The introduction to a case study research paper, however, should not only describe the research problem and its significance, but you should also succinctly describe why the case is being used and how it relates to addressing the problem. The two elements should be linked. With this in mind, a good introduction answers these four questions:

• What is being studied? Describe the research problem and describe the subject of analysis [the case] you have chosen to address the problem. Explain how they are linked and what elements of the case will help to expand knowledge and understanding about the problem.
• Why is this topic important to investigate? Describe the significance of the research problem and state why a case study design and the subject of analysis that the paper is designed around is appropriate in addressing the problem.
• What did we know about this topic before I did this study? Provide background that helps lead the reader into the more in-depth literature review to follow. If applicable, summarize prior case study research applied to the research problem and why it fails to adequately address the problem. Describe why your case will be useful. If no prior case studies have been used to address the research problem, explain why you have selected this subject of analysis.
• How will this study advance new knowledge or new ways of understanding? Explain why your case study will be suitable in helping to expand knowledge and understanding about the research problem.

Each of these questions should be addressed in no more than a few paragraphs. Exceptions to this can be when you are addressing a complex research problem or subject of analysis that requires more in-depth background information.

II.  Literature Review

The literature review for a case study research paper is generally structured the same as it is for any college-level research paper. The difference, however, is that the literature review is focused on providing background information and  enabling historical interpretation of the subject of analysis in relation to the research problem the case is intended to address . This includes synthesizing studies that help to:

• Place relevant works in the context of their contribution to understanding the case study being investigated . This would involve summarizing studies that have used a similar subject of analysis to investigate the research problem. If there is literature using the same or a very similar case to study, you need to explain why duplicating past research is important [e.g., conditions have changed; prior studies were conducted long ago, etc.].
• Describe the relationship each work has to the others under consideration that informs the reader why this case is applicable . Your literature review should include a description of any works that support using the case to investigate the research problem and the underlying research questions.
• Identify new ways to interpret prior research using the case study . If applicable, review any research that has examined the research problem using a different research design. Explain how your use of a case study design may reveal new knowledge or a new perspective or that can redirect research in an important new direction.
• Resolve conflicts amongst seemingly contradictory previous studies . This refers to synthesizing any literature that points to unresolved issues of concern about the research problem and describing how the subject of analysis that forms the case study can help resolve these existing contradictions.
• Point the way in fulfilling a need for additional research . Your review should examine any literature that lays a foundation for understanding why your case study design and the subject of analysis around which you have designed your study may reveal a new way of approaching the research problem or offer a perspective that points to the need for additional research.
• Expose any gaps that exist in the literature that the case study could help to fill . Summarize any literature that not only shows how your subject of analysis contributes to understanding the research problem, but how your case contributes to a new way of understanding the problem that prior research has failed to do.
• Locate your own research within the context of existing literature [very important!] . Collectively, your literature review should always place your case study within the larger domain of prior research about the problem. The overarching purpose of reviewing pertinent literature in a case study paper is to demonstrate that you have thoroughly identified and synthesized prior studies in relation to explaining the relevance of the case in addressing the research problem.

III.  Method

In this section, you explain why you selected a particular case [i.e., subject of analysis] and the strategy you used to identify and ultimately decide that your case was appropriate in addressing the research problem. The way you describe the methods used varies depending on the type of subject of analysis that constitutes your case study.

If your subject of analysis is an incident or event . In the social and behavioral sciences, the event or incident that represents the case to be studied is usually bounded by time and place, with a clear beginning and end and with an identifiable location or position relative to its surroundings. The subject of analysis can be a rare or critical event or it can focus on a typical or regular event. The purpose of studying a rare event is to illuminate new ways of thinking about the broader research problem or to test a hypothesis. Critical incident case studies must describe the method by which you identified the event and explain the process by which you determined the validity of this case to inform broader perspectives about the research problem or to reveal new findings. However, the event does not have to be a rare or uniquely significant to support new thinking about the research problem or to challenge an existing hypothesis. For example, Walo, Bull, and Breen conducted a case study to identify and evaluate the direct and indirect economic benefits and costs of a local sports event in the City of Lismore, New South Wales, Australia. The purpose of their study was to provide new insights from measuring the impact of a typical local sports event that prior studies could not measure well because they focused on large "mega-events." Whether the event is rare or not, the methods section should include an explanation of the following characteristics of the event: a) when did it take place; b) what were the underlying circumstances leading to the event; and, c) what were the consequences of the event in relation to the research problem.

If your subject of analysis is a person. Explain why you selected this particular individual to be studied and describe what experiences they have had that provide an opportunity to advance new understandings about the research problem. Mention any background about this person which might help the reader understand the significance of their experiences that make them worthy of study. This includes describing the relationships this person has had with other people, institutions, and/or events that support using them as the subject for a case study research paper. It is particularly important to differentiate the person as the subject of analysis from others and to succinctly explain how the person relates to examining the research problem [e.g., why is one politician in a particular local election used to show an increase in voter turnout from any other candidate running in the election]. Note that these issues apply to a specific group of people used as a case study unit of analysis [e.g., a classroom of students].

If your subject of analysis is a place. In general, a case study that investigates a place suggests a subject of analysis that is unique or special in some way and that this uniqueness can be used to build new understanding or knowledge about the research problem. A case study of a place must not only describe its various attributes relevant to the research problem [e.g., physical, social, historical, cultural, economic, political], but you must state the method by which you determined that this place will illuminate new understandings about the research problem. It is also important to articulate why a particular place as the case for study is being used if similar places also exist [i.e., if you are studying patterns of homeless encampments of veterans in open spaces, explain why you are studying Echo Park in Los Angeles rather than Griffith Park?]. If applicable, describe what type of human activity involving this place makes it a good choice to study [e.g., prior research suggests Echo Park has more homeless veterans].

If your subject of analysis is a phenomenon. A phenomenon refers to a fact, occurrence, or circumstance that can be studied or observed but with the cause or explanation to be in question. In this sense, a phenomenon that forms your subject of analysis can encompass anything that can be observed or presumed to exist but is not fully understood. In the social and behavioral sciences, the case usually focuses on human interaction within a complex physical, social, economic, cultural, or political system. For example, the phenomenon could be the observation that many vehicles used by ISIS fighters are small trucks with English language advertisements on them. The research problem could be that ISIS fighters are difficult to combat because they are highly mobile. The research questions could be how and by what means are these vehicles used by ISIS being supplied to the militants and how might supply lines to these vehicles be cut off? How might knowing the suppliers of these trucks reveal larger networks of collaborators and financial support? A case study of a phenomenon most often encompasses an in-depth analysis of a cause and effect that is grounded in an interactive relationship between people and their environment in some way.

NOTE:   The choice of the case or set of cases to study cannot appear random. Evidence that supports the method by which you identified and chose your subject of analysis should clearly support investigation of the research problem and linked to key findings from your literature review. Be sure to cite any studies that helped you determine that the case you chose was appropriate for examining the problem.

IV.  Discussion

The main elements of your discussion section are generally the same as any research paper, but centered around interpreting and drawing conclusions about the key findings from your analysis of the case study. Note that a general social sciences research paper may contain a separate section to report findings. However, in a paper designed around a case study, it is common to combine a description of the results with the discussion about their implications. The objectives of your discussion section should include the following:

Reiterate the Research Problem/State the Major Findings Briefly reiterate the research problem you are investigating and explain why the subject of analysis around which you designed the case study were used. You should then describe the findings revealed from your study of the case using direct, declarative, and succinct proclamation of the study results. Highlight any findings that were unexpected or especially profound.

Explain the Meaning of the Findings and Why They are Important Systematically explain the meaning of your case study findings and why you believe they are important. Begin this part of the section by repeating what you consider to be your most important or surprising finding first, then systematically review each finding. Be sure to thoroughly extrapolate what your analysis of the case can tell the reader about situations or conditions beyond the actual case that was studied while, at the same time, being careful not to misconstrue or conflate a finding that undermines the external validity of your conclusions.

Relate the Findings to Similar Studies No study in the social sciences is so novel or possesses such a restricted focus that it has absolutely no relation to previously published research. The discussion section should relate your case study results to those found in other studies, particularly if questions raised from prior studies served as the motivation for choosing your subject of analysis. This is important because comparing and contrasting the findings of other studies helps support the overall importance of your results and it highlights how and in what ways your case study design and the subject of analysis differs from prior research about the topic.

Consider Alternative Explanations of the Findings Remember that the purpose of social science research is to discover and not to prove. When writing the discussion section, you should carefully consider all possible explanations revealed by the case study results, rather than just those that fit your hypothesis or prior assumptions and biases. Be alert to what the in-depth analysis of the case may reveal about the research problem, including offering a contrarian perspective to what scholars have stated in prior research if that is how the findings can be interpreted from your case.

Acknowledge the Study's Limitations You can state the study's limitations in the conclusion section of your paper but describing the limitations of your subject of analysis in the discussion section provides an opportunity to identify the limitations and explain why they are not significant. This part of the discussion section should also note any unanswered questions or issues your case study could not address. More detailed information about how to document any limitations to your research can be found here .

Suggest Areas for Further Research Although your case study may offer important insights about the research problem, there are likely additional questions related to the problem that remain unanswered or findings that unexpectedly revealed themselves as a result of your in-depth analysis of the case. Be sure that the recommendations for further research are linked to the research problem and that you explain why your recommendations are valid in other contexts and based on the original assumptions of your study.

V.  Conclusion

As with any research paper, you should summarize your conclusion in clear, simple language; emphasize how the findings from your case study differs from or supports prior research and why. Do not simply reiterate the discussion section. Provide a synthesis of key findings presented in the paper to show how these converge to address the research problem. If you haven't already done so in the discussion section, be sure to document the limitations of your case study and any need for further research.

The function of your paper's conclusion is to: 1) reiterate the main argument supported by the findings from your case study; 2) state clearly the context, background, and necessity of pursuing the research problem using a case study design in relation to an issue, controversy, or a gap found from reviewing the literature; and, 3) provide a place to persuasively and succinctly restate the significance of your research problem, given that the reader has now been presented with in-depth information about the topic.

Consider the following points to help ensure your conclusion is appropriate:

• If the argument or purpose of your paper is complex, you may need to summarize these points for your reader.
• If prior to your conclusion, you have not yet explained the significance of your findings or if you are proceeding inductively, use the conclusion of your paper to describe your main points and explain their significance.
• Move from a detailed to a general level of consideration of the case study's findings that returns the topic to the context provided by the introduction or within a new context that emerges from your case study findings.

Note that, depending on the discipline you are writing in or the preferences of your professor, the concluding paragraph may contain your final reflections on the evidence presented as it applies to practice or on the essay's central research problem. However, the nature of being introspective about the subject of analysis you have investigated will depend on whether you are explicitly asked to express your observations in this way.

Problems to Avoid

Overgeneralization One of the goals of a case study is to lay a foundation for understanding broader trends and issues applied to similar circumstances. However, be careful when drawing conclusions from your case study. They must be evidence-based and grounded in the results of the study; otherwise, it is merely speculation. Looking at a prior example, it would be incorrect to state that a factor in improving girls access to education in Azerbaijan and the policy implications this may have for improving access in other Muslim nations is due to girls access to social media if there is no documentary evidence from your case study to indicate this. There may be anecdotal evidence that retention rates were better for girls who were engaged with social media, but this observation would only point to the need for further research and would not be a definitive finding if this was not a part of your original research agenda.

Failure to Document Limitations No case is going to reveal all that needs to be understood about a research problem. Therefore, just as you have to clearly state the limitations of a general research study , you must describe the specific limitations inherent in the subject of analysis. For example, the case of studying how women conceptualize the need for water conservation in a village in Uganda could have limited application in other cultural contexts or in areas where fresh water from rivers or lakes is plentiful and, therefore, conservation is understood more in terms of managing access rather than preserving access to a scarce resource.

Failure to Extrapolate All Possible Implications Just as you don't want to over-generalize from your case study findings, you also have to be thorough in the consideration of all possible outcomes or recommendations derived from your findings. If you do not, your reader may question the validity of your analysis, particularly if you failed to document an obvious outcome from your case study research. For example, in the case of studying the accident at the railroad crossing to evaluate where and what types of warning signals should be located, you failed to take into consideration speed limit signage as well as warning signals. When designing your case study, be sure you have thoroughly addressed all aspects of the problem and do not leave gaps in your analysis that leave the reader questioning the results.

Case Studies. Writing@CSU. Colorado State University; Gerring, John. Case Study Research: Principles and Practices . New York: Cambridge University Press, 2007; Merriam, Sharan B. Qualitative Research and Case Study Applications in Education . Rev. ed. San Francisco, CA: Jossey-Bass, 1998; Miller, Lisa L. “The Use of Case Studies in Law and Social Science Research.” Annual Review of Law and Social Science 14 (2018): TBD; Mills, Albert J., Gabrielle Durepos, and Eiden Wiebe, editors. Encyclopedia of Case Study Research . Thousand Oaks, CA: SAGE Publications, 2010; Putney, LeAnn Grogan. "Case Study." In Encyclopedia of Research Design , Neil J. Salkind, editor. (Thousand Oaks, CA: SAGE Publications, 2010), pp. 116-120; Simons, Helen. Case Study Research in Practice . London: SAGE Publications, 2009;  Kratochwill,  Thomas R. and Joel R. Levin, editors. Single-Case Research Design and Analysis: New Development for Psychology and Education .  Hilldsale, NJ: Lawrence Erlbaum Associates, 1992; Swanborn, Peter G. Case Study Research: What, Why and How? London : SAGE, 2010; Yin, Robert K. Case Study Research: Design and Methods . 6th edition. Los Angeles, CA, SAGE Publications, 2014; Walo, Maree, Adrian Bull, and Helen Breen. “Achieving Economic Benefits at Local Events: A Case Study of a Local Sports Event.” Festival Management and Event Tourism 4 (1996): 95-106.

Writing Tip

At Least Five Misconceptions about Case Study Research

Social science case studies are often perceived as limited in their ability to create new knowledge because they are not randomly selected and findings cannot be generalized to larger populations. Flyvbjerg examines five misunderstandings about case study research and systematically "corrects" each one. To quote, these are:

Misunderstanding 1 :  General, theoretical [context-independent] knowledge is more valuable than concrete, practical [context-dependent] knowledge. Misunderstanding 2 :  One cannot generalize on the basis of an individual case; therefore, the case study cannot contribute to scientific development. Misunderstanding 3 :  The case study is most useful for generating hypotheses; that is, in the first stage of a total research process, whereas other methods are more suitable for hypotheses testing and theory building. Misunderstanding 4 :  The case study contains a bias toward verification, that is, a tendency to confirm the researcher’s preconceived notions. Misunderstanding 5 :  It is often difficult to summarize and develop general propositions and theories on the basis of specific case studies [p. 221].

While writing your paper, think introspectively about how you addressed these misconceptions because to do so can help you strengthen the validity and reliability of your research by clarifying issues of case selection, the testing and challenging of existing assumptions, the interpretation of key findings, and the summation of case outcomes. Think of a case study research paper as a complete, in-depth narrative about the specific properties and key characteristics of your subject of analysis applied to the research problem.

Flyvbjerg, Bent. “Five Misunderstandings About Case-Study Research.” Qualitative Inquiry 12 (April 2006): 219-245.

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How to Write a Great Hypothesis

Hypothesis Format, Examples, and Tips

Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

Amy Morin, LCSW, is a psychotherapist and international bestselling author. Her books, including "13 Things Mentally Strong People Don't Do," have been translated into more than 40 languages. Her TEDx talk,  "The Secret of Becoming Mentally Strong," is one of the most viewed talks of all time.

Verywell / Alex Dos Diaz

• The Scientific Method

Hypothesis Format

Falsifiability of a hypothesis, operational definitions, types of hypotheses, hypotheses examples.

• Collecting Data

Frequently Asked Questions

A hypothesis is a tentative statement about the relationship between two or more  variables. It is a specific, testable prediction about what you expect to happen in a study.

One hypothesis example would be a study designed to look at the relationship between sleep deprivation and test performance might have a hypothesis that states: "This study is designed to assess the hypothesis that sleep-deprived people will perform worse on a test than individuals who are not sleep-deprived."

This article explores how a hypothesis is used in psychology research, how to write a good hypothesis, and the different types of hypotheses you might use.

The Hypothesis in the Scientific Method

In the scientific method , whether it involves research in psychology, biology, or some other area, a hypothesis represents what the researchers think will happen in an experiment. The scientific method involves the following steps:

• Forming a question
• Performing background research
• Creating a hypothesis
• Designing an experiment
• Collecting data
• Analyzing the results
• Drawing conclusions
• Communicating the results

The hypothesis is a prediction, but it involves more than a guess. Most of the time, the hypothesis begins with a question which is then explored through background research. It is only at this point that researchers begin to develop a testable hypothesis. Unless you are creating an exploratory study, your hypothesis should always explain what you  expect  to happen.

In a study exploring the effects of a particular drug, the hypothesis might be that researchers expect the drug to have some type of effect on the symptoms of a specific illness. In psychology, the hypothesis might focus on how a certain aspect of the environment might influence a particular behavior.

Remember, a hypothesis does not have to be correct. While the hypothesis predicts what the researchers expect to see, the goal of the research is to determine whether this guess is right or wrong. When conducting an experiment, researchers might explore a number of factors to determine which ones might contribute to the ultimate outcome.

In many cases, researchers may find that the results of an experiment  do not  support the original hypothesis. When writing up these results, the researchers might suggest other options that should be explored in future studies.

In many cases, researchers might draw a hypothesis from a specific theory or build on previous research. For example, prior research has shown that stress can impact the immune system. So a researcher might hypothesize: "People with high-stress levels will be more likely to contract a common cold after being exposed to the virus than people who have low-stress levels."

In other instances, researchers might look at commonly held beliefs or folk wisdom. "Birds of a feather flock together" is one example of folk wisdom that a psychologist might try to investigate. The researcher might pose a specific hypothesis that "People tend to select romantic partners who are similar to them in interests and educational level."

Elements of a Good Hypothesis

So how do you write a good hypothesis? When trying to come up with a hypothesis for your research or experiments, ask yourself the following questions:

• Is your hypothesis based on your research on a topic?
• Can your hypothesis be tested?
• Does your hypothesis include independent and dependent variables?

Before you come up with a specific hypothesis, spend some time doing background research. Once you have completed a literature review, start thinking about potential questions you still have. Pay attention to the discussion section in the  journal articles you read . Many authors will suggest questions that still need to be explored.

To form a hypothesis, you should take these steps:

• Collect as many observations about a topic or problem as you can.
• Evaluate these observations and look for possible causes of the problem.
• Create a list of possible explanations that you might want to explore.
• After you have developed some possible hypotheses, think of ways that you could confirm or disprove each hypothesis through experimentation. This is known as falsifiability.

In the scientific method ,  falsifiability is an important part of any valid hypothesis.   In order to test a claim scientifically, it must be possible that the claim could be proven false.

Students sometimes confuse the idea of falsifiability with the idea that it means that something is false, which is not the case. What falsifiability means is that  if  something was false, then it is possible to demonstrate that it is false.

One of the hallmarks of pseudoscience is that it makes claims that cannot be refuted or proven false.

A variable is a factor or element that can be changed and manipulated in ways that are observable and measurable. However, the researcher must also define how the variable will be manipulated and measured in the study.

For example, a researcher might operationally define the variable " test anxiety " as the results of a self-report measure of anxiety experienced during an exam. A "study habits" variable might be defined by the amount of studying that actually occurs as measured by time.

These precise descriptions are important because many things can be measured in a number of different ways. One of the basic principles of any type of scientific research is that the results must be replicable.   By clearly detailing the specifics of how the variables were measured and manipulated, other researchers can better understand the results and repeat the study if needed.

Some variables are more difficult than others to define. How would you operationally define a variable such as aggression ? For obvious ethical reasons, researchers cannot create a situation in which a person behaves aggressively toward others.

In order to measure this variable, the researcher must devise a measurement that assesses aggressive behavior without harming other people. In this situation, the researcher might utilize a simulated task to measure aggressiveness.

Hypothesis Checklist

• Does your hypothesis focus on something that you can actually test?
• Does your hypothesis include both an independent and dependent variable?
• Can you manipulate the variables?
• Can your hypothesis be tested without violating ethical standards?

The hypothesis you use will depend on what you are investigating and hoping to find. Some of the main types of hypotheses that you might use include:

• Simple hypothesis : This type of hypothesis suggests that there is a relationship between one independent variable and one dependent variable.
• Complex hypothesis : This type of hypothesis suggests a relationship between three or more variables, such as two independent variables and a dependent variable.
• Null hypothesis : This hypothesis suggests no relationship exists between two or more variables.
• Alternative hypothesis : This hypothesis states the opposite of the null hypothesis.
• Statistical hypothesis : This hypothesis uses statistical analysis to evaluate a representative sample of the population and then generalizes the findings to the larger group.
• Logical hypothesis : This hypothesis assumes a relationship between variables without collecting data or evidence.

A hypothesis often follows a basic format of "If {this happens} then {this will happen}." One way to structure your hypothesis is to describe what will happen to the  dependent variable  if you change the  independent variable .

The basic format might be: "If {these changes are made to a certain independent variable}, then we will observe {a change in a specific dependent variable}."

A few examples of simple hypotheses:

• "Students who eat breakfast will perform better on a math exam than students who do not eat breakfast."
• Complex hypothesis: "Students who experience test anxiety before an English exam will get lower scores than students who do not experience test anxiety."​
• "Motorists who talk on the phone while driving will be more likely to make errors on a driving course than those who do not talk on the phone."

Examples of a complex hypothesis include:

• "People with high-sugar diets and sedentary activity levels are more likely to develop depression."
• "Younger people who are regularly exposed to green, outdoor areas have better subjective well-being than older adults who have limited exposure to green spaces."

Examples of a null hypothesis include:

• "Children who receive a new reading intervention will have scores different than students who do not receive the intervention."
• "There will be no difference in scores on a memory recall task between children and adults."

Examples of an alternative hypothesis:

• "Children who receive a new reading intervention will perform better than students who did not receive the intervention."
• "Adults will perform better on a memory task than children." 

Collecting Data on Your Hypothesis

Once a researcher has formed a testable hypothesis, the next step is to select a research design and start collecting data. The research method depends largely on exactly what they are studying. There are two basic types of research methods: descriptive research and experimental research.

Descriptive Research Methods

Descriptive research such as  case studies ,  naturalistic observations , and surveys are often used when it would be impossible or difficult to  conduct an experiment . These methods are best used to describe different aspects of a behavior or psychological phenomenon.

Once a researcher has collected data using descriptive methods, a correlational study can then be used to look at how the variables are related. This type of research method might be used to investigate a hypothesis that is difficult to test experimentally.

Experimental Research Methods

Experimental methods  are used to demonstrate causal relationships between variables. In an experiment, the researcher systematically manipulates a variable of interest (known as the independent variable) and measures the effect on another variable (known as the dependent variable).

Unlike correlational studies, which can only be used to determine if there is a relationship between two variables, experimental methods can be used to determine the actual nature of the relationship—whether changes in one variable actually  cause  another to change.

A Word From Verywell

The hypothesis is a critical part of any scientific exploration. It represents what researchers expect to find in a study or experiment. In situations where the hypothesis is unsupported by the research, the research still has value. Such research helps us better understand how different aspects of the natural world relate to one another. It also helps us develop new hypotheses that can then be tested in the future.

Some examples of how to write a hypothesis include:

• "Staying up late will lead to worse test performance the next day."
• "People who consume one apple each day will visit the doctor fewer times each year."
• "Breaking study sessions up into three 20-minute sessions will lead to better test results than a single 60-minute study session."

The four parts of a hypothesis are:

• The research question
• The independent variable (IV)
• The dependent variable (DV)
• The proposed relationship between the IV and DV

Castillo M. The scientific method: a need for something better? . AJNR Am J Neuroradiol. 2013;34(9):1669-71. doi:10.3174/ajnr.A3401

Nevid J. Psychology: Concepts and Applications. Wadworth, 2013.

By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

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• v.36(50); 2021 Dec 27

Formulating Hypotheses for Different Study Designs

Durga prasanna misra.

1 Department of Clinical Immunology and Rheumatology, Sanjay Gandhi Postgraduate Institute of Medical Sciences, Lucknow, India.

Armen Yuri Gasparyan

2 Departments of Rheumatology and Research and Development, Dudley Group NHS Foundation Trust (Teaching Trust of the University of Birmingham, UK), Russells Hall Hospital, Dudley, UK.

Olena Zimba

3 Department of Internal Medicine #2, Danylo Halytsky Lviv National Medical University, Lviv, Ukraine.

Marlen Yessirkepov

4 Department of Biology and Biochemistry, South Kazakhstan Medical Academy, Shymkent, Kazakhstan.

Vikas Agarwal

George d. kitas.

5 Centre for Epidemiology versus Arthritis, University of Manchester, Manchester, UK.

Generating a testable working hypothesis is the first step towards conducting original research. Such research may prove or disprove the proposed hypothesis. Case reports, case series, online surveys and other observational studies, clinical trials, and narrative reviews help to generate hypotheses. Observational and interventional studies help to test hypotheses. A good hypothesis is usually based on previous evidence-based reports. Hypotheses without evidence-based justification and a priori ideas are not received favourably by the scientific community. Original research to test a hypothesis should be carefully planned to ensure appropriate methodology and adequate statistical power. While hypotheses can challenge conventional thinking and may be controversial, they should not be destructive. A hypothesis should be tested by ethically sound experiments with meaningful ethical and clinical implications. The coronavirus disease 2019 pandemic has brought into sharp focus numerous hypotheses, some of which were proven (e.g. effectiveness of corticosteroids in those with hypoxia) while others were disproven (e.g. ineffectiveness of hydroxychloroquine and ivermectin).

Graphical Abstract

DEFINING WORKING AND STANDALONE SCIENTIFIC HYPOTHESES

Science is the systematized description of natural truths and facts. Routine observations of existing life phenomena lead to the creative thinking and generation of ideas about mechanisms of such phenomena and related human interventions. Such ideas presented in a structured format can be viewed as hypotheses. After generating a hypothesis, it is necessary to test it to prove its validity. Thus, hypothesis can be defined as a proposed mechanism of a naturally occurring event or a proposed outcome of an intervention. 1 , 2

Hypothesis testing requires choosing the most appropriate methodology and adequately powering statistically the study to be able to “prove” or “disprove” it within predetermined and widely accepted levels of certainty. This entails sample size calculation that often takes into account previously published observations and pilot studies. 2 , 3 In the era of digitization, hypothesis generation and testing may benefit from the availability of numerous platforms for data dissemination, social networking, and expert validation. Related expert evaluations may reveal strengths and limitations of proposed ideas at early stages of post-publication promotion, preventing the implementation of unsupported controversial points. 4

Thus, hypothesis generation is an important initial step in the research workflow, reflecting accumulating evidence and experts' stance. In this article, we overview the genesis and importance of scientific hypotheses and their relevance in the era of the coronavirus disease 2019 (COVID-19) pandemic.

DO WE NEED HYPOTHESES FOR ALL STUDY DESIGNS?

Broadly, research can be categorized as primary or secondary. In the context of medicine, primary research may include real-life observations of disease presentations and outcomes. Single case descriptions, which often lead to new ideas and hypotheses, serve as important starting points or justifications for case series and cohort studies. The importance of case descriptions is particularly evident in the context of the COVID-19 pandemic when unique, educational case reports have heralded a new era in clinical medicine. 5

Case series serve similar purpose to single case reports, but are based on a slightly larger quantum of information. Observational studies, including online surveys, describe the existing phenomena at a larger scale, often involving various control groups. Observational studies include variable-scale epidemiological investigations at different time points. Interventional studies detail the results of therapeutic interventions.

Secondary research is based on already published literature and does not directly involve human or animal subjects. Review articles are generated by secondary research. These could be systematic reviews which follow methods akin to primary research but with the unit of study being published papers rather than humans or animals. Systematic reviews have a rigid structure with a mandatory search strategy encompassing multiple databases, systematic screening of search results against pre-defined inclusion and exclusion criteria, critical appraisal of study quality and an optional component of collating results across studies quantitatively to derive summary estimates (meta-analysis). 6 Narrative reviews, on the other hand, have a more flexible structure. Systematic literature searches to minimise bias in selection of articles are highly recommended but not mandatory. 7 Narrative reviews are influenced by the authors' viewpoint who may preferentially analyse selected sets of articles. 8

In relation to primary research, case studies and case series are generally not driven by a working hypothesis. Rather, they serve as a basis to generate a hypothesis. Observational or interventional studies should have a hypothesis for choosing research design and sample size. The results of observational and interventional studies further lead to the generation of new hypotheses, testing of which forms the basis of future studies. Review articles, on the other hand, may not be hypothesis-driven, but form fertile ground to generate future hypotheses for evaluation. Fig. 1 summarizes which type of studies are hypothesis-driven and which lead on to hypothesis generation.

STANDARDS OF WORKING AND SCIENTIFIC HYPOTHESES

A review of the published literature did not enable the identification of clearly defined standards for working and scientific hypotheses. It is essential to distinguish influential versus not influential hypotheses, evidence-based hypotheses versus a priori statements and ideas, ethical versus unethical, or potentially harmful ideas. The following points are proposed for consideration while generating working and scientific hypotheses. 1 , 2 Table 1 summarizes these points.

Evidence-based data

A scientific hypothesis should have a sound basis on previously published literature as well as the scientist's observations. Randomly generated (a priori) hypotheses are unlikely to be proven. A thorough literature search should form the basis of a hypothesis based on published evidence. 7

Unless a scientific hypothesis can be tested, it can neither be proven nor be disproven. Therefore, a scientific hypothesis should be amenable to testing with the available technologies and the present understanding of science.

Supported by pilot studies

If a hypothesis is based purely on a novel observation by the scientist in question, it should be grounded on some preliminary studies to support it. For example, if a drug that targets a specific cell population is hypothesized to be useful in a particular disease setting, then there must be some preliminary evidence that the specific cell population plays a role in driving that disease process.

Testable by ethical studies

The hypothesis should be testable by experiments that are ethically acceptable. 9 For example, a hypothesis that parachutes reduce mortality from falls from an airplane cannot be tested using a randomized controlled trial. 10 This is because it is obvious that all those jumping from a flying plane without a parachute would likely die. Similarly, the hypothesis that smoking tobacco causes lung cancer cannot be tested by a clinical trial that makes people take up smoking (since there is considerable evidence for the health hazards associated with smoking). Instead, long-term observational studies comparing outcomes in those who smoke and those who do not, as was performed in the landmark epidemiological case control study by Doll and Hill, 11 are more ethical and practical.

Balance between scientific temper and controversy

Novel findings, including novel hypotheses, particularly those that challenge established norms, are bound to face resistance for their wider acceptance. Such resistance is inevitable until the time such findings are proven with appropriate scientific rigor. However, hypotheses that generate controversy are generally unwelcome. For example, at the time the pandemic of human immunodeficiency virus (HIV) and AIDS was taking foot, there were numerous deniers that refused to believe that HIV caused AIDS. 12 , 13 Similarly, at a time when climate change is causing catastrophic changes to weather patterns worldwide, denial that climate change is occurring and consequent attempts to block climate change are certainly unwelcome. 14 The denialism and misinformation during the COVID-19 pandemic, including unfortunate examples of vaccine hesitancy, are more recent examples of controversial hypotheses not backed by science. 15 , 16 An example of a controversial hypothesis that was a revolutionary scientific breakthrough was the hypothesis put forth by Warren and Marshall that Helicobacter pylori causes peptic ulcers. Initially, the hypothesis that a microorganism could cause gastritis and gastric ulcers faced immense resistance. When the scientists that proposed the hypothesis themselves ingested H. pylori to induce gastritis in themselves, only then could they convince the wider world about their hypothesis. Such was the impact of the hypothesis was that Barry Marshall and Robin Warren were awarded the Nobel Prize in Physiology or Medicine in 2005 for this discovery. 17 , 18

DISTINGUISHING THE MOST INFLUENTIAL HYPOTHESES

Influential hypotheses are those that have stood the test of time. An archetype of an influential hypothesis is that proposed by Edward Jenner in the eighteenth century that cowpox infection protects against smallpox. While this observation had been reported for nearly a century before this time, it had not been suitably tested and publicised until Jenner conducted his experiments on a young boy by demonstrating protection against smallpox after inoculation with cowpox. 19 These experiments were the basis for widespread smallpox immunization strategies worldwide in the 20th century which resulted in the elimination of smallpox as a human disease today. 20

Other influential hypotheses are those which have been read and cited widely. An example of this is the hygiene hypothesis proposing an inverse relationship between infections in early life and allergies or autoimmunity in adulthood. An analysis reported that this hypothesis had been cited more than 3,000 times on Scopus. 1

LESSONS LEARNED FROM HYPOTHESES AMIDST THE COVID-19 PANDEMIC

The COVID-19 pandemic devastated the world like no other in recent memory. During this period, various hypotheses emerged, understandably so considering the public health emergency situation with innumerable deaths and suffering for humanity. Within weeks of the first reports of COVID-19, aberrant immune system activation was identified as a key driver of organ dysfunction and mortality in this disease. 21 Consequently, numerous drugs that suppress the immune system or abrogate the activation of the immune system were hypothesized to have a role in COVID-19. 22 One of the earliest drugs hypothesized to have a benefit was hydroxychloroquine. Hydroxychloroquine was proposed to interfere with Toll-like receptor activation and consequently ameliorate the aberrant immune system activation leading to pathology in COVID-19. 22 The drug was also hypothesized to have a prophylactic role in preventing infection or disease severity in COVID-19. It was also touted as a wonder drug for the disease by many prominent international figures. However, later studies which were well-designed randomized controlled trials failed to demonstrate any benefit of hydroxychloroquine in COVID-19. 23 , 24 , 25 , 26 Subsequently, azithromycin 27 , 28 and ivermectin 29 were hypothesized as potential therapies for COVID-19, but were not supported by evidence from randomized controlled trials. The role of vitamin D in preventing disease severity was also proposed, but has not been proven definitively until now. 30 , 31 On the other hand, randomized controlled trials identified the evidence supporting dexamethasone 32 and interleukin-6 pathway blockade with tocilizumab as effective therapies for COVID-19 in specific situations such as at the onset of hypoxia. 33 , 34 Clues towards the apparent effectiveness of various drugs against severe acute respiratory syndrome coronavirus 2 in vitro but their ineffectiveness in vivo have recently been identified. Many of these drugs are weak, lipophilic bases and some others induce phospholipidosis which results in apparent in vitro effectiveness due to non-specific off-target effects that are not replicated inside living systems. 35 , 36

Another hypothesis proposed was the association of the routine policy of vaccination with Bacillus Calmette-Guerin (BCG) with lower deaths due to COVID-19. This hypothesis emerged in the middle of 2020 when COVID-19 was still taking foot in many parts of the world. 37 , 38 Subsequently, many countries which had lower deaths at that time point went on to have higher numbers of mortality, comparable to other areas of the world. Furthermore, the hypothesis that BCG vaccination reduced COVID-19 mortality was a classic example of ecological fallacy. Associations between population level events (ecological studies; in this case, BCG vaccination and COVID-19 mortality) cannot be directly extrapolated to the individual level. Furthermore, such associations cannot per se be attributed as causal in nature, and can only serve to generate hypotheses that need to be tested at the individual level. 39

IS TRADITIONAL PEER REVIEW EFFICIENT FOR EVALUATION OF WORKING AND SCIENTIFIC HYPOTHESES?

Traditionally, publication after peer review has been considered the gold standard before any new idea finds acceptability amongst the scientific community. Getting a work (including a working or scientific hypothesis) reviewed by experts in the field before experiments are conducted to prove or disprove it helps to refine the idea further as well as improve the experiments planned to test the hypothesis. 40 A route towards this has been the emergence of journals dedicated to publishing hypotheses such as the Central Asian Journal of Medical Hypotheses and Ethics. 41 Another means of publishing hypotheses is through registered research protocols detailing the background, hypothesis, and methodology of a particular study. If such protocols are published after peer review, then the journal commits to publishing the completed study irrespective of whether the study hypothesis is proven or disproven. 42 In the post-pandemic world, online research methods such as online surveys powered via social media channels such as Twitter and Instagram might serve as critical tools to generate as well as to preliminarily test the appropriateness of hypotheses for further evaluation. 43 , 44

Some radical hypotheses might be difficult to publish after traditional peer review. These hypotheses might only be acceptable by the scientific community after they are tested in research studies. Preprints might be a way to disseminate such controversial and ground-breaking hypotheses. 45 However, scientists might prefer to keep their hypotheses confidential for the fear of plagiarism of ideas, avoiding online posting and publishing until they have tested the hypotheses.

SUGGESTIONS ON GENERATING AND PUBLISHING HYPOTHESES

Publication of hypotheses is important, however, a balance is required between scientific temper and controversy. Journal editors and reviewers might keep in mind these specific points, summarized in Table 2 and detailed hereafter, while judging the merit of hypotheses for publication. Keeping in mind the ethical principle of primum non nocere, a hypothesis should be published only if it is testable in a manner that is ethically appropriate. 46 Such hypotheses should be grounded in reality and lend themselves to further testing to either prove or disprove them. It must be considered that subsequent experiments to prove or disprove a hypothesis have an equal chance of failing or succeeding, akin to tossing a coin. A pre-conceived belief that a hypothesis is unlikely to be proven correct should not form the basis of rejection of such a hypothesis for publication. In this context, hypotheses generated after a thorough literature search to identify knowledge gaps or based on concrete clinical observations on a considerable number of patients (as opposed to random observations on a few patients) are more likely to be acceptable for publication by peer-reviewed journals. Also, hypotheses should be considered for publication or rejection based on their implications for science at large rather than whether the subsequent experiments to test them end up with results in favour of or against the original hypothesis.

Hypotheses form an important part of the scientific literature. The COVID-19 pandemic has reiterated the importance and relevance of hypotheses for dealing with public health emergencies and highlighted the need for evidence-based and ethical hypotheses. A good hypothesis is testable in a relevant study design, backed by preliminary evidence, and has positive ethical and clinical implications. General medical journals might consider publishing hypotheses as a specific article type to enable more rapid advancement of science.

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

Author Contributions:

• Data curation: Gasparyan AY, Misra DP, Zimba O, Yessirkepov M, Agarwal V, Kitas GD.

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• Case Study | Definition, Examples & Methods

Case Study | Definition, Examples & Methods

Published on 5 May 2022 by Shona McCombes . Revised on 30 January 2023.

A case study is a detailed study of a specific subject, such as a person, group, place, event, organisation, or phenomenon. Case studies are commonly used in social, educational, clinical, and business research.

A case study research design usually involves qualitative methods , but quantitative methods are sometimes also used. Case studies are good for describing , comparing, evaluating, and understanding different aspects of a research problem .

Table of contents

When to do a case study, step 1: select a case, step 2: build a theoretical framework, step 3: collect your data, step 4: describe and analyse the case.

A case study is an appropriate research design when you want to gain concrete, contextual, in-depth knowledge about a specific real-world subject. It allows you to explore the key characteristics, meanings, and implications of the case.

Case studies are often a good choice in a thesis or dissertation . They keep your project focused and manageable when you don’t have the time or resources to do large-scale research.

You might use just one complex case study where you explore a single subject in depth, or conduct multiple case studies to compare and illuminate different aspects of your research problem.

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Once you have developed your problem statement and research questions , you should be ready to choose the specific case that you want to focus on. A good case study should have the potential to:

• Provide new or unexpected insights into the subject
• Challenge or complicate existing assumptions and theories
• Propose practical courses of action to resolve a problem
• Open up new directions for future research

Unlike quantitative or experimental research, a strong case study does not require a random or representative sample. In fact, case studies often deliberately focus on unusual, neglected, or outlying cases which may shed new light on the research problem.

If you find yourself aiming to simultaneously investigate and solve an issue, consider conducting action research . As its name suggests, action research conducts research and takes action at the same time, and is highly iterative and flexible. 

However, you can also choose a more common or representative case to exemplify a particular category, experience, or phenomenon.

While case studies focus more on concrete details than general theories, they should usually have some connection with theory in the field. This way the case study is not just an isolated description, but is integrated into existing knowledge about the topic. It might aim to:

• Exemplify a theory by showing how it explains the case under investigation
• Expand on a theory by uncovering new concepts and ideas that need to be incorporated
• Challenge a theory by exploring an outlier case that doesn’t fit with established assumptions

To ensure that your analysis of the case has a solid academic grounding, you should conduct a literature review of sources related to the topic and develop a theoretical framework . This means identifying key concepts and theories to guide your analysis and interpretation.

There are many different research methods you can use to collect data on your subject. Case studies tend to focus on qualitative data using methods such as interviews, observations, and analysis of primary and secondary sources (e.g., newspaper articles, photographs, official records). Sometimes a case study will also collect quantitative data .

The aim is to gain as thorough an understanding as possible of the case and its context.

In writing up the case study, you need to bring together all the relevant aspects to give as complete a picture as possible of the subject.

How you report your findings depends on the type of research you are doing. Some case studies are structured like a standard scientific paper or thesis, with separate sections or chapters for the methods , results , and discussion .

Others are written in a more narrative style, aiming to explore the case from various angles and analyse its meanings and implications (for example, by using textual analysis or discourse analysis ).

In all cases, though, make sure to give contextual details about the case, connect it back to the literature and theory, and discuss how it fits into wider patterns or debates.

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Hacking the Case Interview

A hypothesis is an educated guess on the answer to the case based on the data and information that you have gathered so far.

Every single consulting firm uses a hypothesis-driven approach when working on projects to solve their clients’ business problems. Therefore, you should also use a hypothesis-driven approach when solving your case interviews.

Having a hypothesis-driven approach is critical to solving a case efficiently. A hypothesis ensures that you are prioritizing the most important issues or questions. It also helps you proactively lead the direction of the case in candidate-led case interviews.

If you can master the practice of developing and refining your hypothesis, you will demonstrate to consulting firms that you have the skills needed to be a successful consultant. You’ll be much more likely to pass your case interviews and receive consulting job offers.

In this article, we’ll cover:

• Why you should always use a hypothesis-driven approach in your case interviews
• When you should state your hypothesis during a case interview
• How specific or broad your hypothesis needs to be
• What to do if your hypothesis is wrong
• What to do if your hypothesis is right

If you’re looking for a step-by-step shortcut to learn case interviews quickly, enroll in our case interview course . These insider strategies from a former Bain interviewer helped 30,000+ land consulting offers while saving hundreds of hours of prep time.

Why You Should Always Use a Hypothesis in Case Interviews

There are many reasons why you should use a hypothesis in a case interview.

A hypothesis helps you focus on relevant issues or questions

By having a hypothesis, you have an idea of what questions or issues will be relevant to supporting or rejecting your hypothesis. Therefore, you’ll be spending your time answering questions and conducting analyses that are relevant to getting you closer to solving the case.

If a question or analysis does not help you refine your hypothesis, it is likely not relevant to the case. Without a hypothesis, you’ll have a harder time determining what questions or issues are relevant.

A hypothesis helps you prioritize your time

In a case interview, you won’t have time to answer every question that you can think of. By having a hypothesis, you can focus your time and efforts on answering questions that will help you refine your hypothesis. 

This ensures that all of your time is spent on answering the most important questions of the case. Answering questions that have little impact on your hypothesis should be deprioritized.

A hypothesis helps you steer the direction of the case

With a hypothesis, you’ll always have some kind of idea of what to do next. You can propose answering a question or performing an analysis that would strengthen the support for your hypothesis. You could also propose a next step that would refine your hypothesis and make it more specific.

A hypothesis helps you develop your ultimate recommendation

Throughout the case, your hypothesis is basically a work in progress version of your recommendation. Once you have gathered enough information to support your hypothesis with data and evidence, your hypothesis becomes your recommendation at the end of the case.

By developing a hypothesis early in the case and continuing to refine it, you are getting a head start on developing your recommendation.  

Example of a non-hypothesis driven approach

Let’s see how much of a difference a hypothesis makes when going through a case interview. We’ll start with an example of a candidate solving a case without a hypothesis.

Interviewer : Our client is an airline company that services the United States. They have recently been experiencing a decline in profits. Your task for this case is to identify what is causing the decline in profits and what our client should do to address this issue.

Candidate : Has customer demand for travel decreased over this time?

Interviewer : This does not seem to be the case. Customer demand for travel has actually slightly increased over this time period.

Candidate : That’s interesting. Are there new competitors that have entered the market, thus taking market share from our client?

Interviewer : There are no major competitors that have entered the market.

Candidate : Have our fuel costs gone up?

Interviewer : Prices for fuel have been steady over the past few years.

Candidate : Perhaps demand for business travel has declined?

Interviewer : Yes, we are seeing a decline in business travelers. Let me share with you this exhibit…

Notice how unorganized the candidate’s approach is. It almost feels like the candidate is blindly guessing at what the cause of the decline in profits is. They ask a variety of different questions related to customer demand, competition, fuel costs, and business travel.

The candidate was lucky to eventually guess correctly what was causing the decline in profits. However, if business travel was not the answer, who knows how long it would take for the candidate to finally end up going down the right direction in this case.

Example of a hypothesis driven approach

Let’s look at how differently the case would proceed if the candidate had instead used a hypothesis-driven approach.

Candidate : A decline in profits is either due to a decrease in revenues, an increase in costs, or both. Perhaps the client’s costs have gone up. Do we have any information on how costs have changed over this time period?

Interviewer : Costs have remained flat during this time period.

Candidate : Okay, so an increase in costs is not what is driving a decline in profits. Therefore, the decline in profits is probably driven by a decrease in revenues. Do we have any information on how revenues have changed over this period?

Interviewer : Yes, revenues have gone down. What else would you like to know?

Candidate : Revenues are driven by quantity of tickets sold and price per ticket. Perhaps our client is selling fewer tickets. Do we have information on this?

Interviewer : There are two types of tickets, economy class and business class. Sales of economy tickets have been flat, but sales of business class tickets have gone down.

Candidate : I see. It seems that a decline in business class ticket sales is causing a decline in profits. I’d like to understand why business class ticket sales have declined. First, it’d be helpful to know whether this is an industry-wide problem or a company-specific problem. Have competitors also seen a decline in business class ticket sales?

Interviewer : Let me share with you this exhibit…

Notice that by developing a hypothesis from the beginning, the candidate is able to systematically tackle this case. Instead of blindly asking questions, the candidate methodically asks questions to support or reject their hypothesis.

When the candidate’s initial hypothesis that costs have increased was incorrect, the candidate quickly revised their hypothesis and continued testing it.

Regardless of whether or not the candidate’s hypothesis was correct, each hypothesis brought the candidate closer to the actual answer.

When to State Your Hypothesis in a Case Interview

You should try to state your hypothesis as early as you can in a case interview. Typically, candidates state their hypotheses after presenting their case framework to the interviewer and before proposing which area of their framework to start in.

Interviewer : Our client, Apple, is looking to enter the gaming computer market. Should they enter?

Candidate : Would you mind if I take a moment to develop a structure to tackle this question?

Interviewer : Sure, go ahead.

Candidate : To determine whether or not Apple should enter the gaming market, there are four areas I’d like to look into. 

First, I’d like to look at the gaming computer market attractiveness to see if it is an attractive market to enter. What is the market size and growth rate?

Second, I’d like to look into the competitive landscape to determine if Apple would be able to capture meaningful market share. Who are the competitors and how strong are they?

Third, I’d like to look at Apple’s capabilities to determine if they could successfully produce and launch a gaming computer product. Does Apple have the manufacturing capabilities and design expertise?

Finally, I’d like to look at expected profitability. What are expected revenues and costs from entering this market?

My initial thoughts are that Apple should enter the market because it is likely a large, growing market with decent profit margins. However, I need to confirm whether or not this is true. Do we have further information on the market size or growth rate of the gaming computer market?

Sometimes, you won’t have enough data or information to even make a hypothesis. In these circumstances, you should first explicitly state to the interviewer that you do not have sufficient information to make a well-informed hypothesis. Then, state what information you would first need to know to develop a reasonable hypothesis.

This way, you can demonstrate to the interviewer that you would like to use a hypothesis-driven approach without forcing yourself to make an arbitrary hypothesis.

Once you have gathered further information on the case, you should make a hypothesis as early as possible.

Interviewer : Our client, Coca-Cola, is looking to launch a new drink product. What type of product should they launch?

Candidate : There are many different types of drink products such as soft drinks, teas, coffees, fruit juices, and alcoholic beverages. To better narrow down what type of product Coca-Cola should launch, I’d like to first understand what Coca-Cola’s goals are for launching this product.

Interviewer : Coca-Cola is looking to diversify its revenue streams by expanding into drink categories that are growing rapidly that Coca-Cola does not have a presence in.

Candidate : I do know that healthy drink beverages is a small, but rapidly growing segment. This could be a potential market. However, to be more thorough, I’d like to look at all of the drink categories that Coca-Cola does not have a presence in and compare each categories’ growth rates, average profit margins, and potential synergies with Coca-Cola’s existing capabilities.

Candidate : From looking at this exhibit, it seems that low-calorie alcoholic beverages is the fastest grown segment with the highest margins. There is a reasonable level of production synergies Coca-Cola can take advantage. This seems like an attractive product to launch. 

To confirm my hypothesis, I’d like to see whether Coca-Cola could capture meaningful market share by looking at the competitive landscape. How many competitors are there and how much market share do they each have?

How Specific Your Case Interview Hypothesis Needs to Be

In general, your hypotheses near the beginning of the case will be broad while your hypotheses near the end of the case will be more specific. This makes sense because your hypothesis becomes more and more refined and focused as the case goes on.

Each time that you test your hypothesis, you should be getting slightly closer to the answer. In each of the previous two examples, notice how the hypothesis gets much more specific as the case progresses.

For example, if you are dealing with a  profitability case , the following hypotheses would be too specific to state as your first hypothesis:  

• The decline in profits could be driven by the recent trade embargo between the United States and China
• The decline in profits could be driven by a new competitor that has entered the market that is taking market share from our client by charging lower prices
• The decline in profits could be driven by an increase in costs due to rising foreign currency exchange rates

These are specific hypotheses that are more appropriate near the end of the case interview if the information and data suggests these possibilities.

Conversely, the following hypotheses would be too broad to state near the end of the case interview:  

• The decline in profits is due to a decline in revenue
• The decline in profits is due to an increase in costs

These are broad hypotheses that should have been used near the beginning of the case interview as a starting point to narrow down the answer.

What to Do if Your Case Interview Hypothesis is Wrong

If your hypothesis is completely wrong, do not worry. This is not a reflection of your case interview capabilities or skills. Even the best case interview candidates will get their initial hypothesis wrong about 50% of the time.

If your hypothesis is wrong, you will need to develop another hypothesis. Most likely, the direction of the case that you are going down is going to be a dead end. Therefore, you need to be flexible and adaptable in developing a new hypothesis and picking a new direction of the case to pursue.

Here is an example of what this might look like: 

Candidate : I think the decline in profits could be driven by a decrease in revenue. Do we have further information on how revenues have changed over the past few years?

Interviewer : Revenues have remained flat.

Candidate : Okay, then a decline in revenue is not the driver behind the decline in profits. Therefore, I’d like to shift my focus onto costs. If revenue has been flat, costs must have gone up, which is why profits have gone down. Do we have a breakdown of our client’s costs and how they’ve changed over the past few years?

What to Do if Your Case Interview Hypothesis is Right  

If your hypothesis is right, know that you have made a significant step towards solving the case. However, the case does not end just because your hypothesis is correct. The next step is to refine your hypothesis by making it more specific.

Remember, at the end of the case interview, you want to recommend a specific course of action that the client should take.

Your initial hypothesis will likely be a fairly broad statement. Even if your hypothesis is correct, you may not have an idea of a specific course of action the client should take. Therefore, spend the time to hone in on the exact answer.

Here is an example of what this might look like:

Interviewer : Revenues have decreased by 30% over the past few years.

Candidate : Okay, then this means that a decline in revenue is a driver behind the decline in profits. I’d like to identify if there is a particular component of revenue that is responsible. Do we have a breakdown of revenue by some kind of meaningful segmentation?

  Interviewer : Yes, if we break down revenue by country, we see that revenue in China has declined significantly.

Candidate:  Okay, I think we have found the primary driver for the decline in profits. A decline in revenue in China is causing the decline in profits. I’d like to understand why this is happening by looking at customer needs in China, recent competitor moves, and market trends that may be impacting sales.

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How to Develop a Good Research Hypothesis

The story of a research study begins by asking a question. Researchers all around the globe are asking curious questions and formulating research hypothesis. However, whether the research study provides an effective conclusion depends on how well one develops a good research hypothesis. Research hypothesis examples could help researchers get an idea as to how to write a good research hypothesis.

This blog will help you understand what is a research hypothesis, its characteristics and, how to formulate a research hypothesis

Table of Contents

What is Hypothesis?

Hypothesis is an assumption or an idea proposed for the sake of argument so that it can be tested. It is a precise, testable statement of what the researchers predict will be outcome of the study.  Hypothesis usually involves proposing a relationship between two variables: the independent variable (what the researchers change) and the dependent variable (what the research measures).

What is a Research Hypothesis?

Research hypothesis is a statement that introduces a research question and proposes an expected result. It is an integral part of the scientific method that forms the basis of scientific experiments. Therefore, you need to be careful and thorough when building your research hypothesis. A minor flaw in the construction of your hypothesis could have an adverse effect on your experiment. In research, there is a convention that the hypothesis is written in two forms, the null hypothesis, and the alternative hypothesis (called the experimental hypothesis when the method of investigation is an experiment).

Characteristics of a Good Research Hypothesis

As the hypothesis is specific, there is a testable prediction about what you expect to happen in a study. You may consider drawing hypothesis from previously published research based on the theory.

A good research hypothesis involves more effort than just a guess. In particular, your hypothesis may begin with a question that could be further explored through background research.

To help you formulate a promising research hypothesis, you should ask yourself the following questions:

• Is the language clear and focused?
• What is the relationship between your hypothesis and your research topic?
• Is your hypothesis testable? If yes, then how?
• What are the possible explanations that you might want to explore?
• Does your hypothesis include both an independent and dependent variable?
• Can you manipulate your variables without hampering the ethical standards?
• Does your research predict the relationship and outcome?
• Is your research simple and concise (avoids wordiness)?
• Is it clear with no ambiguity or assumptions about the readers’ knowledge
• Is your research observable and testable results?
• Is it relevant and specific to the research question or problem?

The questions listed above can be used as a checklist to make sure your hypothesis is based on a solid foundation. Furthermore, it can help you identify weaknesses in your hypothesis and revise it if necessary.

Source: Educational Hub

How to formulate a research hypothesis.

A testable hypothesis is not a simple statement. It is rather an intricate statement that needs to offer a clear introduction to a scientific experiment, its intentions, and the possible outcomes. However, there are some important things to consider when building a compelling hypothesis.

1. State the problem that you are trying to solve.

Make sure that the hypothesis clearly defines the topic and the focus of the experiment.

2. Try to write the hypothesis as an if-then statement.

Follow this template: If a specific action is taken, then a certain outcome is expected.

3. Define the variables

Independent variables are the ones that are manipulated, controlled, or changed. Independent variables are isolated from other factors of the study.

Dependent variables , as the name suggests are dependent on other factors of the study. They are influenced by the change in independent variable.

4. Scrutinize the hypothesis

Evaluate assumptions, predictions, and evidence rigorously to refine your understanding.

Types of Research Hypothesis

The types of research hypothesis are stated below:

1. Simple Hypothesis

It predicts the relationship between a single dependent variable and a single independent variable.

2. Complex Hypothesis

It predicts the relationship between two or more independent and dependent variables.

3. Directional Hypothesis

It specifies the expected direction to be followed to determine the relationship between variables and is derived from theory. Furthermore, it implies the researcher’s intellectual commitment to a particular outcome.

4. Non-directional Hypothesis

It does not predict the exact direction or nature of the relationship between the two variables. The non-directional hypothesis is used when there is no theory involved or when findings contradict previous research.

5. Associative and Causal Hypothesis

The associative hypothesis defines interdependency between variables. A change in one variable results in the change of the other variable. On the other hand, the causal hypothesis proposes an effect on the dependent due to manipulation of the independent variable.

6. Null Hypothesis

Null hypothesis states a negative statement to support the researcher’s findings that there is no relationship between two variables. There will be no changes in the dependent variable due the manipulation of the independent variable. Furthermore, it states results are due to chance and are not significant in terms of supporting the idea being investigated.

7. Alternative Hypothesis

It states that there is a relationship between the two variables of the study and that the results are significant to the research topic. An experimental hypothesis predicts what changes will take place in the dependent variable when the independent variable is manipulated. Also, it states that the results are not due to chance and that they are significant in terms of supporting the theory being investigated.

Research Hypothesis Examples of Independent and Dependent Variables

Research Hypothesis Example 1 The greater number of coal plants in a region (independent variable) increases water pollution (dependent variable). If you change the independent variable (building more coal factories), it will change the dependent variable (amount of water pollution).

Research Hypothesis Example 2 What is the effect of diet or regular soda (independent variable) on blood sugar levels (dependent variable)? If you change the independent variable (the type of soda you consume), it will change the dependent variable (blood sugar levels)

You should not ignore the importance of the above steps. The validity of your experiment and its results rely on a robust testable hypothesis. Developing a strong testable hypothesis has few advantages, it compels us to think intensely and specifically about the outcomes of a study. Consequently, it enables us to understand the implication of the question and the different variables involved in the study. Furthermore, it helps us to make precise predictions based on prior research. Hence, forming a hypothesis would be of great value to the research. Here are some good examples of testable hypotheses.

More importantly, you need to build a robust testable research hypothesis for your scientific experiments. A testable hypothesis is a hypothesis that can be proved or disproved as a result of experimentation.

Importance of a Testable Hypothesis

To devise and perform an experiment using scientific method, you need to make sure that your hypothesis is testable. To be considered testable, some essential criteria must be met:

• There must be a possibility to prove that the hypothesis is true.
• There must be a possibility to prove that the hypothesis is false.
• The results of the hypothesis must be reproducible.

Without these criteria, the hypothesis and the results will be vague. As a result, the experiment will not prove or disprove anything significant.

What are your experiences with building hypotheses for scientific experiments? What challenges did you face? How did you overcome these challenges? Please share your thoughts with us in the comments section.

Frequently Asked Questions

The steps to write a research hypothesis are: 1. Stating the problem: Ensure that the hypothesis defines the research problem 2. Writing a hypothesis as an 'if-then' statement: Include the action and the expected outcome of your study by following a ‘if-then’ structure. 3. Defining the variables: Define the variables as Dependent or Independent based on their dependency to other factors. 4. Scrutinizing the hypothesis: Identify the type of your hypothesis

Hypothesis testing is a statistical tool which is used to make inferences about a population data to draw conclusions for a particular hypothesis.

Hypothesis in statistics is a formal statement about the nature of a population within a structured framework of a statistical model. It is used to test an existing hypothesis by studying a population.

Research hypothesis is a statement that introduces a research question and proposes an expected result. It forms the basis of scientific experiments.

The different types of hypothesis in research are: • Null hypothesis: Null hypothesis is a negative statement to support the researcher’s findings that there is no relationship between two variables. • Alternate hypothesis: Alternate hypothesis predicts the relationship between the two variables of the study. • Directional hypothesis: Directional hypothesis specifies the expected direction to be followed to determine the relationship between variables. • Non-directional hypothesis: Non-directional hypothesis does not predict the exact direction or nature of the relationship between the two variables. • Simple hypothesis: Simple hypothesis predicts the relationship between a single dependent variable and a single independent variable. • Complex hypothesis: Complex hypothesis predicts the relationship between two or more independent and dependent variables. • Associative and casual hypothesis: Associative and casual hypothesis predicts the relationship between two or more independent and dependent variables. • Empirical hypothesis: Empirical hypothesis can be tested via experiments and observation. • Statistical hypothesis: A statistical hypothesis utilizes statistical models to draw conclusions about broader populations.

Wow! You really simplified your explanation that even dummies would find it easy to comprehend. Thank you so much.

Thanks a lot for your valuable guidance.

I enjoy reading the post. Hypotheses are actually an intrinsic part in a study. It bridges the research question and the methodology of the study.

Useful piece!

This is awesome.Wow.

It very interesting to read the topic, can you guide me any specific example of hypothesis process establish throw the Demand and supply of the specific product in market

Nicely explained

It is really a useful for me Kindly give some examples of hypothesis

It was a well explained content ,can you please give me an example with the null and alternative hypothesis illustrated

clear and concise. thanks.

So Good so Amazing

Good to learn

Thanks a lot for explaining to my level of understanding

Explained well and in simple terms. Quick read! Thank you

It awesome. It has really positioned me in my research project

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• Introduction to Hypothesis Testing in R
• Testing of Hypothesis in R
• p-value: An Alternative way of Hypothesis Testing:
• t-test: Hypothesis Testing of Population Mean when Population Standard Deviation is Unknown:
• Two Samples Tests: Hypothesis Testing for the difference between two population means
• Hypothesis Testing for Equality of Population Variances
• Let’s Look at some Case studies:
• References:

Hypothesis Testing in R- Introduction Examples and Case Study

– By Dr. Masood H. Siddiqui, Professor & Dean (Research) at Jaipuria Institute of Management, Lucknow

The premise of Data Analytics is based on the philosophy of the “ Data-Driven Decision Making ” that univocally states that decision-making based on data has less probability of error than those based on subjective judgement and gut-feeling. So, we require data to make decisions and to answer the business/functional questions. Data may be collected from each and every unit/person, connected with the problem-situation (totality related to the situation). This is known as Census or Complete Enumeration and the ‘totality’ is known as Population . Obv.iously, this will generally give the most optimum results with maximum correctness but this may not be always possible. Actually, it is rare to have access to information from all the members connected with the situation. So, due to practical considerations, we take up a representative subset from the population, known as Sample . A sample is a representative in the sense that it is expected to exhibit the properties of the population, from where it has been drawn. 

So, we have evidence (data) from the sample and we need to decide for the population on the basis of that data from the sample i.e. inferring about the population on the basis of a sample. This concept is known as Statistical Inference . 

Before going into details, we should be clear about certain terms and concepts that will be useful:

Parameter and Statistic

Parameters are unknown constants that effectively define the population distribution , and in turn, the population , e.g. population mean (µ), population standard deviation (σ), population proportion (P) etc. Statistics are the values characterising the sample i.e. characteristics of the sample. They are actually functions of sample values e. g. sample mean (x̄), sample standard deviation (s), sample proportion (p) etc. 

Sampling Distribution

A large number of samples may be drawn from a population. Each sample may provide a value of sample statistic, so there will be a distribution of sample statistic value from all the possible samples i.e. frequency distribution of sample statistic . This is better known as Sampling distribution of the sample statistic . Alternatively, the sample statistic is a random variable , being a function of sample values (which are random variables themselves). The probability distribution of the sample statistic is known as sampling distribution of sample statistic. Just like any other distribution, sampling distribution may partially be described by its mean and standard deviation . The standard deviation of sampling distribution of a sample statistic is better known as the Standard Error of the sample statistic. 

Standard Error

It is a measure of the extent of variation among different values of statistics from different possible samples. Higher the standard error, higher is the variation among different possible values of statistics. Hence, less will be the confidence that we may place on the value of the statistic for estimation purposes. Hence, the sample statistic having a lower value of standard error is supposed to be better for estimation of the population parameter. 

1(a). A sample of size ‘n’ has been drawn for a normal population N (µ, σ). We are considering sample mean (x̄) as the sample statistic. Then, the sampling distribution of sample statistic x̄ will follow Normal Distribution with mean µ x̄ = µ and standard error σ x̄ = σ/ √ n.

Even if the population is not following the Normal Distribution but for a large sample (n = large), the sampling distribution of x̄ will approach to (approximated by) normal distribution with mean µ x̄ = µ and standard error σ x̄ = σ/ √ n, as per the Central Limit Theorem . 

(b). A sample of size ‘n’ has been drawn for a normal population N (µ, σ), but population standard deviation σ is unknown, so in this case σ will be estimated by sample standard deviation(s). Then, sampling distribution of sample statistic x̄ will follow the student’s t distribution (with degree of freedom = n-1) having mean µ x̄ = µ and standard error σ x̄ = s/ √ n.

2. When we consider proportions for categorical data. Sampling distribution of sample proportion p =x/n (where x = Number of success out of a total of n) will follow Normal Distribution with mean µ p = P and standard error σ p = √( PQ/n), (where Q = 1-P). This is under the condition that n is large such that both np and nq should be minimum 5.

Statistical Inference

Statistical Inference encompasses two different but related problems:

1. Knowing about the population-values on the basis of data from the sample. This is known as the problem of Estimation . This is a common problem in business decision-making because of lack of complete information and uncertainty but by using sample information, the estimate will be based on the concept of data based decision making. Here, the concept of probability is used through sampling distribution to deal with the uncertainty. If sample statistics is used to estimate the population parameter , then in that situation that is known as the Estimator; {like sample mean (x̄) to estimate population mean µ, sample proportion (p) to estimate population proportion (P) etc.}. A particular value of the estimator for a given sample is known as Estimate . For example, if we want to estimate average sales of 1000+ outlets of a retail chain and we have taken a sample of 40 outlets and sample mean ( estimator ) x̄ is 40000. Then the estimate will be 40000.

There are two types of estimation:

• Point Estimation : Single value/number of the estimator is used to estimate unknown population parameters. The example is given above. 
• Confidence Interval/Interval Estimation : Interval Estimate gives two values of sample statistic/estimator, forming an interval or range, within which an unknown population is expected to lie. This interval estimate provides confidence with the interval vis-à-vis the population parameter. For example: 95% confidence interval for population mean sale is (35000, 45000) i.e. we are 95% confident that interval estimate will contain the population parameter.

2. Examining the declaration/perception/claim about the population for its correctness on the basis of sample data. This is known as the problem of Significant Testing or Testing of Hypothesis . This belongs to the Confirmatory Data Analysis , as to confirm or otherwise the hypothesis developed in the earlier Exploratory Data Analysis stage.

One Sample Tests

z-test – Hypothesis Testing of Population Mean when Population Standard Deviation is known:

Hypothesis testing in R starts with a claim or perception of the population. Hypothesis may be defined as a claim/ positive declaration/ conjecture about the population parameter. If hypothesis defines the distribution completely, it is known as Simple Hypothesis, otherwise Composite Hypothesis . 

Hypothesis may be classified as: 

Null Hypothesis (H 0 ): Hypothesis to be tested is known as Null Hypothesis (H 0 ). It is so known because it assumes no relationship or no difference from the hypothesized value of population parameter(s) or to be nullified. 

Alternative Hypothesis (H 1 ): The hypothesis opposite/complementary to the Null Hypothesis .

Note: Here, two points are needed to be considered. First, both the hypotheses are to be constructed only for the population parameters. Second, since H 0 is to be tested so it is H 0 only that may be rejected or failed to be rejected (retained).

Hypothesis Testing: Hypothesis testing a rule or statistical process that may be resulted in either rejecting or failing to reject the null hypothesis (H 0 ).

The Five Steps Process of Hypothesis Testing

Here, we take an example of Testing of Mean:

1. Setting up the Hypothesis:

This step is used to define the problem after considering the business situation and deciding the relevant hypotheses H 0 and H 1 , after mentioning the hypotheses in the business language.

We are considering the random variable X = Quarterly sales of the sales executive working in a big FMCG company. Here, we assume that sales follow normal distribution with mean µ (unknown) and standard deviation σ (known) . The value of the population parameter (population mean) to be tested be µ 0 (Hypothesised Value).

Here the hypothesis may be:

H 0 : µ = µ 0  or µ ≤ µ 0  or µ ≥ µ 0  (here, the first one is Simple Hypothesis , rest two variants are composite hypotheses ) 

H 1 : µ > µ 0 or

H 1 : µ < µ 0 or

H 1 : µ ≠ µ 0 

(Here, all three variants are Composite Hypothesis )

2. Defining Test and Test Statistic:

The test is the statistical rule/process of deciding to ‘reject’ or ‘fail to reject’ (retain) the H0. It consists of dividing the sample space (the totality of all the possible outcomes) into two complementary parts. One part, providing the rejection of H 0 , known as Critical Region . The other part, representing the failing to reject H 0 situation , is known as Acceptance Region .

The logic is, since we have evidence only from the sample, we use sample data to decide about the rejection/retaining of the hypothesised value. Sample, in principle, can never be a perfect replica of the population so we do expect that there will be variation in between population and sample values. So the issue is not the difference but actually the magnitude of difference . Suppose, we want to test the claim that the average quarterly sale of the executive is 75k vs sale is below 75k. Here, the hypothesised value for the population mean is µ 0 =75 i.e.

H 0 : µ = 75

H 1 : µ < 75.

Suppose from a sample, we get a value of sample mean x̄=73. Here, the difference is too small to reject the claim under H 0 since the chances (probability) of happening of such a random sample is quite large so we will retain H 0 . Suppose, in some other situation, we get a sample with a sample mean x̄=33. Here, the difference between the sample mean and hypothesised population mean is too large. So the claim under H 0 may be rejected as the chance of having such a sample for this population is quite low.

So, there must be some dividing value (s) that differentiates between the two decisions: rejection (critical region) and retention (acceptance region), this boundary value is known as the critical value .

Type I and Type II Error:

There are two types of situations (H 0 is true or false) which are complementary to each other and two types of complementary decisions (Reject H 0 or Failing to Reject H 0 ). So we have four types of cases:

So, the two possible errors in hypothesis testing can be:

Type I Error = [Reject H 0 when H 0 is true]

Type II Error = [Fails to reject H 0 when H 0 is false].

Type I Error is also known as False Positive and Type II Error is also known as False Negative in the language of Business Analytics.

Since these two are probabilistic events, so we measure them using probabilities:

α = Probability of committing Type I error = P [Reject H 0 / H 0 is true] 

β = Probability of committing Type II error = P [Fails to reject H 0 / H 0 is false].

For a good testing procedure, both types of errors should be low (minimise α and β) but simultaneous minimisation of both the errors is not possible because they are interconnected. If we minimize one, the other will increase and vice versa. So, one error is fixed and another is tried to be minimised. Normally α is fixed and we try to minimise β. If Type I error is critical, α is fixed at a low value (allowing β to take relatively high value) otherwise at relatively high value (to minimise β to a low value, Type II error being critical).

Example: In Indian Judicial System we have H 0 : Under trial is innocent. Here, Type I Error = An innocent person is sentenced, while Type II Error = A guilty person is set free. Indian (Anglo Saxon) Judicial System considers type I error to be critical so it will have low α for this case.

Power of the test = 1- β = P [Reject H 0 / H 0 is false].

Higher the power of the test, better it is considered and we look for the Most Powerful Test since power of test can be taken as the probability that the test will detect a deviation from H 0 given that the deviation exists.

One Tailed and Two Tailed Tests of Hypothesis:

H 0 : µ ≤ µ 0  

H 1 : µ > µ 0 

When x̄ is significantly above the hypothesized population mean µ 0 then H 0 will be rejected and the test used will be right tailed test (upper tailed test) since the critical region (denoting rejection of H 0 will be in the right tail of the normal curve (representing sampling distribution of sample statistic x̄). (The critical region is shown as a shaded portion in the figure).

H 0 : µ ≥ µ 0

H 1 : µ < µ 0 

In this case, if x̄ is significantly below the hypothesised population mean µ 0 then H 0 will be rejected and the test used will be the left tailed test (lower tailed test) since the critical region (denoting rejection of H 0 ) will be in the left tail of the normal curve (representing sampling distribution of sample statistic x̄). (The critical region is shown as a shaded portion in the figure).

These two tests are also known as One-tailed tests as there will be a critical region in only one tail of the sampling distribution.

H 0 : µ = µ 0

H 1 : µ ≠ µ 0

When x̄ is significantly different (significantly higher or lower than) from the hypothesised population mean µ 0 , then H 0 will be rejected. In this case, the two tailed test will be applicable because there will be two critical regions (denoting rejection of H 0 ) on both the tails of the normal curve (representing sampling distribution of sample statistic x̄). (The critical regions are shown as shaded portions in the figure). 

Hypothesis Testing using Standardized Scale: Here, instead of measuring sample statistic (variable) in the original unit, standardised value is taken (better known as test statistic ). So, the comparison will be between observed value of test statistic (estimated from sample), and critical value of test statistic (obtained from relevant theoretical probability distribution).

Here, since population standard deviation (σ) is known, so the test statistics :

Z=  (x- µx̄ x )/σ x̄ = (x- µ 0 )/(σ/√n)  follows Standard Normal Distribution N (0, 1).

3.Deciding the Criteria for Rejection or otherwise:

As discussed, hypothesis testing means deciding a rule for rejection/retention of H 0 . Here, the critical region decides rejection of H 0 and there will be a value, known as Critical Value , to define the boundary of the critical region/acceptance region. The size (probability/area) of a critical region is taken as α . Here, α may be known as Significance Level , the level at which hypothesis testing is performed. It is equal to type I error , as discussed earlier.

Suppose, α has been decided as 5%, so the critical value of test statistic (Z) will be +1.645 (for right tail test), -1.645 (for left tail test). For the two tails test, the critical value will be -1.96 and +1.96 (as per the Standard Normal Distribution Z table). The value of α may be chosen as per the criticality of type I and type II. Normally, the value of α is taken as 5% in most of the analytical situations (Fisher, 1956). 

4. Taking sample, data collection and estimating the observed value of test statistic:

In this stage, a proper sample of size n is taken and after collecting the data, the values of sample mean (x̄) and the observed value of test statistic Z obs is being estimated, as per the test statistic formula.

5. Taking the Decision to reject or otherwise:

On comparing the observed value of Test statistic with that of the critical value, we may identify whether the observed value lies in the critical region (reject H 0 ) or in the acceptance region (do not reject H 0 ) and decide accordingly.

• Right Tailed Test:          If Z obs > 1.645                   : Reject H 0 at 5% Level of Significance.
• Left Tailed Test:            If Z obs < -1.645                  : Reject H 0 at 5% Level of Significance.
• Two Tailed Test:    If Z obs > 1.96 or If Z obs < -1.96  : Reject H 0 at 5% Level of Significance.

There is an alternative approach for hypothesis testing, this approach is very much used in all the software packages. It is known as probability value/ prob. value/ p-value. It gives the probability of getting a value of statistic this far or farther from the hypothesised value if H0 is true. This denotes how likely is the result that we have observed. It may be further explained as the probability of observing the test statistic if H 0 is true i.e. what are the chances in support of occurrence of H 0 . If p-value is small, it means there are less chances (rare case) in favour of H 0 occuring, as the difference between a sample value and hypothesised value is significantly large so H 0 may be rejected, otherwise it may be retained.

If p-value < α       : Reject H 0

If p-value ≥ α : Fails to Reject H 0

So, it may be mentioned that the level of significance (α) is the maximum threshold for p-value. It should be noted that p-value (two tailed test) = 2* p-value (one tailed test). 

Note: Though the application of z-test requires the ‘Normality Assumption’ for the parent population with known standard deviation/ variance but if sample is large (n>30), the normality assumption for the parent population may be relaxed, provided population standard deviation/variance is known (as per Central Limit Theorem).

As we discussed in the previous case, for testing of population mean, we assume that sample has been drawn from the population following normal distribution mean µ and standard deviation σ. In this case test statistic Z = (x- µ 0 )/(σ/√n)  ~ Standard Normal Distribution N (0, 1). But in the situations where population s.d. σ is not known (it is a very common situation in all the real life business situations), we estimate population s.d. (σ) by sample s.d. (s).

Hence the corresponding test statistic: 

t=  (x- µx̄ x )/σ x̄ = (x- µ 0 )/(s/√n) follows Student’s t distribution with (n-1) degrees of freedom. One degree of freedom has been sacrificed for estimating population s.d. (σ) by sample s.d. (s).

Everything else in the testing process remains the same. 

t-test is not much affected if assumption of normality is violated provided data is slightly asymmetrical (near to symmetry) and data-set does not contain outliers.  

t-distribution:

The Student’s t-distribution, is much similar to the normal distribution. It is a symmetric distribution (bell shaped distribution). In general Student’s t distribution is flatter i.e. having heavier tails. Shape of t distribution changes with degrees of freedom (exact distribution) and becomes approximately close to Normal distribution for large n. 

In many business decision making situations, decision makers are interested in comparison of two populations i.e. interested in examining the difference between two population parameters. Example: comparing sales of rural and urban outlets, comparing sales before the advertisement and after advertisement, comparison of salaries in between male and female employees, comparison of salary before and after joining the data science courses etc.

Independent Samples and Dependent (Paired Samples):

Depending on method of collection data for the two samples, samples may be termed as independent or dependent samples. If two samples are drawn independently without any relation (may be from different units/respondents in the two samples), then it is said that samples are drawn independently . If samples are related or paired or having two observations at different points of time on the same unit/respondent, then the samples are said to be dependent or paired .  This approach (paired samples) enables us to compare two populations after controlling the extraneous effect on them.  

Testing the Difference Between Means: Independent Samples

Two samples z test:.

We have two populations, both following Normal populations as N (µ 1 , σ 1 ) and N (µ 2 , σ 2 ). We want to test the Null Hypothesis:

H 0 : µ 1 – µ 2 = θ or µ 1 – µ 2 ≤ θ or µ 1 – µ 2 ≥ θ 

Alternative hypothesis:

H 1 : µ 1 – µ 2 > θ or

H 0 : µ 1 – µ 2 < θ or

H 1 : µ 1 – µ 2 ≠ θ 

(where θ may take any value as per the situation or θ =0). 

Two samples of size n 1 and n 2 have been taken randomly from the two normal populations respectively and the corresponding sample means are x̄ 1 and x̄ 2 .

Here, we are not interested in individual population parameters (means) but in the difference of population means (µ 1 – µ 2 ). So, the corresponding statistic is = (x̄ 1 – x̄ 2 ).

According, sampling distribution of the statistic (x̄ 1 – x̄ 2 ) will follow Normal distribution with mean µ x̄ = µ 1 – µ 2 and standard error σ x̄ = √ (σ² 1 / n 1 + σ² 2 / n 2 ). So, the corresponding Test Statistics will be: 

Other things remaining the same as per the One Sample Tests (as explained earlier).

Two Independent Samples t-Test (when Population Standard Deviations are Unknown):

Here, for testing the difference of two population mean, we assume that samples have been drawn from populations following Normal Distributions, but it is a very common situation that population standard deviations (σ 1 and σ 2 ) are unknown. So they are estimated by sample standard deviations (s 1 and s 2 ) from the respective two samples.

Here, two situations are possible:

(a) Population Standard Deviations are unknown but equal:

In this situation (where σ 1 and σ 2 are unknown but assumed to be equal), sampling distribution of the statistic (x̄ 1 – x̄ 2 ) will follow Student’s t distribution with mean µ x̄ = µ 1 – µ 2 and standard error σ x̄ = √ Sp 2 (1/ n 1 + 1/ n 2 ).  Where Sp 2 is the pooled estimate, given by:

Sp 2 = (n 1 -1) S 1 2 +(n 2 -1) S 2 2 /(n 1 +n 2 -2)

So, the corresponding Test Statistics will be: 

t =  {(x̄ 1 – x̄ 2 ) – (µ 1 – µ 2 )}/{√ Sp 2 (1/n 1 +1/n 2 )}

Here, t statistic will follow t distribution with d.f. (n 1 +n 2 -2).

(b) Population Standard Deviations are unknown but unequal:

In this situation (where σ 1 and σ 2 are unknown and unequal).

Then the sampling distribution of the statistic (x̄ 1 – x̄ 2 ) will follow Student’s t distribution with mean µ x̄ = µ 1 – µ 2 and standard error Se =√ (s² 1 / n 1 + s² 2 / n 2 ). 

t =  {(x̄ 1 – x̄ 2 ) – (µ 1 – µ 2 )}/{√ (s2 1 /n 1 +s2 2 /n 2 )}

The test statistic will follow Student’s t distribution with degrees of freedom (rounding down to nearest integers):

As discussed in the aforementioned two cases, it is important to figure out whether the two population variances are equal or otherwise. For this purpose, F test can be employed as:

H 0 : σ² 1 = σ² 2 and H 1 : σ² 1 ≠ σ² 2

Two samples of sizes n 1 and n 2 have been drawn from two populations respectively. They provide sample standard deviations s 1 and s 2 . The test statistic is F =  s 1 ²/s 2 ²

The test statistic will follow F-distribution with (n 1 -1) df for numerator and (n 2 -1) df for denominator.

Note: There are many other tests that are applied for this purpose.

Paired Sample t-Test (Testing Difference between Means with Dependent Samples):

As discussed earlier, in the situation of Before-After Tests, to examine the impact of any intervention like a training program, health program, any campaign to change status, we have two set of observations (x i and y i ) on the same test unit (respondent or units) before and after the program. Each sample has “n” paired observations. The Samples are said to be dependent or paired.

Here, we consider a random variable: d i = x i – y i . 

Accordingly, the sampling distribution of the sample statistic (sample mean of the differentces d i ’s) will follow Student’s t distribution with mean = θ and standard error = sd/ √ n, where sd is the sample standard deviation of d i ’s.

Hence, the corresponding test statistic: t = (d̅- θ)/sd/√n will follow t distribution with (n-1).

As we have observed, paired t-test is actually one sample test since two samples got converted into one sample of differences. If ‘Two Independent Samples t-Test’ and ‘Paired t-test’ are applied on the same data set then two tests will give much different results because in case of Paired t-Test, standard error will be quite low as compared to Two Independent Samples t-Test. The Paired t-Test is applied essentially on one sample while the earlier one is applied on two samples. The result of the difference in standard error is that t-statistic will take larger value in case of ‘Paired t-Test’ in comparison to the ‘Two Independent Samples t-Test and finally p-values get affected accordingly. 

t-Test in SPSS:

One sample t-test.

• Analyze => Compare Means => One-Sample T-Test to open relevant dialogue box.
• Test variable (variable under consideration) in the Test variable(s) box and hypothesised value µ 0 = 75 (for example) in the Test Value box are to be entered.
• Press Ok to have the output. 

Here, we consider the example of Ventura Sales, and want to examine the perception that average sales in the first quarter is 75 (thousand) vs it is not. So, the Hypotheses:

Null Hypothesis H 0 : µ=75  

Alternative Hypothesis H 1 : µ≠75

One-Sample Statistics

Descriptive table showing the sample size n = 60, sample mean x̄=72.02, sample sd s=9.724.

One-Sample Test

One Sample Test Table shows the result of the t-test. Here, test statistic value (from the sample) is t = -2.376 and the corresponding p-value (2 tailed) = 0.021 <0.05. So, H 0 got rejected and it can be said that the claim of average first quarterly sales being 75 (thousand) does not hold. 

Two Independent Samples t-Test

• Analyze => Compare Means => Independent-Samples T-Test to open the dialogue box.
• Enter the Test variable (variable under consideration) in the Test Variable(s) box and variable categorising the groups in the Grouping Variable box.
• Define the groups by clicking on Define Groups and enter the relevant numeric-codes into the relevant groups in the Define Groups sub-dialogue box. Press Continue to return back to the main dialogue box.

We continue with the example of Ventura Sales, and want to compare the average first quarter sales with respect to Urban Outlets and Rural Outlets (two independent samples/groups). Here, the claim is that urban outlets are giving lower sales as compared to rural outlets. So, the Hypotheses:

H 0 : µ 1 – µ 2 = 0 or µ 1 = µ 2   (Where, µ 1 = Population Mean Sale of Urban Outlets and µ 2 = Population Mean Sale of Rural Outlets)

H 1 : µ 1 < µ 2  

Group Statistics

Descriptive table showing the sample sizes n 1 =37 and n 2 =23, sample means x̄ 1 =67.86 and x̄ 2 =78.70, sample standard deviations s 1 =8.570 and s 2 = 7.600.

The below table is the Independent Sample Test Table, proving all the relevant test statistics and p-values.  Here, both the outputs for Equal Variance (assumed) and Unequal Variance (assumed) are presented.

Independent Samples Test

So, we have to figure out whether we should go for ‘equal variance’ case or for ‘unequal variances’ case. 

Here, Levene’s Test for Equality of Variances has to be applied for this purpose with the hypotheses: H 0 : σ² 1 = σ² 2 and H 1 : σ² 1 ≠ σ² 2 . The p-value (Sig) = 0.460 >0.05, so we can’t reject (so retained) H 0 . Hence, variances can be assumed to be equal. 

So, “Equal Variances assumed” case is to be taken up. Accordingly, the value of t statistic = -4.965 and the p-value (two tailed) = 0.000, so the p-value (one tailed) = 0.000/2 = 0.000 <0.05. Hence, H 0 got rejected and it can be said that urban outlets are giving lower sales in the first quarter. So, the claim stands.

Paired t-Test (Testing Difference between Means with Dependent Samples):

•   Analyze => Compare Means => Paired-Samples T-Test to open the dialogue box.
• Enter the relevant pair of variables (paired samples) in the Paired Variables box.
• After entering the paired samples, press Ok to have the output.

We continue with the example of Ventura Sales, and want to compare the average first quarter sales with the second quarter sales. Some sales promotion interventions were executed with an expectation of increasing sales in the second quarter. So, the Hypotheses:

H 0 : µ 1 = µ 2 (Where, µ 1 = Population Mean Sale of Quarter-I and µ 2 = Population Mean Sale of Quarter-II)

H 1 : µ 1 < µ 2 (representing the increase of sales i.e. implying the success of sales interventions)

Paired Samples Statistics

Descriptive table showing the sample size n=60, sample means x̄ 1 =72.02 and x̄ 2 =72.43.

As per the following output table (Paired Samples Test), sample mean of differences d̅ = -0.417 with standard deviation of differences sd = 8.011 and value of t statistic = -0.403. Accordingly, the p-value (two tailed) = 0.688, so the p-value (one tailed) = 0.688/2 = 0.344 > 0.05. So, there have not been sufficient reasons to Reject H 0 i.e. H 0 should be retained. So, the effectiveness (success) of the sales promotion interventions is doubtful i.e. it didn’t result in significant increase in sales, provided all other extraneous factors remain the same.

Paired Samples Test   

t-Test Application One Sample

Experience Marketing Services reported that the typical American spends a mean of 144 minutes (2.4 hours) per day accessing the Internet via a mobile device. (Source: The 2014 Digital Marketer, available at ex.pn/1kXJifX.) To test the validity of this statement, you select a sample of 30 friends and family. The result for the time spent per day accessing the Internet via a mobile device (in minutes) are stored in Internet_Mobile_Time.csv file.

Is there evidence that the populations mean time spent per day accessing the Internet via a mobile device is different from 144 minutes? Use the p-value approach and a level of significance of 0.05

What assumption about the population distribution is needed to conduct the test in A?

Solution In R

[1] 1.224674

[1] 0.2305533

[1] “Accepted”

Independent t-test two sample

A hotel manager looks to enhance the initial impressions that hotel guests have when they check-in. Contributing to initial impressions is the time it takes to deliver a guest’s luggage to the room after check-in. A random sample of 20 deliveries on a particular day was selected each from Wing A and Wing B of the hotel. The data collated is given in Luggage.csv file. Analyze the data and determine whether there is a difference in the mean delivery times in the two wings of the hotel. (use alpha = 0.05).

    Two Sample t-test data:  WingA and WingB t = 5.1615, df = 38, p-value = 4.004e-06 alternative hypothesis: true difference in means is greater than 0 95 percent confidence interval: 1.531895   Inf sample estimates: mean of x mean of y  10.3975 8.1225 > t.test(WingA,WingB)    Welch Two Sample t-test

t = 5.1615, df = 37.957, p-value = 8.031e-06 alternative hypothesis: true difference in means is not equal to 0 95 per cent confidence interval: 1.38269 3.16731 sample estimates: mean of x mean of y  10.3975 8.1225

Case Study- Titan Insurance Company

The Titan Insurance Company has just installed a new incentive payment scheme for its lift policy salesforce. It wants to have an early view of the success or failure of the new scheme. Indications are that the sales force is selling more policies, but sales always vary in an unpredictable pattern from month to month and it is not clear that the scheme has made a significant difference.

Life Insurance companies typically measure the monthly output of a salesperson as the total sum assured for the policies sold by that person during the month. For example, suppose salesperson X has, in the month, sold seven policies for which the sums assured are £1000, £2500, £3000, £5000, £10000, £35000. X’s output for the month is the total of these sums assured, £61,500.

Titan’s new scheme is that the sales force receives low regular salaries but are paid large bonuses related to their output (i.e. to the total sum assured of policies sold by them). The scheme is expensive for the company, but they are looking for sales increases which more than compensate. The agreement with the sales force is that if the scheme does not at least break even for the company, it will be abandoned after six months.

The scheme has now been in operation for four months. It has settled down after fluctuations in the first two months due to the changeover.

To test the effectiveness of the scheme, Titan has taken a random sample of 30 salespeople measured their output in the penultimate month before changeover and then measured it in the fourth month after the changeover (they have deliberately chosen months not too close to the changeover). Ta ble 1 shows t he outputs of the salespeople in Table 1

Data preparation

Since the given data are in 000, it will be better to convert them in thousands. Problem 1 Describe the five per cent significance test you would apply to these data to determine whether the new scheme has significantly raised outputs? What conclusion does the test lead to? Solution: It is asked that whether the new scheme has significantly raised the output, it is an example of the one-tailed t-test. Note: Two-tailed test could have been used if it was asked “new scheme has significantly changed the output” Mean of amount assured before the introduction of scheme = 68450 Mean of amount assured after the introduction of scheme = 72000 Difference in mean = 72000 – 68450 = 3550 Let, μ1 = Average sums assured by salesperson BEFORE changeover. μ2 = Average sums assured by salesperson AFTER changeover. H0: μ1 = μ2  ; μ2 – μ1 = 0 HA: μ1 < μ2   ; μ2 – μ1 > 0 ; true difference of means is greater than zero. Since population standard deviation is unknown, paired sample t-test will be used.

Since p-value (=0.06529) is higher than 0.05, we accept (fail to reject) NULL hypothesis. The new scheme has NOT significantly raised outputs .

Problem 2 Suppose it has been calculated that for Titan to break even, the average output must increase by £5000. If this figure is an alternative hypothesis, what is: (a)  The probability of a type 1 error? (b)  What is the p-value of the hypothesis test if we test for a difference of $5000? (c)   Power of the test: Solution: 2.a.  The probability of a type 1 error? Solution: Probability of Type I error = significant level = 0.05 or 5% 2.b.  What is the p-value of the hypothesis test if we test for a difference of $5000? Solution: Let  μ2 = Average sums assured by salesperson AFTER changeover. μ1 = Average sums assured by salesperson BEFORE changeover. μd = μ2 – μ1   H0: μd ≤ 5000 HA: μd > 5000 This is a right tail test.

P-value = 0.6499 2.c. Power of the test. Solution: Let  μ2 = Average sums assured by salesperson AFTER changeover. μ1 = Average sums assured by salesperson BEFORE changeover. μd = μ2 – μ1   H0: μd = 4000 HA: μd > 0

H0 will be rejected if test statistics > t_critical. With α = 0.05 and df = 29, critical value for t statistic (or t_critical ) will be   1.699127. Hence, H0 will be rejected for test statistics ≥  1.699127. Hence, H0 will be rejected if for  𝑥̅ ≥ 4368.176

Graphically,

      Probability (type II error) is P(Do not reject H0 | H0 is false)       Our NULL hypothesis is TRUE at μd = 0 so that  H0: μd = 0 ; HA: μd > 0       Probability of type II error at μd = 5000

= P (Do not reject H0 | H0 is false) = P (Do not reject H0 | μd = 5000)  = P (𝑥̅ < 4368.176 | μd = 5000) = P (t <  | μd = 5000) = P (t < -0.245766) = 0.4037973

R Code: Now,  β=0.5934752, Power of test = 1- β = 1- 0.5934752 = 0.4065248

• While performing Hypothesis-Testing, Hypotheses can’t be proved or disproved since we have evidence from sample (s) only. At most, Hypotheses may be rejected or retained.
• Use of the term “accept H 0 ” in place of “do not reject” should be avoided even if the test statistic falls in the Acceptance Region or p-value ≥ α. This simply means that the sample does not provide sufficient statistical evidence to reject the H 0 . Since we have tried to nullify (reject) H 0 but we haven’t found sufficient support to do so, we may retain it but it won’t be accepted.
• Confidence Interval (Interval Estimation) can also be used for testing of hypotheses. If the hypothesis parameter falls within the confidence interval, we do not reject H 0 . Otherwise, if the hypothesised parameter falls outside the confidence interval i.e. confidence interval does not contain the hypothesized parameter, we reject H 0 .
• Downey, A. B. (2014). Think Stat: Exploratory Data Analysis , 2 nd Edition, Sebastopol, CA: O’Reilly Media Inc
• Fisher, R. A. (1956). Statistical Methods and Scientific Inference , New York: Hafner Publishing Company.
• Hogg, R. V.; McKean, J. W. & Craig, A. T. (2013). Introduction to Mathematical Statistics , 7 th Edition, New Delhi: Pearson India.
• IBM SPSS Statistics. (2020). IBM Corporation. 
• Levin, R. I.; Rubin, D. S; Siddiqui, M. H. & Rastogi, S. (2017). Statistics for Management , 8 th Edition, New Delhi: Pearson India. 

If you want to get a detailed understanding of Hypothesis testing, you can take up this hypothesis testing in machine learning course. This course will also provide you with a certificate at the end of the course.

If you want to learn more about R programming and other concepts of Business Analytics or Data Science, sign up for Great Learning ’s PG program in Data Science and Business Analytics.

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Table of contents

• Feb 28, 2023

Law & Legal Research- Hypothesis |Case Study| Questionnaire

So, what is ‘law’ really.

The law can be defined as a body of rules of action or conduct prescribed by a controlling authority, and having binding legal force/ authority. Law is an instrument which regulates human conduct/behaviour.

Law essentially means Justice, Morality, Reason, Order, and Righteous from the point of view of the society. Law also means Statutes, Acts, Rules, Regulations, Orders, and ordinances from the point of view of the legislature.

It has also been considered as a social construct that defines the extent of people’s rights and duties towards their nation.

Here are some of the definitions of law by popular jurists of their time:

According to Austin:

“A law is a command which obliges a person or persons to a course of conduct"

According to Salmond:

“The law may be defined as the body of principles recognized and applied by the State in the administration of Justice”.

Here are the four major types of law in the Indian Judicial System:

1. Criminal Law

This is a set of laws that takes cognizance of crimes committed by individuals in society. These set of laws are enforced by the police and adjudicated upon by Magistrates, the Court of Sessions, the High Court and the Supreme Court. Crimes are not taken up against an individual but against the State itself (as it is viewed as a hindrance to the harmony existing in society i.e. a social pathology).

For example: Murdering someone leads to a penalty under Section 302 of the Indian Penal Code with punishment by death, life imprisonment or fine or both.

2. Civil Law

This is a set of laws that deal with actions that aren’t a crime. It is a part of the law dealing with disputes between organizations and people. It covers different areas similar to defamation, custody of youngsters, proper training, divorce, commerce union membership, property disputes, possession points, insurance coverage claims etc.

3. Common Law

Common law is a body of unwritten laws based on legal precedents established by the courts. Common law influences the decision-making process in unusual cases where the outcome cannot be determined based on existing statutes or written rules of law.

For example: In adjudicating upon matters under the Indian Contract Act, the courts consider common law doctrines and allow case precedents that are held under the aegis of the Privy Council or the House of Lords in England.

Also, in Indian Trademark Law (Trademarks Act, 1999), the doctrine of prior use is incorporated from the existing common law rights of a proprietor.

4. Statutory Law

Statute or Statutory Law is a law established by an act of the legislature that’s signed by the Executive or Legislative body. For State law, the Acts are handled by the state legislature and signed by the State governor. In rare circumstances, the Chief (President or Governor) could refuse to assent the law or reject it, which is similar to the ‘veto’ power.

For example The Indian Contract Act of 1872, The Finance Act, of 2020, GST Act, of 2017.

How research gets added to the mix

Research is defined as the careful consideration of study regarding a particular concern or problem using scientific methods.

Legal research has been defined as a process of finding the law that governs an activity and materials that explain or analyse that law.

Legal research includes various processes ranging from information gathering to analysing the facts of a problem and communicating the investigation results. It is the amalgamation of scientific methods (pertaining to the study of data) and the law to make the latter better and more efficient for society.

A research problem can be simply defined as a problem which a researcher wants to solve or analyse and get valuable insights on. Post the indentification of "problem", generally a Hypothesis follows.

Now, what is a Hypothesis?

A Hypothesis can be defined as an idea formed beforehand which has less value than the generally formed view about a particular problem.

A hypothesis is a specific, clear, and testable proposition or predictive statement about the possible outcome of a scientific research study based on a particular property of a population, such as presumed differences between groups on a particular variable or relationships between variables.

According to Robert A Berslein and James A Dryer :

“A hypothesis is an assertion of the causal association between two properties”

Importance of Hypothesis in Legal Research:

A hypothesis gives a point of enquiry i.e. a starting point in delving into a particular research problem. In the absence of a hypothesis, a researcher is a lost ship on a wide sea without a navigation system.

Hypothesis helps a researcher in deciding the direction of the study and helps him formulate the required materials for the same.

Hypothesis provides precision to a research problem.

A hypothesis helps in drawing relevant and specific conclusions to a study.

A hypothesis helps in identifying the nature of the research and its extent.

Hypothesis helps in the collection and analysis of data by equipping the researcher with the input of “what to look for”.

The two major ways to put a hypothesis to the test

The case study method.

A case study is a research method that involves an up-close, in-depth and detailed investigation of a subject of study and its related contextual position. They can be produced following a form of research.

A case study helps in bringing the understanding of a complex issue or object. It can extend experience or add strength to the existing knowledge through previous research. Their contextual analysis revolves around a limited number of events or conditions and how they relate.

Therefore, a case study is a research method which allows a person to understand why and how to investigate questions. Here, a researcher has no control over variables, especially in situations when the case is current. In a studied case, many additional factors affect the phenomenon and can be described or analysed only by a case study.

In legal research, a case study can be used for many purposes as it allows the capacity to describe different factors and interactions with each other in real contexts. It offers various learning opportunities and experiences by influencing the different practices of theories.

For researchers, it is considered a valuable data source in terms of the diversity and complexity of educational purposes and settings. It plays a significant role in putting theories into regular practice. It is always important for the student to understand the clarity in nature and focus of the case study.

The importance of case study in research:

Major aspects of a problem can be understood and analysed easily. The results can be then presented comprehensively.

Case studies help secure a wealth of details about a unit of study and the techniques that can be used to research a similar problem. The data and direction of research can be adopted or modified to enter a new domain of a problem.

Case studies help researchers arrive at the actual human experience and attitudes which constitute the full and actual reality of a problem.

A case study is a suitable method when the problem under study forms a process rather than one isolated incident.

Case studies are regarded as scientific as they are conducted by analysing historical/empirical data about a problem.

The Questionnaire Method

A questionnaire is a research instrument that consists of a set of questions or other types of prompts that aims to collect information from a respondent. It is essentially one of the primary methods of data collection for the investigation of research problems.

Lundberg defines a questionnaire as

“a set of stimuli to which literal people are exposed to observe their behaviour under these stimuli”

According to Bogardus : A questionnaire is

“A list of questions sent to several persons for their answers and which contains standardised results that can be tabulated and treated statistically”

Types of Questionnaires:

Pauline V. Young (PV Young) classified questionnaires into:

1. Structured Questionnaires : These include pre-coded questions with well-defined skipping patterns to follow the sequence of questions. Most of the quantitative data collection operations use structured questionnaires.

As per PV young:

"Structured questionnaires are those which pose definitive, concrete and pre-oriented questions i.e. they are prepared in advance and not constructed on the spot during the questioning period”

This type of questionnaire can be categorized into further two types:

Closed-form: A questionnaire that has few alternative answers (like a yes/no, true/false)

Open-ended: A questionnaire that provides the answerer with the freedom to express his opinion without an endpoint. This method is used primarily for intensive studies.

2. Unstructured Questionnaire : These include open-ended and vague opinion-type questions. Some of them may be questions that are not in the format of interrogative sentences and the moderator or the enumerator has to elaborate on the sense of the question. Focus group discussions use such a questionnaire.

This type assumes insight, articulateness, and fact possession and aims for precision to attain maximum information regarding a particular problem. Because it is flexible, this is one of the most common types of questionnaires used by modern lawmakers.

The Distinction between Questionnaire and a normal Interview:

A questionnaire is self-administered whereas, in an interview, an interviewer needs to conduct the proceeding.

A questionnaire is geared at collecting data from literate people who can comprehend the questions whereas, interviews are admissible to both literates and illiterates as the interviewer acts as a medium.

The rate of response is poor in questionnaires whereas, in interviews, people generally answer the questions then and there.

The questionnaire method is less expensive to administer whereas, interviews are generally expensive and hard to conduct.

Questionnaires provide anonymity to the answerers whereas, in interviews, there is an absence of complete anonymity.

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Open Access

Peer-reviewed

Research Article

Digital economy, innovation factor allocation and industrial structure transformation—A case study of the Yangtze River Delta city cluster in China

Roles Supervision, Writing – review & editing

Affiliation School of Finance and Economics, Jiangsu University, Zhenjiang, 212013, China

Roles Formal analysis, Methodology, Software, Validation, Visualization, Writing – original draft

* E-mail: [email protected]

Roles Writing – review & editing

Affiliation Pakistan Air Force Karachi Institute of Economics and Technology, College of Management Sciences, Karachi, Pakistan

• Xinfeng Chang, 
• Zihe Yang, 

• Published: April 10, 2024
• https://doi.org/10.1371/journal.pone.0300788
• Peer Review
• Reader Comments

The attainment of regional high-quality development necessitates the critical role of the digital economy in facilitating the transformation of industrial structures. This study intends to investigate the effect of the digital economy on industrial structure transformation from the perspective of innovation factor allocation using a panel dataset of 41 cities in the Yangtze River Delta region for the period from 2011 to 2020. This paper considers four dimensions to measure the level of industrial structure transformation i.e. industrial structure servitization, industrial structure upgradation, service industry structure upgradation and industrial interaction level. The results of the study suggest that the digital economy can significantly improve industrial structure transformation. The results remain consistent even after several robustness checks. Further, the analysis of the mechanism of action shows that the digital economy can promote industrial structure transformation by optimizing the innovation factor allocation. The study provides several policy implications for the digital economy and its role in the promotion of industrial structure transformation.

Citation: Chang X, Yang Z, Abdullah (2024) Digital economy, innovation factor allocation and industrial structure transformation—A case study of the Yangtze River Delta city cluster in China. PLoS ONE 19(4): e0300788. https://doi.org/10.1371/journal.pone.0300788

Editor: Jianhua Zhu, Harbin Institute of Technology, CHINA

Received: August 25, 2023; Accepted: March 5, 2024; Published: April 10, 2024

Copyright: © 2024 Chang et al. This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Data Availability: All relevant data are within the manuscript and its Supporting Information files.

Funding: This research was supported by the College Student Scientific Research Project of Jiangsu University (Project No. 22C089).

Competing interests: The authors have declared that no competing interests exist.

1. Introduction

At present, China ’s economy is at an important node in the transition from high-speed growth to high-quality development. In the new stage, China is facing multiple challenges from home and abroad, such as the impact of the COVID19 and anti-globalization. The contradiction between the traditional low-end locked industrial structure and the new stage is becoming increasingly prominent. Therefore, it is the only way for China ’s high-quality economic development to continuously promote the evolution of the economy from factor-driven to innovation-driven and promote the balanced optimization of industrial structure. At the same time, the economies around the globe are transforming from traditional to digital economies that use artificial intelligence, blockchain, cloud computing and big data as a new economic model. The change has penetrated into all aspects of the economy from production to sales [ 1 ]. Digital economy can promote the flow of resource elements, reduce resource mismatches, enable the upgrading of traditional production factors. According to the data, the scale of China ’s digital economy will reach 50.2 trillion yuan in 2022, and the proportion of digital economy in GDP will reach 41.5%. Digital economy is gradually becoming a key force driving a new round of scientific and technological revolution and industrial transformation. Further, it is worth noting that the Yangtze River Delta city cluster is the only world-class city cluster in China. It is a metropolitan area covering 41 cities, with a GDP of $427 million, an area of 350,000 square kilometers and a population of 235 million. The dataset from the Yangtze River Delta cities seems adequate for this study as it has a high degree of openness and strong innovation ability.

Industrial structure transformation remains an interesting domain for the researchers and academicians. The extant literature on industrial structure transformation can be categorized into three main domains i.e. connotation, measurement and the driving factors. Previous studies have used the theory of economic growth stages proposed by Austrian economist Walte that has laid its theoretical foundation. Scholars suggest that industrial structure transformation is an important tool to promote economic transformation [ 2 ]. Several studies argue that the transformation of industrial structure is the evolution process that moves from low to high added value [ 3 , 4 ]. Further, the measurement of industrial structure transformation domain can be divided into two categories i.e. single index measurement and multi-index measurement. The single index measurement includes industrial structure advance coefficient, Moore value, industrial structure level coefficient, output value ratio, the proportion of output value of each industry and the sum of product of productivity [ 5 , 6 ]. Moreover, the multi-index measurement measures the transformation of industrial structure from two aspects i.e. rationalization and advancement [ 7 ]. Portes and Evans [ 4 ] used the degree of industrial structure optimisation and the speed of industrial structure transition to measure. Ganadded the perspective of industrial integration development in the measurement [ 8 ]. Moreover, past studies suggested different factors that contribute to the industrial structure transformation such as industrial policies [ 6 ], capital investment [ 9 ], technological innovation [ 10 ], and financial development [ 11 ].

The digital economy and its effect on the industrial structure transformation has gained the attention of many researchers recently. Past studies have explored the internal mechanism of a digital economy and its effect on industrial structure transformation from several paths. First, several scholars argue that the digital economy can significantly promote the transformation of industrial structure. For example, digital economy has a positive spatial spillover effect on upgradation of the industrial structure[ 12 , 13 ]. Second, scholars struggled to find how digital economy promote industrial structure transformation and suggest that urbanization [ 14 ], technology innovation[ 15 ], labor efficiency (Wu, 2022) and factor allocation [ 16 ] help in industrial structure transformation.

In summary, the existing literature has conducted in-depth research on digital economy and industrial structure transformation from different perspectives, but there are still the following limitations: (1) the existing literature focus on how digital economy affect the industrial structure transformation. However, few studies have discussed how internal mechanism of digital economy helps in transforming the industrial structure from the perspective of innovation factor allocation. (2) Majority of the past studies have considered macro factors for the measurement of industrial structure transformation i.e. the ratio of the added value of the tertiary industry to the added value of the secondary industry, while ignoring the impact of labor within the industry, industrial integration and lacks systematic research on upgradation of the industrial structure. (3) It is worth noting that in China ’s development plan, the city and county levels are more instructive in the specific implementation of the policy [ 17 ]. Previous studies have provided evidence from the perspective of province, few studies have been conducted from the level of prefecture-level cities to grasp the intra-regional connections.

By analyzing the shortcomings of the existing literature, this paper focuses on the effect and mechanism of digital economy on industrial transformation from the perspective of innovation factor allocation. The contributions of this paper are: (1) We incorporate digital economy, innovation factor allocation and industrial structure transformation in a single framework. We have considered digital economy as the basis of industrial transformation and analyzed the intermediary role of innovation factor allocation in the promotion of industrial structure transformation by digital economy. (2) we extended the literature by using a comprehensive measurement of industrial structure transformation that considered its four dimensions which are industrial structure servitization, industrial upgradation, service industry structure upgradation and industrial interaction level. (3) This paper extends the existing literature by providing evidence from the perspective of the Yangtze River Delta city where the digital economy is developing rapidly. The rest of the article is structured as follows: section 2 highlights the theoretical analysis and research hypothesis, while sections 3 and 4 deal with methods and data, and results and discussion, respectively. Lastly, section 5 presents the conclusion and recommendations.

2. Theoretical analysis and research hypothesis

Some studies have found that although the evolution of the economic structure measured by increasing the proportion of the service industry shows that China ’s economy is moving towards a higher level, the structural problems within the industry have caused the benign interaction of the industry to be hindered [ 18 ]. This kind of economic servitization will make the economy face the risk of moving from the real to the virtual, and there will be excessive servitization. Based on the background of high-quality development, this paper defines the transformation of industrial structure: The change in the proportional relationship between macro industries based on the optimization of factor composition and ratio within microenterprises and the upgrading of technology and products within meso-industries is the endogenous basis of industrial structure transformation. This paper will explain the impact of the digital economy on the transformation of industrial structure from the four dimensions of industrial structure servitization, industrial structure upgradation, service industry structure upgradation, and industrial interaction level, and then put forward the corresponding research hypothesis.

2.1. The direct effect of the digital economy on the transformation of industrial structure

The impact of the digital economy on the transformation of industrial structure is visible as it promotes the servitization of industrial structure, the upgradation of industrial structure, the upgradation of service industry structure, and the level of industrial interaction. The digital economy reduces transaction cost and transform the servitization of industrial structures. The digital economy penetrates through digital technology and reduces the information barriers between enterprises and industries. Further, it promotes industrial efficiency and create synergy while using modern science and technology [ 19 ]. It innovates the production process of traditional industries through innovative management options and realizes the servitization of industrial structure [ 20 ]. Further, digital economy is profoundly changing all interrelated value-added links within the product lifecycle of the manufacturing industry and promotes transformation and upgradation of the manufacturing enterprises [ 21 ]. It helps in immediate gathering and disseminating important information that may help in efficient decision-making through different digital technologies such as big data and the internet of things and have overcome several issues of the labors in the manufacturing industry [ 22 ]. Digital economy also promote the transformation and upgradation of traditional industrial enterprises [ 23 ]. Moreover, the digital economy supports the rapid development of new forms of knowledge-intensive services, which helps to upgrade the structure of the service industry. The development of the digital economy has brought convenience to data integration, resource flow, and value sharing. The wide application of digital technology in the service industry has greatly promoted the rapid development of new forms of knowledge-intensive services such as integrated offices, online medical care, online education, and cross-border services. The continuous advancement in the digital technology is perhaps fulfilling the modern requirements which are important in upgradation of service industry structure and for the improvement in the labor productivity [ 24 ]. Finally, the digital economy promotes organizational change and helps in gathering important information in lesser time. The digital economy can promote interaction among different industries using the available information on the internet and through digital inclusive finance. The digital technology continues to change the production and organizational methods in various industries. Further, this will reduce the traditional barriers and help industries to integrate leading to sustainable development [ 25 ]. Based on the above discussion, we develop the following hypothesis.

Hypothesis 1: The digital economy has a direct role in promoting the transformation of industrial structures.

2.2. The mediating effect of innovation factor allocation in digital economy promoting industrial structure transformation

Innovation is the key to the transformation of industrial structures. From the perspective of human factor, the digital economy can indirectly promote the transformation of the industrial structure by improving the innovation in elements such as humans, knowledge, technology, and systems. The construction of human organizations may become the source of innovation research [ 26 ]. At the same time, the labor force engaged in R&D activities has high education and strong skills [ 27 ], which can provide intellectual support for the transformation of industrial structure. The implementation of the internet and modern communication technology, the integration of data elements and labor force can promote the allocation efficiency of human innovation elements. Thus, innovation in the human factor may help them to perform creative activities which results in transformation of industrial structure.

From the perspective of innovation in the knowledge elements, the digital economy can use modern digital technologies to swiftly screen out information that is conducive to innovation, improve the capacity of information storage and use it innovative ways to maximize value and drive industries to higher level maximize value [ 28 , 29 ]. From the perspective of technological innovation elements, the development of the digital economy has accelerated the speed of information transmission. The digital economy may be helpful in build an information-sharing platform, integrate internal and external resources of enterprises which will create opportunities for collaboration and result into transparent environment. This efficiency in the technological innovation may improve the environment of enterprise and upgrade the industrial structure. From the perspective of system innovation elements, with the development and expansion of the digital economy, the country has gradually attached importance to institutional innovation in digital platforms, data security, and artificial intelligence. The improvement in the institutional innovation can motivate the innovative behavior among employees that will smoothly transform the industrial culture and bring technological innovation in the industry [ 30 ]. Based on the above discussion, we develop the following hypothesis:

Hypothesis 2 : The digital economy can indirectly promote the transformation of the industrial structure by improving the level of innovation factor allocation.

3. Models, variables and data

3.1. model setting, 3.1.1. benchmark model construction..

3.1.2. Mediating effect model.

3.2. Variable measure and description

3.2.1. explanatory variables: industrial structure transformation..

The transformation of industrial structure refers to the improvement of production efficiency and the transfer of production factors from low-efficiency industries to high-efficiency industries. It is usually measured by the upgradation and the rationalization of industrial structure. On one hand, the digital economy shifts the factors of production from low-efficiency industries to high-efficiency industries, which promotes the improvement of production efficiency. On the other hand, it makes the development trend of mutual integration and blurred boundaries between industries more effectively. At the same time, the industrial policy that intend to enhance service industry proportion may misallocate resources between industries which results in excessive servitization. It is impossible to accurately analyze the transformation of the industrial structure by using one proxy i.e. upgradation and rationalization of the industrial structure. Therefore, this paper measures it from the four dimensions to accurately measure it i.e. industrial structure servitization, industrial structure upgradation, service industry structure upgradation, and industrial interaction level, as shown in Table 1 .

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https://doi.org/10.1371/journal.pone.0300788.t001

• Industrial structure servitization (Insev) In this paper, the servitization of industrial structure is used to describe the transformation of industrial structure at the macro level. It represents the changes in the proportion of the three industries at the macro level. It is measured by the ratio of the added value of the tertiary industry to the secondary industry, and combined with the other three indicators to comprehensively evaluate the transformation of industrial structure.
• Industrial structure upgradation (Manh): The increase in the manufacturing value chain or the transformation and upgradation from traditional to advanced manufacturing industry will be reflected through the increase in the value chain. Therefore, this study uses the total regional industrial profits and taxes to measure the advanced industrial structure. To a certain extent, this index reflects the value added in the manufacturing industry. It is believed that the total profit and tax of the high-tech industry is usually higher as compared to others. If the total amount of industrial profits and taxes in a region is higher, it shows that the industrial level in the region is also higher.
• Service industry structure upgradation (Sevh): The upgradation of service industry structure shows the rapid development of emerging industries and producer services compared to traditional industries. Producer services can not only effectively overcome the Baumol ’s disease because of its high productivity, but also support the development of advanced manufacturing industry. This paper uses the ratio of employment in producer services to employment in the tertiary industry to measure the structure of the service industry [ 32 ]. According to the classification criteria of the National Bureau of Statistics (2005), producer services mainly cover transportation, warehousing and postal services, financial services, leasing and business services, scientific research, technical services and geological exploration, information transmission, computer services and software industries.
• Industrial interaction level (Indi): In the modern era, industrial interaction and integration is an effective development model that improves productivity and competitiveness. Industrial interactive integration refers to the process of removing the barriers in the industry for industrial growth. This cross-industry interaction enhances technology innovation which enhances industrial agglomeration and industrial interactive integration. In the era of service economy and digital economy, service products will be put into the economic production activities of various industrial sectors as intermediate products on a large scale. Therefore, the level of industrial interaction is one of the important characteristics of industrial structure transformation. In this study, Herfindahl index (HHI) is used to represent, Q i represents the output value of the i industry, Q represents the regional GDP which is presented in the following model:

3.2.2. Core explanatory variables: Digital economy development level.

This study measures the digital economy at the prefecture-level city level. The data has been collected based on its availability [ 33 ]. Kapur and Kesavan [ 34 ]stated that, when the data source produces a low-entropy value, the event carries more “information”. The entropy method is an objective and comprehensive weighting method, which is based on the dispersion degree of the evaluation index data to measure the index weight, so we use the entropy method to calculate the digital economy considering the level of development of internet and digital inclusive finance. Further, the level of Internet development is divided into four three-level indicators: first, the output level of internet-related industries measured by the total amount of telecommunications business; second, the internet-related industry practitioners with the number of computer services and software industry practitioners to characterize; third, the internet penetration rate expressed by the number of Internet broadband access users in 100 people; the fourth is the mobile phone penetration rate expressed as the number of mobile phone users per 100 people. The development level of digital inclusive finance is characterized by the digital inclusive finance index compiled by the Digital Finance Research Center of Peking University and Ant Financial Services Group. The principal component analysis method is used to standardize the relevant data and reduce the dimension, so as to obtain the development level of the digital economy at the city level.

3.2.3. Mediating variable: The level of innovation factor allocation.

We constructed a comprehensive index for the allocation of innovation elements comprising four dimensions i.e. human, knowledge, technological and institutional innovation. We measured human innovation by the full-time personnel for R&D while the number of colleges and universities were used to measure the human organizations. Further, for the knowledge innovation several aspects are considered such as knowledge retention, technological innovation, quality of technological innovation. The internal R&D expenditure was used to measure the knowledge retention and the quantity of invention patents were used to measure the quality of technological innovation. Similarly, the sum of the quantity of utility model patents and design patents is used to measure the quantity of technological innovation. Moreover, we measured the institutional innovation factor by the total collection of books in the public libraries and government’s expenditures on science and education. As per the objective weighting method, the entropy TOPSIS is used to calculate the level of innovation factor allocation (Inf). The system of measurement indicators is shown in Table 2 .

https://doi.org/10.1371/journal.pone.0300788.t002

3.2.4. Control variables.

To study the effect and mechanism of the digital economy on the transformation of industrial structure more comprehensively, this paper refers to the existing literature [ 11 , 35 – 39 ] and used several control variables such as economic development degree, infrastructure level, financial development level, government intervention and population density. Economic development degree (Pgdp) refers to the degree of economic development which is an important driving force to promote the upgradation of China’s industrial structure. Infrastructure level (Bins) is important for the economic development and is the basis for the transformation of industrial structure. Financial development level (Fin) which is also required for the industrial development and this problem can be solved by the funds available in the capital markets. We used the proportion of loan balance of financial institutions to the GDP for measuring the level of financial development. Government intervention (Gov) also impact the industrial structure and government plays an important role of the regulator. Lastly, Population density (Lnpop) is used as a control variable which is an important factor that affects the transformation of industrial structure. It is measured by the ratio of regional resident population to urban land area.

3.3. Data sources and descriptive statistics

This paper used a balanced panel dataset comprising 41 cities in the Yangtze River Delta for the period 2011 to 2020. The data has been extracted from "Jiangsu Statistical Yearbook ", "Zhejiang Statistical Yearbook", "Anhui Statistical Yearbook ", "China City Statistical Yearbook ", each city Statistical Yearbook, and the EPS database. Some missing data was supplemented by the linear interpolation method. Table 3 presents the descriptive statistics of all the variables used in this study.

https://doi.org/10.1371/journal.pone.0300788.t003

Table 3 suggests that the standard deviation of industrial structure servitization, service industry structure upgradation, and industrial interaction level is small which implies that the data fluctuation is not large. Further, the minimum and maximum values of industrial structure upgradation are significantly different, indicating that the development gap of industrial structure among cities in the Yangtze River Delta region is large. Moreover, the descriptive statistics suggests that the mean value of digital economy is small but the standard deviation is large. This finding is consistent with [ 12 ]. Similarly, the allocation level of innovation elements also has a similar mean and standard deviation. The descriptive statistics of control variables suggest significant differences in economic development, infrastructure level, financial development level, government size, and population density among different cities.

4. Empirical results and analysis

4.1. benchmark regression analysis.

We perform several diagnostic checks to ensure that the dataset meets the basic assumptions of regression. First, we perform a 1% tail reduction on the panel data in order to remove outliers. Second, we use Hausman test to check whether fixed or random effect model is appropriate, and the results support the use of the fixed effect model. In the actual regression, the time trend of industrial structure servitization and service industry structure upgradation is not obvious, so the one-way fixed effect model without time effect is chosen for the final regression of the two dimensions.

Table 4 reports the benchmark regression results of industrial structure transformation driven by the digital economy. The results of columns 1, 3, 5 and 7 show that the development of the digital economy has significantly promoted the servitization of industrial structure, the upgradation of industrial structure, the upgradation of service industry structure and the level of industrial interaction without considering the control variables. Further columns 2, 4, 6, and 8 report results after inclusion of control variables. The results are consistent which suggest that considering the differences in the degree of economic development and infrastructure construction in different cities, the development of a digital economy can significantly promote the transformation of industrial structure. It is also found that the promotion effect of the digital economy on industrial structure servitization and industrial structure upgradation is much greater than that on service industrial structure upgradation and industrial interaction level. Overall, the results suggest that the digital economy may enable transformation of industrial structure, which not only promote the servitization of industrial structure at the macro level but also effectively promote the integration of service industry and agriculture which optimize the industrial internal structure, promote the development of high-tech industry, and produce productive service industries. The digital economy may serve as a strong driving force which promote the evolution of industrial structure and industrial internal structure to the middle and high end. Therefore, the development of the digital economy in the Yangtze River Delta region enables the servitization of advanced industrial structure instead of "real-to-virtual " transformation of the economy. Hence, we find support for H1.

https://doi.org/10.1371/journal.pone.0300788.t004

Further, the results suggest that the degree of economic development is conducive to improving the level of industrial structure upgradation and industrial interaction level, which is consistent with scholars [ 3 , 40 ]. However, the impact of the industrial structure upgradation and the upgradation of the service industry structure is significantly negative, which suggest that China suffers from insufficient supply of high-quality products and the dependence on foreign products. The positive coefficient of infrastructure construction for the servitization of industrial structure indicates that infrastructure construction can improve the cost of factor flow which promotes the digital economy, and transform the industrial structure to servitization. The level of financial development also promotes the upgradation of the service industry structure and new products are developed using internet and finance that has significantly improved the industry. However, the demand of finance from industrial upgradation does not match the supply from financial institutions which may be a hindrance towards industrial structure upgradation. The population density promotes the service of industrial structure and the advancement of industrial structure, which indicates that the development of a digital economy can attract a large number of high-tech talents which helps in transforming traditional industry to tertiary industry. However, the increase in population will shift the focus of labor to low-end service industries which may become the hindrance in the development of the service industry.

4.2. Mediation effect test

This study analyzes the transmission path of digital economy development to industrial structure transformation. Table 5 reports the regression results of the intermediary effect model. Column 1 and 4 present the results that test the impact of the digital economy on the innovation factors allocation without controlling the time effect and with controlling the time effect, respectively. The significant coefficients indicate that the development of digital economy can significantly improve the innovation factors allocation level. As the economy started transition into digitalization, the transaction cost of innovation factors is reduced which will promote the flow of factors such as talents and knowledge which efficiently allocate innovation factors.

https://doi.org/10.1371/journal.pone.0300788.t005

The columns 2, 3, 5, and 6 present the regression results of the benchmark regression plus the mediating variables. It is found that in columns 2 and 6, the coefficients of the development level of the digital economy and the allocation of innovation factors are significantly positive, and the absolute value of the coefficient of the development level of the digital economy is reduced compared with the benchmark regression, indicating that the digital economy plays a significant mediating role in driving the servitization of industrial structure and the level of industrial interaction. Further, the innovation factors allocation does not have any significant impact on the upgradation of the service industry structure and the industrial structure in column 3 and 5. However, after the Sobel’s test, the hypothesis that there is no mediating effect is significantly rejected which implies that the digital economy indirectly affects the service structure upgradation and the industrial structure upgradation by promoting the innovation factors allocation. The development of digital economy stimulates the demand for innovative factors, and expands the supply scale of innovative factors through the informatization and digitization of enabling factors, which lays a factor foundation for industrial transformation. At the same time, the innovation of participation mode accelerates product innovation, business integration and high-end upgrading. Hence, we find support for H2.

4.3. Endogeneity and robustness test

4.3.1. treatment of endogenous problems..

In the above models, there are two possible endogenous problems: First, there may be a two-way causal relationship between the digital economy and industrial structure transformation as the increase in technological demand for industrial structure transformation may in turn affect the development of the digital economy. Second, there may be several variables which are omitted that can make results bias although the impact of control variables such as economic development level and financial development level is considered. To overcome these possible endogenous problems, we have used an instrumental variable approach to estimate the model. By constructing the interaction term between the number of fixed telephones per 100 people in 1984 and the number of urban internet users in the previous year as the instrumental variable of the digital economy development level. We used the two-stage least squares method for analysis and the results are presented in Table 6 . The first-stage regression results show that there is a significant positive correlation between the instrumental variables and the digital economy. The rationality test results for instrumental variables show that the p-value corresponding to the Kleibergen-Paaprk LM statistic is less than 0.01, which significantly rejects the null hypothesis that "insufficient identification of instrumental variables" at the 1% level. Further, the Kleibergen-Paapr-Wald F test value is 37.398 which is greater than the critical value of 16.38 at the 10% level of the Stock Yogo test passing the weak tool test which indicates that the instrumental variables selected in this paper are reasonable. Moreover, the second stage regression results show that the development level of the digital economy still promotes the servitization of industrial structure, the advancement of industrial structure, the advancement of service industry structure, and the level of industrial interaction. Both are significant at the 1% level, which is consistent with the main regression results.

https://doi.org/10.1371/journal.pone.0300788.t006

4.3.2. Stability test.

As discussed earlier, we have measured the explanatory variables i.e. industrial structure transformation from four dimensions. These four dimensions are complementary, and the regression results between them can explain the promotion effect of the digital economy on industrial structure transformation to a certain extent. In addition, we use the alternate variable measurement, excluding municipalities and provincial capitals to further validate the robustness of the results.

(1) Replacement variable measure method

In order to eliminate the interference of the variable measurement method with the estimation results, this paper uses the entropy method to measure the digital economic development index and re-estimate the model and the results after replacement are presented in Table 7 . The coefficient sign and significance of the digital economy development level are consistent with the main results which implies that the results are robust to several measurements of digital economy.

https://doi.org/10.1371/journal.pone.0300788.t007

(2) Delete provincial capitals and municipalities

The sample data in this paper includes 41 cities of the Yangtze River Delta region.

Since, the level of each city in terms of economy, finance and policy is different from other therefore, the regression results are also different. In this section, we exclude four cities from our sample and re-estimated our models. The results are presented in Table 8 which suggest that the results are consistent with our main results which imply that the digital economy has a significant positive effect on the transformation of industrial structure.

https://doi.org/10.1371/journal.pone.0300788.t008

5. Conclusions and recommendations

This study intends to investigate the effect of the digital economy on industrial structure transformation from the perspective of innovation factor allocation using panel dataset of 41 cities in the Yangtze River Delta region for the period from 2011 to 2020. We have considered digital economy as the basis for industrial structure transformation and measured the industrial structure transformation comprehensively using its four dimensions i.e. industrial structure servitization, industrial structure upgradation, service industry structure upgradation and industrial interaction level. We have employed panel regression technique for ascertaining the relationship between the variables. The results suggest that digital economy has a significant impact on industrial structure transformation. It does not only promote the servitization but plays a crucial role in industrial structure upgradation, service industry structure upgradation and enhance industrial interaction. Further, we find that innovation factor allocation mediates the relationship between digital economy and industrial structure transformation. Digital economy can accelerate the flow and combination optimization of various innovative resources through digital, intelligent and networked organization, improve the efficiency of resource allocation and the coordinated development of industrial structure, and help to build a modern industrial system with coordinated allocation of factors, intra-industry development and inter-industry deep integration. The findings are robust to different measurements and several estimation techniques.

The results have several implications. First, the government should promote digital economy in all regions that will transform into high-quality development which will results in sustainable economic development. All regions should make a strategy to implement digital economy using artificial intelligence and blockchain which will transform the industrial structure. Second, all regions should promote innovation and incentivize firms that innovate at all levels. Government should also allocate special funds that help firms in adopting technologies that brings innovation. All regions may collaborate with each other to enhance the innovation as is it will help in industrial transformation. Third, digital economy policies may be developed according to the regional conditions. All regions should devise own strategies to enhance digital economy in order to enhance its impact on the region. Metropolitan cities may strengthen their relationship with small cities and promote innovation and digital economy which will enhance collaboration and industrial transformation. It is also suggested that the policy obstacles may be removed which restrict cities to collaborate with each other. Multi-stakeholders have an interactive effect on the choice of governance strategies, which is affected by the cost-benefit relationship of various stakeholders [ 41 ]. Local governments should assess the information technology infrastructure and make information technology investment plans accordingly to promote digital economy which will help in overall sustainable economic development and growth.

Based on the panel data from 41 cities in the Yangtze River Delta, this study takes industrial structure transformation as the explanatory variable and digital economy as the main explanatory variable and draws the key conclusion that digital economy can significantly promote industrial structure transformation. However, there are still some limitations. First, Limited to the limitations of the index data, the measurement of industrial structure upgrading in this paper is only measured from the macro inter industry and the meso industry, and the micro factors are not included in the index measurement. In the case of available data, more detailed research can be further carried out based on the level of micro enterprises. Second, limited to the limitations of index data, only representative and data-accessible indicators are selected for research in the construction of digital economy index system. With the rapid development of digital technology, the measurement index system of digital economy should keep up with the pace of development. In the future research, it is necessary to build a more perfect and more realistic digital economic evaluation index system.

Supporting information

https://doi.org/10.1371/journal.pone.0300788.s001

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