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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."

hypothesis case study example

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.

hypothesis case study example

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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The Craft of Writing a Strong Hypothesis

Deeptanshu D

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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  • How to Write a Strong Hypothesis | Guide & Examples

How to Write a Strong Hypothesis | Guide & Examples

Published on 6 May 2022 by Shona McCombes .

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

Table of contents

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

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

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

Variables in hypotheses

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

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

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Step 1: ask a question.

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

Step 2: Do some preliminary research

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

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

Step 3: Formulate your hypothesis

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

Step 4: Refine your hypothesis

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

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

Step 5: Phrase your hypothesis in three ways

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

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

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

Step 6. Write a null hypothesis

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

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

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

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

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

Cite this Scribbr article

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  • What Is a Case Study? | Definition, Examples & Methods

What Is a Case Study? | Definition, Examples & Methods

Published on May 8, 2019 by Shona McCombes . Revised on November 20, 2023.

A case study is a detailed study of a specific subject, such as a person, group, place, event, organization, 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 analyze the case, other interesting articles.

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

TipIf your research is more practical in nature and aims to simultaneously investigate an issue as you solve it, consider conducting action research instead.

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.

Example of an outlying case studyIn the 1960s the town of Roseto, Pennsylvania was discovered to have extremely low rates of heart disease compared to the US average. It became an important case study for understanding previously neglected causes of heart disease.

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

Example of a representative case studyIn the 1920s, two sociologists used Muncie, Indiana as a case study of a typical American city that supposedly exemplified the changing culture of the US at the time.

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.

Example of a mixed methods case studyFor a case study of a wind farm development in a rural area, you could collect quantitative data on employment rates and business revenue, collect qualitative data on local people’s perceptions and experiences, and analyze local and national media coverage of the development.

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 analyze 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.

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

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What is and How to Write a Good Hypothesis in Research?

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One of the most important aspects of conducting research is constructing a strong hypothesis. But what makes a hypothesis in research effective? In this article, we’ll look at the difference between a hypothesis and a research question, as well as the elements of a good hypothesis in research. We’ll also include some examples of effective hypotheses, and what pitfalls to avoid.

What is a Hypothesis in Research?

Simply put, a hypothesis is a research question that also includes the predicted or expected result of the research. Without a hypothesis, there can be no basis for a scientific or research experiment. As such, it is critical that you carefully construct your hypothesis by being deliberate and thorough, even before you set pen to paper. Unless your hypothesis is clearly and carefully constructed, any flaw can have an adverse, and even grave, effect on the quality of your experiment and its subsequent results.

Research Question vs Hypothesis

It’s easy to confuse research questions with hypotheses, and vice versa. While they’re both critical to the Scientific Method, they have very specific differences. Primarily, a research question, just like a hypothesis, is focused and concise. But a hypothesis includes a prediction based on the proposed research, and is designed to forecast the relationship of and between two (or more) variables. Research questions are open-ended, and invite debate and discussion, while hypotheses are closed, e.g. “The relationship between A and B will be C.”

A hypothesis is generally used if your research topic is fairly well established, and you are relatively certain about the relationship between the variables that will be presented in your research. Since a hypothesis is ideally suited for experimental studies, it will, by its very existence, affect the design of your experiment. The research question is typically used for new topics that have not yet been researched extensively. Here, the relationship between different variables is less known. There is no prediction made, but there may be variables explored. The research question can be casual in nature, simply trying to understand if a relationship even exists, descriptive or comparative.

How to Write Hypothesis in Research

Writing an effective hypothesis starts before you even begin to type. Like any task, preparation is key, so you start first by conducting research yourself, and reading all you can about the topic that you plan to research. From there, you’ll gain the knowledge you need to understand where your focus within the topic will lie.

Remember that a hypothesis is a prediction of the relationship that exists between two or more variables. Your job is to write a hypothesis, and design the research, to “prove” whether or not your prediction is correct. A common pitfall is to use judgments that are subjective and inappropriate for the construction of a hypothesis. It’s important to keep the focus and language of your hypothesis objective.

An effective hypothesis in research is clearly and concisely written, and any terms or definitions clarified and defined. Specific language must also be used to avoid any generalities or assumptions.

Use the following points as a checklist to evaluate the effectiveness of your research hypothesis:

  • Predicts the relationship and outcome
  • Simple and concise – avoid wordiness
  • Clear with no ambiguity or assumptions about the readers’ knowledge
  • Observable and testable results
  • Relevant and specific to the research question or problem

Research Hypothesis Example

Perhaps the best way to evaluate whether or not your hypothesis is effective is to compare it to those of your colleagues in the field. There is no need to reinvent the wheel when it comes to writing a powerful research hypothesis. As you’re reading and preparing your hypothesis, you’ll also read other hypotheses. These can help guide you on what works, and what doesn’t, when it comes to writing a strong research hypothesis.

Here are a few generic examples to get you started.

Eating an apple each day, after the age of 60, will result in a reduction of frequency of physician visits.

Budget airlines are more likely to receive more customer complaints. A budget airline is defined as an airline that offers lower fares and fewer amenities than a traditional full-service airline. (Note that the term “budget airline” is included in the hypothesis.

Workplaces that offer flexible working hours report higher levels of employee job satisfaction than workplaces with fixed hours.

Each of the above examples are specific, observable and measurable, and the statement of prediction can be verified or shown to be false by utilizing standard experimental practices. It should be noted, however, that often your hypothesis will change as your research progresses.

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Elsevier’s Language Editing Plus service can help ensure that your research hypothesis is well-designed, and articulates your research and conclusions. Our most comprehensive editing package, you can count on a thorough language review by native-English speakers who are PhDs or PhD candidates. We’ll check for effective logic and flow of your manuscript, as well as document formatting for your chosen journal, reference checks, and much more.

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The case study approach

Sarah crowe.

1 Division of Primary Care, The University of Nottingham, Nottingham, UK

Kathrin Cresswell

2 Centre for Population Health Sciences, The University of Edinburgh, Edinburgh, UK

Ann Robertson

3 School of Health in Social Science, The University of Edinburgh, Edinburgh, UK

Anthony Avery

Aziz sheikh.

The case study approach allows in-depth, multi-faceted explorations of complex issues in their real-life settings. The value of the case study approach is well recognised in the fields of business, law and policy, but somewhat less so in health services research. Based on our experiences of conducting several health-related case studies, we reflect on the different types of case study design, the specific research questions this approach can help answer, the data sources that tend to be used, and the particular advantages and disadvantages of employing this methodological approach. The paper concludes with key pointers to aid those designing and appraising proposals for conducting case study research, and a checklist to help readers assess the quality of case study reports.


The case study approach is particularly useful to employ when there is a need to obtain an in-depth appreciation of an issue, event or phenomenon of interest, in its natural real-life context. Our aim in writing this piece is to provide insights into when to consider employing this approach and an overview of key methodological considerations in relation to the design, planning, analysis, interpretation and reporting of case studies.

The illustrative 'grand round', 'case report' and 'case series' have a long tradition in clinical practice and research. Presenting detailed critiques, typically of one or more patients, aims to provide insights into aspects of the clinical case and, in doing so, illustrate broader lessons that may be learnt. In research, the conceptually-related case study approach can be used, for example, to describe in detail a patient's episode of care, explore professional attitudes to and experiences of a new policy initiative or service development or more generally to 'investigate contemporary phenomena within its real-life context' [ 1 ]. Based on our experiences of conducting a range of case studies, we reflect on when to consider using this approach, discuss the key steps involved and illustrate, with examples, some of the practical challenges of attaining an in-depth understanding of a 'case' as an integrated whole. In keeping with previously published work, we acknowledge the importance of theory to underpin the design, selection, conduct and interpretation of case studies[ 2 ]. In so doing, we make passing reference to the different epistemological approaches used in case study research by key theoreticians and methodologists in this field of enquiry.

This paper is structured around the following main questions: What is a case study? What are case studies used for? How are case studies conducted? What are the potential pitfalls and how can these be avoided? We draw in particular on four of our own recently published examples of case studies (see Tables ​ Tables1, 1 , ​ ,2, 2 , ​ ,3 3 and ​ and4) 4 ) and those of others to illustrate our discussion[ 3 - 7 ].

Example of a case study investigating the reasons for differences in recruitment rates of minority ethnic people in asthma research[ 3 ]

Example of a case study investigating the process of planning and implementing a service in Primary Care Organisations[ 4 ]

Example of a case study investigating the introduction of the electronic health records[ 5 ]

Example of a case study investigating the formal and informal ways students learn about patient safety[ 6 ]

What is a case study?

A case study is a research approach that is used to generate an in-depth, multi-faceted understanding of a complex issue in its real-life context. It is an established research design that is used extensively in a wide variety of disciplines, particularly in the social sciences. A case study can be defined in a variety of ways (Table ​ (Table5), 5 ), the central tenet being the need to explore an event or phenomenon in depth and in its natural context. It is for this reason sometimes referred to as a "naturalistic" design; this is in contrast to an "experimental" design (such as a randomised controlled trial) in which the investigator seeks to exert control over and manipulate the variable(s) of interest.

Definitions of a case study

Stake's work has been particularly influential in defining the case study approach to scientific enquiry. He has helpfully characterised three main types of case study: intrinsic , instrumental and collective [ 8 ]. An intrinsic case study is typically undertaken to learn about a unique phenomenon. The researcher should define the uniqueness of the phenomenon, which distinguishes it from all others. In contrast, the instrumental case study uses a particular case (some of which may be better than others) to gain a broader appreciation of an issue or phenomenon. The collective case study involves studying multiple cases simultaneously or sequentially in an attempt to generate a still broader appreciation of a particular issue.

These are however not necessarily mutually exclusive categories. In the first of our examples (Table ​ (Table1), 1 ), we undertook an intrinsic case study to investigate the issue of recruitment of minority ethnic people into the specific context of asthma research studies, but it developed into a instrumental case study through seeking to understand the issue of recruitment of these marginalised populations more generally, generating a number of the findings that are potentially transferable to other disease contexts[ 3 ]. In contrast, the other three examples (see Tables ​ Tables2, 2 , ​ ,3 3 and ​ and4) 4 ) employed collective case study designs to study the introduction of workforce reconfiguration in primary care, the implementation of electronic health records into hospitals, and to understand the ways in which healthcare students learn about patient safety considerations[ 4 - 6 ]. Although our study focusing on the introduction of General Practitioners with Specialist Interests (Table ​ (Table2) 2 ) was explicitly collective in design (four contrasting primary care organisations were studied), is was also instrumental in that this particular professional group was studied as an exemplar of the more general phenomenon of workforce redesign[ 4 ].

What are case studies used for?

According to Yin, case studies can be used to explain, describe or explore events or phenomena in the everyday contexts in which they occur[ 1 ]. These can, for example, help to understand and explain causal links and pathways resulting from a new policy initiative or service development (see Tables ​ Tables2 2 and ​ and3, 3 , for example)[ 1 ]. In contrast to experimental designs, which seek to test a specific hypothesis through deliberately manipulating the environment (like, for example, in a randomised controlled trial giving a new drug to randomly selected individuals and then comparing outcomes with controls),[ 9 ] the case study approach lends itself well to capturing information on more explanatory ' how ', 'what' and ' why ' questions, such as ' how is the intervention being implemented and received on the ground?'. The case study approach can offer additional insights into what gaps exist in its delivery or why one implementation strategy might be chosen over another. This in turn can help develop or refine theory, as shown in our study of the teaching of patient safety in undergraduate curricula (Table ​ (Table4 4 )[ 6 , 10 ]. Key questions to consider when selecting the most appropriate study design are whether it is desirable or indeed possible to undertake a formal experimental investigation in which individuals and/or organisations are allocated to an intervention or control arm? Or whether the wish is to obtain a more naturalistic understanding of an issue? The former is ideally studied using a controlled experimental design, whereas the latter is more appropriately studied using a case study design.

Case studies may be approached in different ways depending on the epistemological standpoint of the researcher, that is, whether they take a critical (questioning one's own and others' assumptions), interpretivist (trying to understand individual and shared social meanings) or positivist approach (orientating towards the criteria of natural sciences, such as focusing on generalisability considerations) (Table ​ (Table6). 6 ). Whilst such a schema can be conceptually helpful, it may be appropriate to draw on more than one approach in any case study, particularly in the context of conducting health services research. Doolin has, for example, noted that in the context of undertaking interpretative case studies, researchers can usefully draw on a critical, reflective perspective which seeks to take into account the wider social and political environment that has shaped the case[ 11 ].

Example of epistemological approaches that may be used in case study research

How are case studies conducted?

Here, we focus on the main stages of research activity when planning and undertaking a case study; the crucial stages are: defining the case; selecting the case(s); collecting and analysing the data; interpreting data; and reporting the findings.

Defining the case

Carefully formulated research question(s), informed by the existing literature and a prior appreciation of the theoretical issues and setting(s), are all important in appropriately and succinctly defining the case[ 8 , 12 ]. Crucially, each case should have a pre-defined boundary which clarifies the nature and time period covered by the case study (i.e. its scope, beginning and end), the relevant social group, organisation or geographical area of interest to the investigator, the types of evidence to be collected, and the priorities for data collection and analysis (see Table ​ Table7 7 )[ 1 ]. A theory driven approach to defining the case may help generate knowledge that is potentially transferable to a range of clinical contexts and behaviours; using theory is also likely to result in a more informed appreciation of, for example, how and why interventions have succeeded or failed[ 13 ].

Example of a checklist for rating a case study proposal[ 8 ]

For example, in our evaluation of the introduction of electronic health records in English hospitals (Table ​ (Table3), 3 ), we defined our cases as the NHS Trusts that were receiving the new technology[ 5 ]. Our focus was on how the technology was being implemented. However, if the primary research interest had been on the social and organisational dimensions of implementation, we might have defined our case differently as a grouping of healthcare professionals (e.g. doctors and/or nurses). The precise beginning and end of the case may however prove difficult to define. Pursuing this same example, when does the process of implementation and adoption of an electronic health record system really begin or end? Such judgements will inevitably be influenced by a range of factors, including the research question, theory of interest, the scope and richness of the gathered data and the resources available to the research team.

Selecting the case(s)

The decision on how to select the case(s) to study is a very important one that merits some reflection. In an intrinsic case study, the case is selected on its own merits[ 8 ]. The case is selected not because it is representative of other cases, but because of its uniqueness, which is of genuine interest to the researchers. This was, for example, the case in our study of the recruitment of minority ethnic participants into asthma research (Table ​ (Table1) 1 ) as our earlier work had demonstrated the marginalisation of minority ethnic people with asthma, despite evidence of disproportionate asthma morbidity[ 14 , 15 ]. In another example of an intrinsic case study, Hellstrom et al.[ 16 ] studied an elderly married couple living with dementia to explore how dementia had impacted on their understanding of home, their everyday life and their relationships.

For an instrumental case study, selecting a "typical" case can work well[ 8 ]. In contrast to the intrinsic case study, the particular case which is chosen is of less importance than selecting a case that allows the researcher to investigate an issue or phenomenon. For example, in order to gain an understanding of doctors' responses to health policy initiatives, Som undertook an instrumental case study interviewing clinicians who had a range of responsibilities for clinical governance in one NHS acute hospital trust[ 17 ]. Sampling a "deviant" or "atypical" case may however prove even more informative, potentially enabling the researcher to identify causal processes, generate hypotheses and develop theory.

In collective or multiple case studies, a number of cases are carefully selected. This offers the advantage of allowing comparisons to be made across several cases and/or replication. Choosing a "typical" case may enable the findings to be generalised to theory (i.e. analytical generalisation) or to test theory by replicating the findings in a second or even a third case (i.e. replication logic)[ 1 ]. Yin suggests two or three literal replications (i.e. predicting similar results) if the theory is straightforward and five or more if the theory is more subtle. However, critics might argue that selecting 'cases' in this way is insufficiently reflexive and ill-suited to the complexities of contemporary healthcare organisations.

The selected case study site(s) should allow the research team access to the group of individuals, the organisation, the processes or whatever else constitutes the chosen unit of analysis for the study. Access is therefore a central consideration; the researcher needs to come to know the case study site(s) well and to work cooperatively with them. Selected cases need to be not only interesting but also hospitable to the inquiry [ 8 ] if they are to be informative and answer the research question(s). Case study sites may also be pre-selected for the researcher, with decisions being influenced by key stakeholders. For example, our selection of case study sites in the evaluation of the implementation and adoption of electronic health record systems (see Table ​ Table3) 3 ) was heavily influenced by NHS Connecting for Health, the government agency that was responsible for overseeing the National Programme for Information Technology (NPfIT)[ 5 ]. This prominent stakeholder had already selected the NHS sites (through a competitive bidding process) to be early adopters of the electronic health record systems and had negotiated contracts that detailed the deployment timelines.

It is also important to consider in advance the likely burden and risks associated with participation for those who (or the site(s) which) comprise the case study. Of particular importance is the obligation for the researcher to think through the ethical implications of the study (e.g. the risk of inadvertently breaching anonymity or confidentiality) and to ensure that potential participants/participating sites are provided with sufficient information to make an informed choice about joining the study. The outcome of providing this information might be that the emotive burden associated with participation, or the organisational disruption associated with supporting the fieldwork, is considered so high that the individuals or sites decide against participation.

In our example of evaluating implementations of electronic health record systems, given the restricted number of early adopter sites available to us, we sought purposively to select a diverse range of implementation cases among those that were available[ 5 ]. We chose a mixture of teaching, non-teaching and Foundation Trust hospitals, and examples of each of the three electronic health record systems procured centrally by the NPfIT. At one recruited site, it quickly became apparent that access was problematic because of competing demands on that organisation. Recognising the importance of full access and co-operative working for generating rich data, the research team decided not to pursue work at that site and instead to focus on other recruited sites.

Collecting the data

In order to develop a thorough understanding of the case, the case study approach usually involves the collection of multiple sources of evidence, using a range of quantitative (e.g. questionnaires, audits and analysis of routinely collected healthcare data) and more commonly qualitative techniques (e.g. interviews, focus groups and observations). The use of multiple sources of data (data triangulation) has been advocated as a way of increasing the internal validity of a study (i.e. the extent to which the method is appropriate to answer the research question)[ 8 , 18 - 21 ]. An underlying assumption is that data collected in different ways should lead to similar conclusions, and approaching the same issue from different angles can help develop a holistic picture of the phenomenon (Table ​ (Table2 2 )[ 4 ].

Brazier and colleagues used a mixed-methods case study approach to investigate the impact of a cancer care programme[ 22 ]. Here, quantitative measures were collected with questionnaires before, and five months after, the start of the intervention which did not yield any statistically significant results. Qualitative interviews with patients however helped provide an insight into potentially beneficial process-related aspects of the programme, such as greater, perceived patient involvement in care. The authors reported how this case study approach provided a number of contextual factors likely to influence the effectiveness of the intervention and which were not likely to have been obtained from quantitative methods alone.

In collective or multiple case studies, data collection needs to be flexible enough to allow a detailed description of each individual case to be developed (e.g. the nature of different cancer care programmes), before considering the emerging similarities and differences in cross-case comparisons (e.g. to explore why one programme is more effective than another). It is important that data sources from different cases are, where possible, broadly comparable for this purpose even though they may vary in nature and depth.

Analysing, interpreting and reporting case studies

Making sense and offering a coherent interpretation of the typically disparate sources of data (whether qualitative alone or together with quantitative) is far from straightforward. Repeated reviewing and sorting of the voluminous and detail-rich data are integral to the process of analysis. In collective case studies, it is helpful to analyse data relating to the individual component cases first, before making comparisons across cases. Attention needs to be paid to variations within each case and, where relevant, the relationship between different causes, effects and outcomes[ 23 ]. Data will need to be organised and coded to allow the key issues, both derived from the literature and emerging from the dataset, to be easily retrieved at a later stage. An initial coding frame can help capture these issues and can be applied systematically to the whole dataset with the aid of a qualitative data analysis software package.

The Framework approach is a practical approach, comprising of five stages (familiarisation; identifying a thematic framework; indexing; charting; mapping and interpretation) , to managing and analysing large datasets particularly if time is limited, as was the case in our study of recruitment of South Asians into asthma research (Table ​ (Table1 1 )[ 3 , 24 ]. Theoretical frameworks may also play an important role in integrating different sources of data and examining emerging themes. For example, we drew on a socio-technical framework to help explain the connections between different elements - technology; people; and the organisational settings within which they worked - in our study of the introduction of electronic health record systems (Table ​ (Table3 3 )[ 5 ]. Our study of patient safety in undergraduate curricula drew on an evaluation-based approach to design and analysis, which emphasised the importance of the academic, organisational and practice contexts through which students learn (Table ​ (Table4 4 )[ 6 ].

Case study findings can have implications both for theory development and theory testing. They may establish, strengthen or weaken historical explanations of a case and, in certain circumstances, allow theoretical (as opposed to statistical) generalisation beyond the particular cases studied[ 12 ]. These theoretical lenses should not, however, constitute a strait-jacket and the cases should not be "forced to fit" the particular theoretical framework that is being employed.

When reporting findings, it is important to provide the reader with enough contextual information to understand the processes that were followed and how the conclusions were reached. In a collective case study, researchers may choose to present the findings from individual cases separately before amalgamating across cases. Care must be taken to ensure the anonymity of both case sites and individual participants (if agreed in advance) by allocating appropriate codes or withholding descriptors. In the example given in Table ​ Table3, 3 , we decided against providing detailed information on the NHS sites and individual participants in order to avoid the risk of inadvertent disclosure of identities[ 5 , 25 ].

What are the potential pitfalls and how can these be avoided?

The case study approach is, as with all research, not without its limitations. When investigating the formal and informal ways undergraduate students learn about patient safety (Table ​ (Table4), 4 ), for example, we rapidly accumulated a large quantity of data. The volume of data, together with the time restrictions in place, impacted on the depth of analysis that was possible within the available resources. This highlights a more general point of the importance of avoiding the temptation to collect as much data as possible; adequate time also needs to be set aside for data analysis and interpretation of what are often highly complex datasets.

Case study research has sometimes been criticised for lacking scientific rigour and providing little basis for generalisation (i.e. producing findings that may be transferable to other settings)[ 1 ]. There are several ways to address these concerns, including: the use of theoretical sampling (i.e. drawing on a particular conceptual framework); respondent validation (i.e. participants checking emerging findings and the researcher's interpretation, and providing an opinion as to whether they feel these are accurate); and transparency throughout the research process (see Table ​ Table8 8 )[ 8 , 18 - 21 , 23 , 26 ]. Transparency can be achieved by describing in detail the steps involved in case selection, data collection, the reasons for the particular methods chosen, and the researcher's background and level of involvement (i.e. being explicit about how the researcher has influenced data collection and interpretation). Seeking potential, alternative explanations, and being explicit about how interpretations and conclusions were reached, help readers to judge the trustworthiness of the case study report. Stake provides a critique checklist for a case study report (Table ​ (Table9 9 )[ 8 ].

Potential pitfalls and mitigating actions when undertaking case study research

Stake's checklist for assessing the quality of a case study report[ 8 ]


The case study approach allows, amongst other things, critical events, interventions, policy developments and programme-based service reforms to be studied in detail in a real-life context. It should therefore be considered when an experimental design is either inappropriate to answer the research questions posed or impossible to undertake. Considering the frequency with which implementations of innovations are now taking place in healthcare settings and how well the case study approach lends itself to in-depth, complex health service research, we believe this approach should be more widely considered by researchers. Though inherently challenging, the research case study can, if carefully conceptualised and thoughtfully undertaken and reported, yield powerful insights into many important aspects of health and healthcare delivery.

Competing interests

The authors declare that they have no competing interests.

Authors' contributions

AS conceived this article. SC, KC and AR wrote this paper with GH, AA and AS all commenting on various drafts. SC and AS are guarantors.

Pre-publication history

The pre-publication history for this paper can be accessed here:



We are grateful to the participants and colleagues who contributed to the individual case studies that we have drawn on. This work received no direct funding, but it has been informed by projects funded by Asthma UK, the NHS Service Delivery Organisation, NHS Connecting for Health Evaluation Programme, and Patient Safety Research Portfolio. We would also like to thank the expert reviewers for their insightful and constructive feedback. Our thanks are also due to Dr. Allison Worth who commented on an earlier draft of this manuscript.

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15 Hypothesis Examples

hypothesis definition and example, explained below

A hypothesis is defined as a testable prediction , and is used primarily in scientific experiments as a potential or predicted outcome that scientists attempt to prove or disprove (Atkinson et al., 2021; Tan, 2022).

In my types of hypothesis article, I outlined 13 different hypotheses, including the directional hypothesis (which makes a prediction about an effect of a treatment will be positive or negative) and the associative hypothesis (which makes a prediction about the association between two variables).

This article will dive into some interesting examples of hypotheses and examine potential ways you might test each one.

Hypothesis Examples

1. “inadequate sleep decreases memory retention”.

Field: Psychology

Type: Causal Hypothesis A causal hypothesis explores the effect of one variable on another. This example posits that a lack of adequate sleep causes decreased memory retention. In other words, if you are not getting enough sleep, your ability to remember and recall information may suffer.

How to Test:

To test this hypothesis, you might devise an experiment whereby your participants are divided into two groups: one receives an average of 8 hours of sleep per night for a week, while the other gets less than the recommended sleep amount.

During this time, all participants would daily study and recall new, specific information. You’d then measure memory retention of this information for both groups using standard memory tests and compare the results.

Should the group with less sleep have statistically significant poorer memory scores, the hypothesis would be supported.

Ensuring the integrity of the experiment requires taking into account factors such as individual health differences, stress levels, and daily nutrition.

Relevant Study: Sleep loss, learning capacity and academic performance (Curcio, Ferrara & De Gennaro, 2006)

2. “Increase in Temperature Leads to Increase in Kinetic Energy”

Field: Physics

Type: Deductive Hypothesis The deductive hypothesis applies the logic of deductive reasoning – it moves from a general premise to a more specific conclusion. This specific hypothesis assumes that as temperature increases, the kinetic energy of particles also increases – that is, when you heat something up, its particles move around more rapidly.

This hypothesis could be examined by heating a gas in a controlled environment and capturing the movement of its particles as a function of temperature.

You’d gradually increase the temperature and measure the kinetic energy of the gas particles with each increment. If the kinetic energy consistently rises with the temperature, your hypothesis gets supporting evidence.

Variables such as pressure and volume of the gas would need to be held constant to ensure validity of results.

3. “Children Raised in Bilingual Homes Develop Better Cognitive Skills”

Field: Psychology/Linguistics

Type: Comparative Hypothesis The comparative hypothesis posits a difference between two or more groups based on certain variables. In this context, you might propose that children raised in bilingual homes have superior cognitive skills compared to those raised in monolingual homes.

Testing this hypothesis could involve identifying two groups of children: those raised in bilingual homes, and those raised in monolingual homes.

Cognitive skills in both groups would be evaluated using a standard cognitive ability test at different stages of development. The examination would be repeated over a significant time period for consistency.

If the group raised in bilingual homes persistently scores higher than the other, the hypothesis would thereby be supported.

The challenge for the researcher would be controlling for other variables that could impact cognitive development, such as socio-economic status, education level of parents, and parenting styles.

Relevant Study: The cognitive benefits of being bilingual (Marian & Shook, 2012)

4. “High-Fiber Diet Leads to Lower Incidences of Cardiovascular Diseases”

Field: Medicine/Nutrition

Type: Alternative Hypothesis The alternative hypothesis suggests an alternative to a null hypothesis. In this context, the implied null hypothesis could be that diet has no effect on cardiovascular health, which the alternative hypothesis contradicts by suggesting that a high-fiber diet leads to fewer instances of cardiovascular diseases.

To test this hypothesis, a longitudinal study could be conducted on two groups of participants; one adheres to a high-fiber diet, while the other follows a diet low in fiber.

After a fixed period, the cardiovascular health of participants in both groups could be analyzed and compared. If the group following a high-fiber diet has a lower number of recorded cases of cardiovascular diseases, it would provide evidence supporting the hypothesis.

Control measures should be implemented to exclude the influence of other lifestyle and genetic factors that contribute to cardiovascular health.

Relevant Study: Dietary fiber, inflammation, and cardiovascular disease (King, 2005)

5. “Gravity Influences the Directional Growth of Plants”

Field: Agronomy / Botany

Type: Explanatory Hypothesis An explanatory hypothesis attempts to explain a phenomenon. In this case, the hypothesis proposes that gravity affects how plants direct their growth – both above-ground (toward sunlight) and below-ground (towards water and other resources).

The testing could be conducted by growing plants in a rotating cylinder to create artificial gravity.

Observations on the direction of growth, over a specified period, can provide insights into the influencing factors. If plants consistently direct their growth in a manner that indicates the influence of gravitational pull, the hypothesis is substantiated.

It is crucial to ensure that other growth-influencing factors, such as light and water, are uniformly distributed so that only gravity influences the directional growth.

6. “The Implementation of Gamified Learning Improves Students’ Motivation”

Field: Education

Type: Relational Hypothesis The relational hypothesis describes the relation between two variables. Here, the hypothesis is that the implementation of gamified learning has a positive effect on the motivation of students.

To validate this proposition, two sets of classes could be compared: one that implements a learning approach with game-based elements, and another that follows a traditional learning approach.

The students’ motivation levels could be gauged by monitoring their engagement, performance, and feedback over a considerable timeframe.

If the students engaged in the gamified learning context present higher levels of motivation and achievement, the hypothesis would be supported.

Control measures ought to be put into place to account for individual differences, including prior knowledge and attitudes towards learning.

Relevant Study: Does educational gamification improve students’ motivation? (Chapman & Rich, 2018)

7. “Mathematics Anxiety Negatively Affects Performance”

Field: Educational Psychology

Type: Research Hypothesis The research hypothesis involves making a prediction that will be tested. In this case, the hypothesis proposes that a student’s anxiety about math can negatively influence their performance in math-related tasks.

To assess this hypothesis, researchers must first measure the mathematics anxiety levels of a sample of students using a validated instrument, such as the Mathematics Anxiety Rating Scale.

Then, the students’ performance in mathematics would be evaluated through standard testing. If there’s a negative correlation between the levels of math anxiety and math performance (meaning as anxiety increases, performance decreases), the hypothesis would be supported.

It would be crucial to control for relevant factors such as overall academic performance and previous mathematical achievement.

8. “Disruption of Natural Sleep Cycle Impairs Worker Productivity”

Field: Organizational Psychology

Type: Operational Hypothesis The operational hypothesis involves defining the variables in measurable terms. In this example, the hypothesis posits that disrupting the natural sleep cycle, for instance through shift work or irregular working hours, can lessen productivity among workers.

To test this hypothesis, you could collect data from workers who maintain regular working hours and those with irregular schedules.

Measuring productivity could involve examining the worker’s ability to complete tasks, the quality of their work, and their efficiency.

If workers with interrupted sleep cycles demonstrate lower productivity compared to those with regular sleep patterns, it would lend support to the hypothesis.

Consideration should be given to potential confounding variables such as job type, worker age, and overall health.

9. “Regular Physical Activity Reduces the Risk of Depression”

Field: Health Psychology

Type: Predictive Hypothesis A predictive hypothesis involves making a prediction about the outcome of a study based on the observed relationship between variables. In this case, it is hypothesized that individuals who engage in regular physical activity are less likely to suffer from depression.

Longitudinal studies would suit to test this hypothesis, tracking participants’ levels of physical activity and their mental health status over time.

The level of physical activity could be self-reported or monitored, while mental health status could be assessed using standard diagnostic tools or surveys.

If data analysis shows that participants maintaining regular physical activity have a lower incidence of depression, this would endorse the hypothesis.

However, care should be taken to control other lifestyle and behavioral factors that could intervene with the results.

Relevant Study: Regular physical exercise and its association with depression (Kim, 2022)

10. “Regular Meditation Enhances Emotional Stability”

Type: Empirical Hypothesis In the empirical hypothesis, predictions are based on amassed empirical evidence . This particular hypothesis theorizes that frequent meditation leads to improved emotional stability, resonating with numerous studies linking meditation to a variety of psychological benefits.

Earlier studies reported some correlations, but to test this hypothesis directly, you’d organize an experiment where one group meditates regularly over a set period while a control group doesn’t.

Both groups’ emotional stability levels would be measured at the start and end of the experiment using a validated emotional stability assessment.

If regular meditators display noticeable improvements in emotional stability compared to the control group, the hypothesis gains credit.

You’d have to ensure a similar emotional baseline for all participants at the start to avoid skewed results.

11. “Children Exposed to Reading at an Early Age Show Superior Academic Progress”

Type: Directional Hypothesis The directional hypothesis predicts the direction of an expected relationship between variables. Here, the hypothesis anticipates that early exposure to reading positively affects a child’s academic advancement.

A longitudinal study tracking children’s reading habits from an early age and their consequent academic performance could validate this hypothesis.

Parents could report their children’s exposure to reading at home, while standardized school exam results would provide a measure of academic achievement.

If the children exposed to early reading consistently perform better acadically, it gives weight to the hypothesis.

However, it would be important to control for variables that might impact academic performance, such as socioeconomic background, parental education level, and school quality.

12. “Adopting Energy-efficient Technologies Reduces Carbon Footprint of Industries”

Field: Environmental Science

Type: Descriptive Hypothesis A descriptive hypothesis predicts the existence of an association or pattern related to variables. In this scenario, the hypothesis suggests that industries adopting energy-efficient technologies will resultantly show a reduced carbon footprint.

Global industries making use of energy-efficient technologies could track their carbon emissions over time. At the same time, others not implementing such technologies continue their regular tracking.

After a defined time, the carbon emission data of both groups could be compared. If industries that adopted energy-efficient technologies demonstrate a notable reduction in their carbon footprints, the hypothesis would hold strong.

In the experiment, you would exclude variations brought by factors such as industry type, size, and location.

13. “Reduced Screen Time Improves Sleep Quality”

Type: Simple Hypothesis The simple hypothesis is a prediction about the relationship between two variables, excluding any other variables from consideration. This example posits that by reducing time spent on devices like smartphones and computers, an individual should experience improved sleep quality.

A sample group would need to reduce their daily screen time for a pre-determined period. Sleep quality before and after the reduction could be measured using self-report sleep diaries and objective measures like actigraphy, monitoring movement and wakefulness during sleep.

If the data shows that sleep quality improved post the screen time reduction, the hypothesis would be validated.

Other aspects affecting sleep quality, like caffeine intake, should be controlled during the experiment.

Relevant Study: Screen time use impacts low‐income preschool children’s sleep quality, tiredness, and ability to fall asleep (Waller et al., 2021)

14. Engaging in Brain-Training Games Improves Cognitive Functioning in Elderly

Field: Gerontology

Type: Inductive Hypothesis Inductive hypotheses are based on observations leading to broader generalizations and theories. In this context, the hypothesis deduces from observed instances that engaging in brain-training games can help improve cognitive functioning in the elderly.

A longitudinal study could be conducted where an experimental group of elderly people partakes in regular brain-training games.

Their cognitive functioning could be assessed at the start of the study and at regular intervals using standard neuropsychological tests.

If the group engaging in brain-training games shows better cognitive functioning scores over time compared to a control group not playing these games, the hypothesis would be supported.

15. Farming Practices Influence Soil Erosion Rates

Type: Null Hypothesis A null hypothesis is a negative statement assuming no relationship or difference between variables. The hypothesis in this context asserts there’s no effect of different farming practices on the rates of soil erosion.

Comparing soil erosion rates in areas with different farming practices over a considerable timeframe could help test this hypothesis.

If, statistically, the farming practices do not lead to differences in soil erosion rates, the null hypothesis is accepted.

However, if marked variation appears, the null hypothesis is rejected, meaning farming practices do influence soil erosion rates. It would be crucial to control for external factors like weather, soil type, and natural vegetation.

The variety of hypotheses mentioned above underscores the diversity of research constructs inherent in different fields, each with its unique purpose and way of testing.

While researchers may develop hypotheses primarily as tools to define and narrow the focus of the study, these hypotheses also serve as valuable guiding forces for the data collection and analysis procedures, making the research process more efficient and direction-focused.

Hypotheses serve as a compass for any form of academic research. The diverse examples provided, from Psychology to Educational Studies, Environmental Science to Gerontology, clearly demonstrate how certain hypotheses suit specific fields more aptly than others.

It is important to underline that although these varied hypotheses differ in their structure and methods of testing, each endorses the fundamental value of empiricism in research. Evidence-based decision making remains at the heart of scholarly inquiry, regardless of the research field, thus aligning all hypotheses to the core purpose of scientific investigation.

Testing hypotheses is an essential part of the scientific method . By doing so, researchers can either confirm their predictions, giving further validity to an existing theory, or they might uncover new insights that could potentially shift the field’s understanding of a particular phenomenon. In either case, hypotheses serve as the stepping stones for scientific exploration and discovery.

Atkinson, P., Delamont, S., Cernat, A., Sakshaug, J. W., & Williams, R. A. (2021).  SAGE research methods foundations . SAGE Publications Ltd.

Curcio, G., Ferrara, M., & De Gennaro, L. (2006). Sleep loss, learning capacity and academic performance.  Sleep medicine reviews ,  10 (5), 323-337.

Kim, J. H. (2022). Regular physical exercise and its association with depression: A population-based study short title: Exercise and depression.  Psychiatry Research ,  309 , 114406.

King, D. E. (2005). Dietary fiber, inflammation, and cardiovascular disease.  Molecular nutrition & food research ,  49 (6), 594-600.

Marian, V., & Shook, A. (2012, September). The cognitive benefits of being bilingual. In Cerebrum: the Dana forum on brain science (Vol. 2012). Dana Foundation.

Tan, W. C. K. (2022). Research Methods: A Practical Guide For Students And Researchers (Second Edition) . World Scientific Publishing Company.

Waller, N. A., Zhang, N., Cocci, A. H., D’Agostino, C., Wesolek‐Greenson, S., Wheelock, K., … & Resnicow, K. (2021). Screen time use impacts low‐income preschool children’s sleep quality, tiredness, and ability to fall asleep. Child: care, health and development, 47 (5), 618-626.


Chris Drew (PhD)

Dr. Chris Drew is the founder of the Helpful Professor. He holds a PhD in education and has published over 20 articles in scholarly journals. He is the former editor of the Journal of Learning Development in Higher Education. [Image Descriptor: Photo of Chris]

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hypothesis case study example

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Seeing Through Statistics

Jessica m. utts, hypothesis testing—examples and case studies - all with video answers.

hypothesis case study example

Chapter Questions

Are null and alternative hypotheses statements about populations or samples, or does it depend on the situation?

Roee Shalom

In a February, 2013, CBS News/New York Times poll of 250 American Catholics who attend mass at least once a week, 57% answered yes to the question, “Do you favor allowing women to be priests?” (Source: http://www.nytimes.com/interactive/2013/03/06/us/catholics-america-poll.html?ref=us.) a. Set up the null and alternative hypotheses for deciding whether a majority of American Catholics who attend mass at least once a week favors allowing women to be priests. b. Using Example 23.4 as a guide, compute the test statistic for this situation. c. If you have done everything correctly, the $p$ -value for the test is about 0.0127 . Based on this, make a conclusion for this situation. Write it in both statistical language and in words that someone with no training in statistics would understand.

Rashmi Sinha

Refer to Exercise $2 .$ Is the test described there a one-sided or a two-sided test?

Harsh Gadhiya

Explain the difference between statistical significance and significance as used in everyday language.

Gaurav Kalra

Suppose a one-sided test for a proportion resulted in a $p$ -value of $0.03 .$ What would the $p$ -value be if the test were two-sided instead?

Christopher Stanley

Suppose a two-sided test for a difference in two means resulted in a $p$ -value of 0.08 . a. Using the usual criterion for hypothesis testing, would we conclude that there was a difference in the population means? Explain. b. Suppose the test had been constructed as a one-sided test instead, and the evidence in the sample means was in the direction to support the alternative hypothesis. Using the usual criterion for hypothesis testing, would we be able to conclude that there was a difference in the population means? Explain.

Saeeda Aman

Suppose you were given a hypothesized population mean, a sample mean, a sample standard deviation, and a sample size for a study involving a random sample from one population. What formula would you use for the test statistic?

Bryan Meares

In Example 23.4 , we showed that the Excel command NORMSDIST(z) gives the area below the standardized score $z$. Use Excel or an appropriate calculator, software, website, or table to find the $p$ -value for each of the following examples and case studies, taking into account whether the test is one-sided or two-sided: a. Example $23.3, z=2.17,$ two-sided test (using $z$, not t) b. Example $22.1, z=2.00,$ one-sided test c. Case Study $22.1, z=4.09,$ one-sided test

Thomas Emment

Suppose you wanted to see whether a training program helped raise students' scores on a standardized test. You administer the test to a random sample of students, give them the training program, then readminister the test. For each student, you record the increase (or decrease) in the test score from one time to the next. a. What would the null and alternative hypotheses be for this situation? b. Suppose the mean change for the sample was 10 points and the accompanying standard error was 4 points. What would be the standardized score that corresponded to the sample mean of 10 points? c. Based on the information in part (b), what would you conclude about this situation? (Assume the sample size is large and use $z$, not $t .$ )

Meredith Kempson

Refer to the previous exercise. a. What explanation might be given for the increased scores, other than the fact that the training program had an impact? b. What would have been a better way to design the study in order to rule out the explanation you gave in part (a)?

Carson Merrill

On July 1, 1994, The Press of Atlantic City, NJ, had a headline reading, "Study: Female hormone makes mind keener" (p. A2). Here is part of the report: Halbreich said he tested 36 post-menopausal women before and after they started the estrogen therapy. He gave each one a battery of tests that measured such things as memory, hand-eye coordination, reflexes and the ability to learn new information and apply it to a problem. After estrogen therapy started, he said, there was a subtle but statistically significant increase in the mental scores of the patients. Explain what you learned about the study, in the context of the material in this chapter by reading this quote. Be sure to specify the hypotheses that were being tested and what you know about the statistical results.

Sheryl Ezze

Siegel (1993) reported a study in which she measured the effect of pet ownership on the use of medical care by the elderly. She interviewed 938 elderly adults. One of her results was reported as: "After demographics and health status were controlled for, subjects with pets had fewer total doctor contacts during the one-year period than those without pets (beta $=-.07, p < .05$ )" (p. 164). a. State the null and alternative hypotheses Siegel was testing. Be careful to distinguish between a population and a sample. b. State the conclusion you would make. Be explicit about the wording.

Refer to Exercise $12 .$ Here is another of the results reported by Siegel: "For subjects without a pet, having an above-average number of stressful life events resulted in about two more doctor contacts during the study year $(10.37 \text { vs. } 8.38, p<.005)$. In contrast, the number of stressful life events was not significantly related to doctor visits among subjects with a pet" (1993, p. 164). a. State the null and alternative hypotheses Siegel is testing in this passage. Notice that two tests are being performed; be sure to cover both. b. Pretend you are a news reporter, and write a short story describing the results reported in this exercise. Be sure you do not convey any misleading information. You are writing for a general audience, so do not use statistical jargon that would be unfamiliar to them.

James Kiss

Refer to Example 13.2 , in which we tested whether there was a relationship between gender and driving after drinking alcohol. Remember that the Supreme Court used the data to determine whether a law was justified. The law differentiated between the ages at which young males and young females could purchase $3.2 \%$ beer. Specify what a type 1 and a type 2 error would be for this example. Explain what the consequences of the two types of error would be in that context.

Cerys Evans

A CNN/ORC poll conducted in January, 2013 , asked 814 adults in the United States, "Which of the following do you think is the most pressing issue facing the country today?" and then presented seven choices, one of which was "The Economy." (Source: http://www.pollingreport.com/prioriti.htm, accessed July 16, 2013.) "The Economy" was chosen by $46 \%$ of the respondents. Suppose an unscrupulous politician wanted to show that the economy was not a pressing issue, and stated "Significantly fewer than half of adults think that the economy is a pressing issue." a. What are the null and alternative hypotheses the politician is implicitly testing in this quote? Make sure you specify the population value being tested and the population to which it applies. b. Using the results of the poll, find the value of the standardized score that would be used as the test statistic. c. If you answered parts (a) and (b) correctly, the $p$ -value for the test should be about 0.011 . Explain how the politician reached the conclusion stated in the quote. d. Do you think the statement made by the politician is justified? Explain.

In Example 23.3 , we tested whether the average fat lost from 1 year of dieting versus 1 year of exercise was equivalent. The study also measured lean body weight (muscle) lost or gained. The average for the 47 men who exercised was a gain of $0.1 \mathrm{kg}$, which can be thought of as a loss of -0.1 kg. The standard deviation was 2.2 kg. For the 42 men in the dieting group, there was an average loss of $1.3 \mathrm{kg},$ with a standard deviation of $2.6 \mathrm{kg}$. Test to see whether the average lean body mass lost (or gained) would be different for the population of men similar to the ones in this study. Specify all four steps of your hypothesis test. (Use z instead of t.)

Professors and other researchers use scholarly journals to publish the results of their research. However, only a small minority of the submitted papers is accepted for publication by the most prestigious journals. In many academic fields, there is a debate as to whether submitted papers written by women are treated as well as those submitted by men. In the January 1994 issue of European Science Editing (Maisonneuve, January 1994 ), there was a report on a study that examined this question. Here is part of that report: Similarly, no bias was found to exist at JAMA [lournal of the American Medical Association) in acceptance rates based on the gender of the corresponding author and the assigned editor. In the sample of 1851 articles considered in this study female editors used female reviewers more often than did male editors (P < 0.001). That quote actually contains the results of two separate hypothesis tests. Explain what the two sets of hypotheses tested are and what you can conclude about the $p$ -value for each set.

Victor Salazar

Use Excel or an appropriate calculator, software, website, or table to find the $p$ -value in each of the following situations. a. Alternative hypothesis is "greater than," $t=+2.5, \mathrm{df}=40$ b. Alternative hypothesis is "less than," $t=-2.5, \mathrm{df}=40$ c. Alternative hypothesis is "not equal," $t=2.5, \mathrm{df}=40$ d. Alternative hypothesis is "greater than" $z=+1.75$ e. Alternative hypothesis is "less than," $z=-1.75$ f. Alternative hypothesis is "not equal," $z=-1.75$

Nick Johnson

On January $30,1995,$ Time magazine reported the results of a poll of adult Americans, in which they were asked, "Have you ever driven a car when you probably had too much alcohol to drive safely?" The exact results were not given, but from the information provided we can guess at what they were. Of the 300 men who answered, 189 ( $63 \%$ ) said yes and 108 ( $36 \%$ ) said no. The remaining three weren't sure. Of the 300 women, 87 ( $29 \%$ ) said yes while $210(70 \%)$ said no, and the remaining three weren't sure. a. Ignoring those who said they weren't sure, there were 297 men asked, and 189 said yes, they had driven a car when they probably had too much alcohol. Does this provide statistically significant evidence that a majority of men in the population (that is, more than half) would say that they had driven a car when they probably had too much alcohol, if asked? Go through the four steps to test this hypothesis. b. For the test in part (a), you were instructed to perform a one-sided test. Why do you think it would make sense to do so in this situation? If you do not think it made sense, explain why not. c. Repeat parts (a) and (b) for the women. (Note that of the 297 women who answered, 87 said yes.) The following information is for Exercises 20 to 22 : In Example 23.3 , we tested to see whether dieters and exercisers had significantly different average fat loss. We concluded that they did because the difference for the samples under consideration was $1.8 \mathrm{kg}$, with a standard error of $0.83 \mathrm{kg}$ and a standardized score of $2.17 .$ Fat loss was higher for the dieters.

Construct an approximate $95 \%$ confidence interval for the population difference in mean fat loss. Consider the two different methods for presenting results: 1. the $p$ -value and conclusion from the hypothesis test or 2. the confidence interval. Which do you think is more informative? Explain.

Suppose the alternative hypothesis had been that men who exercised lost more fat on average than men who dieted. Would the null hypothesis have been rejected? Explain why or why not. If yes, give the $p$ -value that would have been used.

Hast Aggarwal

Suppose the alternative hypothesis had been that men who dieted lost more fat on average than men who exercised. Would the null hypothesis have been rejected? Explain why or why not. If yes, give the $p$ -value that would have been used. Exercises 23 to 29 refer to News Story and Original Source 1 , "Alterations in Brain and Immune Function Produced by Mindfulness Meditation," (not available on the companion website). For this study, volunteers were randomly assigned to a meditation group (25 participants) or a control group (16 participants). The meditation group received an 8-week meditation training program. Both groups were given influenza shots and their antibodies were measured. This measurement was taken after the meditation group had been practicing meditation for about 8 weeks. The researchers also measured brain activity, but these exercises will not explore that part of the study.

On page 565 of the article we are told that "Participants were right-handed subjects who were employees of a biotechnology corporation in Madison, Wisconsin." To what population do you think the results of this study apply?

Blank Blank

Participants were given psychological tests measuring positive and negative affect (mood) as well as anxiety at three time periods. Time 1 was before the meditation training. Time 2 was at the end of the 8 weeks of training, and Time 3 was 4 months later. One of the results reported is: There was a significant decrease in trait negative affect with the meditators showing less negative affect at Times 2 and 3 compared with their negative affect at Time $1[t(20)=2.27 \text { and } t(21)=2.45, \text { respectively, } p<.05 \text { for both }] .$ Subjects in the control group showed no change over time in negative affect ( $t<1$ ) (Davidson et al, $p .565$ ). The first sentence of the quote reports the results of two hypothesis tests for the meditators. Specify in words the null hypothesis for each of the two tests. They are the same except that one is for Time 2 and one is for Time 3. State each one separately, referring to what the time periods were. Make sure you don’t confuse the population with the sample and that you state the hypotheses using the correct one.

a. Refer to Exercise $24 .$ State the alternative hypothesis for each test. Explain whether you decided to use a one-sided or a two-sided test and why. b. Write the conclusion for the Time 2 test in statistical language and in plain English.

Karen Song

Refer to the quote in the Exercise 24 . Explain what is meant by the last sentence, "Subjects in the control group showed no change over time in negative affect $(t<1)$ " In particular, do you think the sample difference was exactly zero?

Maxime Rossetti

Another quote in the article is In response to the influenza vaccine, the meditators displayed a significantly greater rise in antibody titers from the 4 to 8 week blood draw compared with the controls $[t(33)=2.05, p<.05, \text { Figure } 5]$ (Davidson et al, p. 566 ). Specify in words the null hypothesis being tested. Make sure you don't confuse the population with the sample and that you state the hypothesis using the correct one.

Refer to the quote in Exercise 27 . Specify in words the alternative hypothesis being tested. Explain whether you decided to use a one-sided or a two-sided test and why.

Refer to the quote in Exercise 27 a. What is the meaning of the word significantly in the quote? b. Explain in plain English what the results of this test mean. Exercises 30 to 32 refer to News Story 14 and the journal article Original Source 14 , "Sex differences in the neural basis of emotional memories" (not available on the companion website). In this study, 12 men and 12 women were shown 96 pictures each. They rated the pictures for emotional intensity on a scale from 0 (no emotion) to 3 (intense emotion). Without being told in advance that this would happen, 3 weeks later they were shown the same set of pictures, interspersed with an additional 48 pictures, called "foils." They were asked which of the pictures they thought that they had seen previously, and if each one of those was just familiar or was distinctly remembered. Results for each picture were coded as 0 (forgotten). 1 (familiar), or 2 (remembered).

Colin Fenster

One of the results was "women rated significantly more pictures as highly arousing (rated 3) than did men $\left.[t(22)=2.41, P < 0.025]^{\prime \prime} \text { (Canli et al. }, 2002, \mathrm{p} .10790\right)$ a. Specify in words the null hypothesis being tested. Make sure you don't confuse the population with the sample and that you state the hypothesis using the correct one. b. Were the researchers using a one-sided or a two-sided alternative hypothesis? Explain how you know. c. Explain in words what is meant by $[t(22)=2.41, P<0.025]$ d. Is the use of the word significantly in the quote the statistical version or the English version or both? Explain how you know.

Neel Faucher

One of the results was "women had better memory for emotional pictures than men; pictures rated as most highly arousing were recognized significantly more often by women than by men as familiar $[t(20)=2.40, P < 0.05]$ or remembered $[t(20)=2.38, P < 0.05]^{\prime \prime}(\text { Canli et al., } 2002, \mathrm{p}$ 10790). There are two separate test results reported in this quote. a. Specify in words the null hypothesis being tested for each of the two tests. Make sure you don't confuse the population with the sample and that you state the hypothesis using the correct one. b. Were the researchers using a one-sided or a two-sided alternative hypothesis? Explain how you know. c. Explain in words what is meant by $[t(20)=2.38, P<0.05]$ d. Is the use of the word "significantly" in the quote the statistical version or the English version or both? Explain how you know.

One of the results was "there were no significant sex differences in memory for pictures rated less intense $(0-2)$ or in false-positive rates $(12 \text { and } 10 \%$ for women and men, respectively)" (Canli et al., 2002, p. 10790). a. What is meant by "false positive rates" in this example? b. Specify in words the null hypothesis being tested regarding false positives. Make sure you don't confuse the population with the sample and that you state the hypothesis using the correct one. c. Is the use of the word significant in the quote the statistical version or the English version or both? Explain how you know.

Charles Carter

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Hypothesis Testing in R- Introduction Examples and Case Study

  • Parameter and Statistic
  • Sampling Distribution
  • Standard Error
  • Statistical Inference
  • One Sample Tests
  • The Five Steps Process of Hypothesis Testing
  • p-value: An Alternative way of Hypothesis Testing:
  • t-test: Hypothesis Testing of Population Mean when Population Standard Deviation is Unknown:
  • Independent Samples and Dependent (Paired Samples):
  • Testing the Difference Between Means: Independent Samples
  • Paired Sample t-Test (Testing Difference between Means with Dependent Samples):
  • t-Test in SPSS:
  • t-Test Application One Sample
  • Independent t-test two sample
  • Case Study- Titan Insurance Company
  • References:

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

Introduction to Hypothesis Testing in R

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:

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. 

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. 

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 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.

Testing of Hypothesis in R

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 ).

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.  


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. 

Two Samples Tests: Hypothesis Testing for the difference between two population means

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.

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.  

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: 

hypothesis case study example

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):

hypothesis case study example

Hypothesis Testing for Equality of Population Variances

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.

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. 

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

hypothesis case study example

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

hypothesis case study example

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

hypothesis case study example

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   

hypothesis case study example

Let’s Look at some Case studies:

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

Hypothesis Testing in R

[1] 1.224674

[1] 0.2305533

[1] “Accepted”

Hypothesis Testing in R

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

Hypothesis Testing in R

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

Hypothesis Testing in R

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.

Hypothesis Testing in R

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

Hypothesis Testing in R


      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

Hypothesis Testing in R

= 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

  • How it works

A Quick Guide to Case Study with Examples

Published by Alvin Nicolas at August 14th, 2021 , Revised On August 29, 2023

A case study is a documented history and detailed analysis of a situation concerning organisations, industries, and markets.

A case study:

  • Focuses on discovering new facts of the situation under observation.
  • Includes data collection from multiple sources over time.
  • Widely used in social sciences to study the underlying information, organisation, community, or event.
  • It does not provide any solution to the problem .

When to Use Case Study? 

You can use a case study in your research when:

  • The focus of your study is to find answers to how and why questions .
  • You don’t have enough time to conduct extensive research; case studies are convenient for completing your project successfully.
  • You want to analyse real-world problems in-depth, then you can use the method of the case study.

You can consider a single case to gain in-depth knowledge about the subject, or you can choose multiple cases to know about various aspects of your  research problem .

What are the Aims of the Case Study?

  • The case study aims at identifying weak areas that can be improved.
  • This method is often used for idiographic research (focuses on individual cases or events).
  • Another aim of the case study is nomothetic research (aims to discover new theories through data analysis of multiple cases).

Types of Case Studies

There are different types of case studies that can be categorised based on the purpose of the investigation.

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How to Conduct a Case Study?

  • Select the Case to Investigate
  • Formulate the Research Question
  • Review of Literature
  • Choose the Precise Case to Use in your Study
  • Select Data Collection and Analysis Techniques
  • Collect the Data
  • Analyse the Data
  • Prepare the Report

Step1: Select the Case to Investigate

The first step is to select a case to conduct your investigation. You should remember the following points.

  • Make sure that you perform the study in the available timeframe.
  • There should not be too much information available about the organisation.
  • You should be able to get access to the organisation.
  • There should be enough information available about the subject to conduct further research.

Step2: Formulate the Research Question

It’s necessary to  formulate a research question  to proceed with your case study. Most of the research questions begin with  how, why, what, or what can . 

You can also use a research statement instead of a research question to conduct your research which can be conditional or non-conditional. 

Step 3: Review of Literature

Once you formulate your research statement or question, you need to extensively  review the documentation about the existing discoveries related to your research question or statement.

Step 4: Choose the Precise Case to Use in your Study

You need to select a specific case or multiple cases related to your research. It would help if you treated each case individually while using multiple cases. The outcomes of each case can be used as contributors to the outcomes of the entire study.  You can select the following cases. 

  • Representing various geographic regions
  • Cases with various size parameters
  • Explaining the existing theories or assumptions
  • Leading to discoveries
  • Providing a base for future research.

Step 5: Select Data Collection and Analysis Techniques

You can choose both  qualitative or quantitative approaches  for  collecting the data . You can use  interviews ,  surveys , artifacts, documentation, newspapers, and photographs, etc. To avoid biased observation, you can triangulate  your research to provide different views of your case. Even if you are focusing on a single case, you need to observe various case angles. It would help if you constructed validity, internal and external validity, as well as reliability.

Example: Identifying the impacts of contaminated water on people’s health and the factors responsible for it. You need to gather the data using qualitative and quantitative approaches to understand the case in such cases.

Construct validity:  You should select the most suitable measurement tool for your research. 

Internal validity:   You should use various methodological tools to  triangulate  the data. Try different methods to study the same hypothesis.

External validity:  You need to effectively apply the data beyond the case’s circumstances to more general issues.

Reliability:   You need to be confident enough to formulate the new direction for future studies based on your findings.

Also Read:  Reliability and Validity

Step 6: Collect the Data

Beware of the following when collecting data:

  • Information should be gathered systematically, and the collected evidence from various sources should contribute to your research objectives.
  • Don’t collect your data randomly.
  • Recheck your research questions to avoid mistakes.
  • You should save the collected data in any popular format for clear understanding.
  • While making any changes to collecting information, make sure to record the changes in a document.
  • You should maintain a case diary and note your opinions and thoughts evolved throughout the study.

Step 7: Analyse the Data

The research data identifies the relationship between the objects of study and the research questions or statements. You need to reconfirm the collected information and tabulate it correctly for better understanding. 

Step 8: Prepare the Report

It’s essential to prepare a report for your case study. You can write your case study in the form of a scientific paper or thesis discussing its detail with supporting evidence. 

A case study can be represented by incorporating  quotations,  stories, anecdotes,  interview transcripts , etc., with empirical data in the result section. 

You can also write it in narrative styles using  textual analysis  or   discourse analysis . Your report should also include evidence from published literature, and you can put it in the discussion section.

Advantages and Disadvantages of Case Study

Frequently asked questions, what is the case study.

A case study is a research method where a specific instance, event, or situation is deeply examined to gain insights into real-world complexities. It involves detailed analysis of context, data, and variables to understand patterns, causes, and effects, often used in various disciplines for in-depth exploration.

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  • How It Works

Organizing Your Social Sciences Research Assignments

  • Annotated Bibliography
  • Analyzing a Scholarly Journal Article
  • Group Presentations
  • Dealing with Nervousness
  • Using Visual Aids
  • Grading Someone Else's Paper
  • Types of Structured Group Activities
  • Group Project Survival Skills
  • Leading a Class Discussion
  • Multiple Book Review Essay
  • Reviewing Collected Works
  • Writing a Case Analysis Paper
  • Writing a Case Study
  • About Informed Consent
  • Writing Field Notes
  • Writing a Policy Memo
  • Writing a Reflective Paper
  • Writing a Research Proposal
  • Generative AI and Writing
  • Acknowledgments

Definition and Introduction

Case analysis is a problem-based teaching and learning method that involves critically analyzing complex scenarios within an organizational setting for the purpose of placing the student in a “real world” situation and applying reflection and critical thinking skills to contemplate appropriate solutions, decisions, or recommended courses of action. It is considered a more effective teaching technique than in-class role playing or simulation activities. The analytical process is often guided by questions provided by the instructor that ask students to contemplate relationships between the facts and critical incidents described in the case.

Cases generally include both descriptive and statistical elements and rely on students applying abductive reasoning to develop and argue for preferred or best outcomes [i.e., case scenarios rarely have a single correct or perfect answer based on the evidence provided]. Rather than emphasizing theories or concepts, case analysis assignments emphasize building a bridge of relevancy between abstract thinking and practical application and, by so doing, teaches the value of both within a specific area of professional practice.

Given this, the purpose of a case analysis paper is to present a structured and logically organized format for analyzing the case situation. It can be assigned to students individually or as a small group assignment and it may include an in-class presentation component. Case analysis is predominately taught in economics and business-related courses, but it is also a method of teaching and learning found in other applied social sciences disciplines, such as, social work, public relations, education, journalism, and public administration.

Ellet, William. The Case Study Handbook: A Student's Guide . Revised Edition. Boston, MA: Harvard Business School Publishing, 2018; Christoph Rasche and Achim Seisreiner. Guidelines for Business Case Analysis . University of Potsdam; Writing a Case Analysis . Writing Center, Baruch College; Volpe, Guglielmo. "Case Teaching in Economics: History, Practice and Evidence." Cogent Economics and Finance 3 (December 2015). doi:https://doi.org/10.1080/23322039.2015.1120977.

How to Approach Writing a Case Analysis Paper

The organization and structure of a case analysis paper can vary depending on the organizational setting, the situation, and how your professor wants you to approach the assignment. Nevertheless, preparing to write a case analysis paper involves several important steps. As Hawes notes, a case analysis assignment “...is useful in developing the ability to get to the heart of a problem, analyze it thoroughly, and to indicate the appropriate solution as well as how it should be implemented” [p.48]. This statement encapsulates how you should approach preparing to write a case analysis paper.

Before you begin to write your paper, consider the following analytical procedures:

  • Review the case to get an overview of the situation . A case can be only a few pages in length, however, it is most often very lengthy and contains a significant amount of detailed background information and statistics, with multilayered descriptions of the scenario, the roles and behaviors of various stakeholder groups, and situational events. Therefore, a quick reading of the case will help you gain an overall sense of the situation and illuminate the types of issues and problems that you will need to address in your paper. If your professor has provided questions intended to help frame your analysis, use them to guide your initial reading of the case.
  • Read the case thoroughly . After gaining a general overview of the case, carefully read the content again with the purpose of understanding key circumstances, events, and behaviors among stakeholder groups. Look for information or data that appears contradictory, extraneous, or misleading. At this point, you should be taking notes as you read because this will help you develop a general outline of your paper. The aim is to obtain a complete understanding of the situation so that you can begin contemplating tentative answers to any questions your professor has provided or, if they have not provided, developing answers to your own questions about the case scenario and its connection to the course readings,lectures, and class discussions.
  • Determine key stakeholder groups, issues, and events and the relationships they all have to each other . As you analyze the content, pay particular attention to identifying individuals, groups, or organizations described in the case and identify evidence of any problems or issues of concern that impact the situation in a negative way. Other things to look for include identifying any assumptions being made by or about each stakeholder, potential biased explanations or actions, explicit demands or ultimatums , and the underlying concerns that motivate these behaviors among stakeholders. The goal at this stage is to develop a comprehensive understanding of the situational and behavioral dynamics of the case and the explicit and implicit consequences of each of these actions.
  • Identify the core problems . The next step in most case analysis assignments is to discern what the core [i.e., most damaging, detrimental, injurious] problems are within the organizational setting and to determine their implications. The purpose at this stage of preparing to write your analysis paper is to distinguish between the symptoms of core problems and the core problems themselves and to decide which of these must be addressed immediately and which problems do not appear critical but may escalate over time. Identify evidence from the case to support your decisions by determining what information or data is essential to addressing the core problems and what information is not relevant or is misleading.
  • Explore alternative solutions . As noted, case analysis scenarios rarely have only one correct answer. Therefore, it is important to keep in mind that the process of analyzing the case and diagnosing core problems, while based on evidence, is a subjective process open to various avenues of interpretation. This means that you must consider alternative solutions or courses of action by critically examining strengths and weaknesses, risk factors, and the differences between short and long-term solutions. For each possible solution or course of action, consider the consequences they may have related to their implementation and how these recommendations might lead to new problems. Also, consider thinking about your recommended solutions or courses of action in relation to issues of fairness, equity, and inclusion.
  • Decide on a final set of recommendations . The last stage in preparing to write a case analysis paper is to assert an opinion or viewpoint about the recommendations needed to help resolve the core problems as you see them and to make a persuasive argument for supporting this point of view. Prepare a clear rationale for your recommendations based on examining each element of your analysis. Anticipate possible obstacles that could derail their implementation. Consider any counter-arguments that could be made concerning the validity of your recommended actions. Finally, describe a set of criteria and measurable indicators that could be applied to evaluating the effectiveness of your implementation plan.

Use these steps as the framework for writing your paper. Remember that the more detailed you are in taking notes as you critically examine each element of the case, the more information you will have to draw from when you begin to write. This will save you time.

NOTE : If the process of preparing to write a case analysis paper is assigned as a student group project, consider having each member of the group analyze a specific element of the case, including drafting answers to the corresponding questions used by your professor to frame the analysis. This will help make the analytical process more efficient and ensure that the distribution of work is equitable. This can also facilitate who is responsible for drafting each part of the final case analysis paper and, if applicable, the in-class presentation.

Framework for Case Analysis . College of Management. University of Massachusetts; Hawes, Jon M. "Teaching is Not Telling: The Case Method as a Form of Interactive Learning." Journal for Advancement of Marketing Education 5 (Winter 2004): 47-54; Rasche, Christoph and Achim Seisreiner. Guidelines for Business Case Analysis . University of Potsdam; Writing a Case Study Analysis . University of Arizona Global Campus Writing Center; Van Ness, Raymond K. A Guide to Case Analysis . School of Business. State University of New York, Albany; Writing a Case Analysis . Business School, University of New South Wales.

Structure and Writing Style

A case analysis paper should be detailed, concise, persuasive, clearly written, and professional in tone and in the use of language . As with other forms of college-level academic writing, declarative statements that convey information, provide a fact, or offer an explanation or any recommended courses of action should be based on evidence. If allowed by your professor, any external sources used to support your analysis, such as course readings, should be properly cited under a list of references. The organization and structure of case analysis papers can vary depending on your professor’s preferred format, but its structure generally follows the steps used for analyzing the case.


The introduction should provide a succinct but thorough descriptive overview of the main facts, issues, and core problems of the case . The introduction should also include a brief summary of the most relevant details about the situation and organizational setting. This includes defining the theoretical framework or conceptual model on which any questions were used to frame your analysis.

Following the rules of most college-level research papers, the introduction should then inform the reader how the paper will be organized. This includes describing the major sections of the paper and the order in which they will be presented. Unless you are told to do so by your professor, you do not need to preview your final recommendations in the introduction. U nlike most college-level research papers , the introduction does not include a statement about the significance of your findings because a case analysis assignment does not involve contributing new knowledge about a research problem.

Background Analysis

Background analysis can vary depending on any guiding questions provided by your professor and the underlying concept or theory that the case is based upon. In general, however, this section of your paper should focus on:

  • Providing an overarching analysis of problems identified from the case scenario, including identifying events that stakeholders find challenging or troublesome,
  • Identifying assumptions made by each stakeholder and any apparent biases they may exhibit,
  • Describing any demands or claims made by or forced upon key stakeholders, and
  • Highlighting any issues of concern or complaints expressed by stakeholders in response to those demands or claims.

These aspects of the case are often in the form of behavioral responses expressed by individuals or groups within the organizational setting. However, note that problems in a case situation can also be reflected in data [or the lack thereof] and in the decision-making, operational, cultural, or institutional structure of the organization. Additionally, demands or claims can be either internal and external to the organization [e.g., a case analysis involving a president considering arms sales to Saudi Arabia could include managing internal demands from White House advisors as well as demands from members of Congress].

Throughout this section, present all relevant evidence from the case that supports your analysis. Do not simply claim there is a problem, an assumption, a demand, or a concern; tell the reader what part of the case informed how you identified these background elements.

Identification of Problems

In most case analysis assignments, there are problems, and then there are problems . Each problem can reflect a multitude of underlying symptoms that are detrimental to the interests of the organization. The purpose of identifying problems is to teach students how to differentiate between problems that vary in severity, impact, and relative importance. Given this, problems can be described in three general forms: those that must be addressed immediately, those that should be addressed but the impact is not severe, and those that do not require immediate attention and can be set aside for the time being.

All of the problems you identify from the case should be identified in this section of your paper, with a description based on evidence explaining the problem variances. If the assignment asks you to conduct research to further support your assessment of the problems, include this in your explanation. Remember to cite those sources in a list of references. Use specific evidence from the case and apply appropriate concepts, theories, and models discussed in class or in relevant course readings to highlight and explain the key problems [or problem] that you believe must be solved immediately and describe the underlying symptoms and why they are so critical.

Alternative Solutions

This section is where you provide specific, realistic, and evidence-based solutions to the problems you have identified and make recommendations about how to alleviate the underlying symptomatic conditions impacting the organizational setting. For each solution, you must explain why it was chosen and provide clear evidence to support your reasoning. This can include, for example, course readings and class discussions as well as research resources, such as, books, journal articles, research reports, or government documents. In some cases, your professor may encourage you to include personal, anecdotal experiences as evidence to support why you chose a particular solution or set of solutions. Using anecdotal evidence helps promote reflective thinking about the process of determining what qualifies as a core problem and relevant solution .

Throughout this part of the paper, keep in mind the entire array of problems that must be addressed and describe in detail the solutions that might be implemented to resolve these problems.

Recommended Courses of Action

In some case analysis assignments, your professor may ask you to combine the alternative solutions section with your recommended courses of action. However, it is important to know the difference between the two. A solution refers to the answer to a problem. A course of action refers to a procedure or deliberate sequence of activities adopted to proactively confront a situation, often in the context of accomplishing a goal. In this context, proposed courses of action are based on your analysis of alternative solutions. Your description and justification for pursuing each course of action should represent the overall plan for implementing your recommendations.

For each course of action, you need to explain the rationale for your recommendation in a way that confronts challenges, explains risks, and anticipates any counter-arguments from stakeholders. Do this by considering the strengths and weaknesses of each course of action framed in relation to how the action is expected to resolve the core problems presented, the possible ways the action may affect remaining problems, and how the recommended action will be perceived by each stakeholder.

In addition, you should describe the criteria needed to measure how well the implementation of these actions is working and explain which individuals or groups are responsible for ensuring your recommendations are successful. In addition, always consider the law of unintended consequences. Outline difficulties that may arise in implementing each course of action and describe how implementing the proposed courses of action [either individually or collectively] may lead to new problems [both large and small].

Throughout this section, you must consider the costs and benefits of recommending your courses of action in relation to uncertainties or missing information and the negative consequences of success.

The conclusion should be brief and introspective. Unlike a research paper, the conclusion in a case analysis paper does not include a summary of key findings and their significance, a statement about how the study contributed to existing knowledge, or indicate opportunities for future research.

Begin by synthesizing the core problems presented in the case and the relevance of your recommended solutions. This can include an explanation of what you have learned about the case in the context of your answers to the questions provided by your professor. The conclusion is also where you link what you learned from analyzing the case with the course readings or class discussions. This can further demonstrate your understanding of the relationships between the practical case situation and the theoretical and abstract content of assigned readings and other course content.

Problems to Avoid

The literature on case analysis assignments often includes examples of difficulties students have with applying methods of critical analysis and effectively reporting the results of their assessment of the situation. A common reason cited by scholars is that the application of this type of teaching and learning method is limited to applied fields of social and behavioral sciences and, as a result, writing a case analysis paper can be unfamiliar to most students entering college.

After you have drafted your paper, proofread the narrative flow and revise any of these common errors:

  • Unnecessary detail in the background section . The background section should highlight the essential elements of the case based on your analysis. Focus on summarizing the facts and highlighting the key factors that become relevant in the other sections of the paper by eliminating any unnecessary information.
  • Analysis relies too much on opinion . Your analysis is interpretive, but the narrative must be connected clearly to evidence from the case and any models and theories discussed in class or in course readings. Any positions or arguments you make should be supported by evidence.
  • Analysis does not focus on the most important elements of the case . Your paper should provide a thorough overview of the case. However, the analysis should focus on providing evidence about what you identify are the key events, stakeholders, issues, and problems. Emphasize what you identify as the most critical aspects of the case to be developed throughout your analysis. Be thorough but succinct.
  • Writing is too descriptive . A paper with too much descriptive information detracts from your analysis of the complexities of the case situation. Questions about what happened, where, when, and by whom should only be included as essential information leading to your examination of questions related to why, how, and for what purpose.
  • Inadequate definition of a core problem and associated symptoms . A common error found in case analysis papers is recommending a solution or course of action without adequately defining or demonstrating that you understand the problem. Make sure you have clearly described the problem and its impact and scope within the organizational setting. Ensure that you have adequately described the root causes w hen describing the symptoms of the problem.
  • Recommendations lack specificity . Identify any use of vague statements and indeterminate terminology, such as, “A particular experience” or “a large increase to the budget.” These statements cannot be measured and, as a result, there is no way to evaluate their successful implementation. Provide specific data and use direct language in describing recommended actions.
  • Unrealistic, exaggerated, or unattainable recommendations . Review your recommendations to ensure that they are based on the situational facts of the case. Your recommended solutions and courses of action must be based on realistic assumptions and fit within the constraints of the situation. Also note that the case scenario has already happened, therefore, any speculation or arguments about what could have occurred if the circumstances were different should be revised or eliminated.

Bee, Lian Song et al. "Business Students' Perspectives on Case Method Coaching for Problem-Based Learning: Impacts on Student Engagement and Learning Performance in Higher Education." Education & Training 64 (2022): 416-432; The Case Analysis . Fred Meijer Center for Writing and Michigan Authors. Grand Valley State University; Georgallis, Panikos and Kayleigh Bruijn. "Sustainability Teaching using Case-Based Debates." Journal of International Education in Business 15 (2022): 147-163; Hawes, Jon M. "Teaching is Not Telling: The Case Method as a Form of Interactive Learning." Journal for Advancement of Marketing Education 5 (Winter 2004): 47-54; Georgallis, Panikos, and Kayleigh Bruijn. "Sustainability Teaching Using Case-based Debates." Journal of International Education in Business 15 (2022): 147-163; .Dean,  Kathy Lund and Charles J. Fornaciari. "How to Create and Use Experiential Case-Based Exercises in a Management Classroom." Journal of Management Education 26 (October 2002): 586-603; Klebba, Joanne M. and Janet G. Hamilton. "Structured Case Analysis: Developing Critical Thinking Skills in a Marketing Case Course." Journal of Marketing Education 29 (August 2007): 132-137, 139; Klein, Norman. "The Case Discussion Method Revisited: Some Questions about Student Skills." Exchange: The Organizational Behavior Teaching Journal 6 (November 1981): 30-32; Mukherjee, Arup. "Effective Use of In-Class Mini Case Analysis for Discovery Learning in an Undergraduate MIS Course." The Journal of Computer Information Systems 40 (Spring 2000): 15-23; Pessoa, Silviaet al. "Scaffolding the Case Analysis in an Organizational Behavior Course: Making Analytical Language Explicit." Journal of Management Education 46 (2022): 226-251: Ramsey, V. J. and L. D. Dodge. "Case Analysis: A Structured Approach." Exchange: The Organizational Behavior Teaching Journal 6 (November 1981): 27-29; Schweitzer, Karen. "How to Write and Format a Business Case Study." ThoughtCo. https://www.thoughtco.com/how-to-write-and-format-a-business-case-study-466324 (accessed December 5, 2022); Reddy, C. D. "Teaching Research Methodology: Everything's a Case." Electronic Journal of Business Research Methods 18 (December 2020): 178-188; Volpe, Guglielmo. "Case Teaching in Economics: History, Practice and Evidence." Cogent Economics and Finance 3 (December 2015). doi:https://doi.org/10.1080/23322039.2015.1120977.

Writing Tip

Ca se Study and Case Analysis Are Not the Same!

Confusion often exists between what it means to write a paper that uses a case study research design and writing a paper that analyzes a case; they are two different types of approaches to learning in the social and behavioral sciences. Professors as well as educational researchers contribute to this confusion because they often use the term "case study" when describing the subject of analysis for a case analysis paper. But you are not studying a case for the purpose of generating a comprehensive, multi-faceted understanding of a research problem. R ather, you are critically analyzing a specific scenario to argue logically for recommended solutions and courses of action that lead to optimal outcomes applicable to professional practice.

To avoid any confusion, here are twelve characteristics that delineate the differences between writing a paper using the case study research method and writing a case analysis paper:

  • Case study is a method of in-depth research and rigorous inquiry ; case analysis is a reliable method of teaching and learning . A case study is a modality of research that investigates a phenomenon for the purpose of creating new knowledge, solving a problem, or testing a hypothesis using empirical evidence derived from the case being studied. Often, the results are used to generalize about a larger population or within a wider context. The writing adheres to the traditional standards of a scholarly research study. A case analysis is a pedagogical tool used to teach students how to reflect and think critically about a practical, real-life problem in an organizational setting.
  • The researcher is responsible for identifying the case to study; a case analysis is assigned by your professor . As the researcher, you choose the case study to investigate in support of obtaining new knowledge and understanding about the research problem. The case in a case analysis assignment is almost always provided, and sometimes written, by your professor and either given to every student in class to analyze individually or to a small group of students, or students select a case to analyze from a predetermined list.
  • A case study is indeterminate and boundless; a case analysis is predetermined and confined . A case study can be almost anything [see item 9 below] as long as it relates directly to examining the research problem. This relationship is the only limit to what a researcher can choose as the subject of their case study. The content of a case analysis is determined by your professor and its parameters are well-defined and limited to elucidating insights of practical value applied to practice.
  • Case study is fact-based and describes actual events or situations; case analysis can be entirely fictional or adapted from an actual situation . The entire content of a case study must be grounded in reality to be a valid subject of investigation in an empirical research study. A case analysis only needs to set the stage for critically examining a situation in practice and, therefore, can be entirely fictional or adapted, all or in-part, from an actual situation.
  • Research using a case study method must adhere to principles of intellectual honesty and academic integrity; a case analysis scenario can include misleading or false information . A case study paper must report research objectively and factually to ensure that any findings are understood to be logically correct and trustworthy. A case analysis scenario may include misleading or false information intended to deliberately distract from the central issues of the case. The purpose is to teach students how to sort through conflicting or useless information in order to come up with the preferred solution. Any use of misleading or false information in academic research is considered unethical.
  • Case study is linked to a research problem; case analysis is linked to a practical situation or scenario . In the social sciences, the subject of an investigation is most often framed as a problem that must be researched in order to generate new knowledge leading to a solution. Case analysis narratives are grounded in real life scenarios for the purpose of examining the realities of decision-making behavior and processes within organizational settings. A case analysis assignments include a problem or set of problems to be analyzed. However, the goal is centered around the act of identifying and evaluating courses of action leading to best possible outcomes.
  • The purpose of a case study is to create new knowledge through research; the purpose of a case analysis is to teach new understanding . Case studies are a choice of methodological design intended to create new knowledge about resolving a research problem. A case analysis is a mode of teaching and learning intended to create new understanding and an awareness of uncertainty applied to practice through acts of critical thinking and reflection.
  • A case study seeks to identify the best possible solution to a research problem; case analysis can have an indeterminate set of solutions or outcomes . Your role in studying a case is to discover the most logical, evidence-based ways to address a research problem. A case analysis assignment rarely has a single correct answer because one of the goals is to force students to confront the real life dynamics of uncertainly, ambiguity, and missing or conflicting information within professional practice. Under these conditions, a perfect outcome or solution almost never exists.
  • Case study is unbounded and relies on gathering external information; case analysis is a self-contained subject of analysis . The scope of a case study chosen as a method of research is bounded. However, the researcher is free to gather whatever information and data is necessary to investigate its relevance to understanding the research problem. For a case analysis assignment, your professor will often ask you to examine solutions or recommended courses of action based solely on facts and information from the case.
  • Case study can be a person, place, object, issue, event, condition, or phenomenon; a case analysis is a carefully constructed synopsis of events, situations, and behaviors . The research problem dictates the type of case being studied and, therefore, the design can encompass almost anything tangible as long as it fulfills the objective of generating new knowledge and understanding. A case analysis is in the form of a narrative containing descriptions of facts, situations, processes, rules, and behaviors within a particular setting and under a specific set of circumstances.
  • Case study can represent an open-ended subject of inquiry; a case analysis is a narrative about something that has happened in the past . A case study is not restricted by time and can encompass an event or issue with no temporal limit or end. For example, the current war in Ukraine can be used as a case study of how medical personnel help civilians during a large military conflict, even though circumstances around this event are still evolving. A case analysis can be used to elicit critical thinking about current or future situations in practice, but the case itself is a narrative about something finite and that has taken place in the past.
  • Multiple case studies can be used in a research study; case analysis involves examining a single scenario . Case study research can use two or more cases to examine a problem, often for the purpose of conducting a comparative investigation intended to discover hidden relationships, document emerging trends, or determine variations among different examples. A case analysis assignment typically describes a stand-alone, self-contained situation and any comparisons among cases are conducted during in-class discussions and/or student presentations.

The Case Analysis . Fred Meijer Center for Writing and Michigan Authors. Grand Valley State University; Mills, Albert J. , Gabrielle Durepos, and Eiden Wiebe, editors. Encyclopedia of Case Study Research . Thousand Oaks, CA: SAGE Publications, 2010; Ramsey, V. J. and L. D. Dodge. "Case Analysis: A Structured Approach." Exchange: The Organizational Behavior Teaching Journal 6 (November 1981): 27-29; Yin, Robert K. Case Study Research and Applications: Design and Methods . 6th edition. Thousand Oaks, CA: Sage, 2017; Crowe, Sarah et al. “The Case Study Approach.” BMC Medical Research Methodology 11 (2011):  doi: 10.1186/1471-2288-11-100; Yin, Robert K. Case Study Research: Design and Methods . 4th edition. Thousand Oaks, CA: Sage Publishing; 1994.

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Hypothesis Case Studies Samples For Students

53 samples of this type

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Good Example Of Case Study On Mean Ounces = 14.87 Ounces

***Your Name*** ***Institution*** 1. Mean ounces = (14.5+14.6+14.7+14.8+14.9+15.5+14.8+15.2+15+15.1+15+14.4+15.8+14+16+16.1+15.8+14.5+14.1+14.2+14+14.9+14.7+14.5+14.6+14.8+14.8+14.6)/30

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The just noticeable difference as a function of the psychophysical method used to measure them..

- Identification of statistical analyses In the following project, we are interested in determining if there is any significant difference in mean for the Just Noticeable Difference as a function of the psychophysical methods. The descriptive statistics that we are interested in comparing the mean performance of the point of subjective equality, since the project have only one variable with different level, the best statistical analysis is the one way Anova.

The hypothesis

Administration in education case study examples.

This study was conducted to analyze the principal efficacy between the first year students (Cohort 8) and the second year students (Cohort 7) of the Masters Educational Leadership University Program. The principal efficacy can be measured via analyzing the responses obtained across the various items of the questionnaire exploring areas of time management, enthusiasm, organizational management, policies and several more. For this reason, the foremost research question is as follows:

Is there a significant difference in the mean efficacy scores for cohort 7 and cohort 8?

It was therefore hypothesized that the principal efficacy of cohort 7 is greater that cohort 8 as shown below: Ho: u1=u2

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9.1 You use the symbol H0 for which hypothesis?

Null hypothesis

9.2 You use the symbol H1 for which hypothesis?

Alternative hypothesis

9.3 What symbol do you use for the chance of committing a Type I error? 9.4 What symbol do you use for the chance of committing a Type II error? β 9.5 What does 1 - α represent? confidence level 9.6 What is the relationship of α to a Type I error? it is the significant level 9.7 What is the relationship of β to a Type II error?

If the null hypothesis is false, then the probability of a Type II error is called β

9.8 How is power related to the probability of making a Type II error?

When the power is decreased, then the chances of you making an error is decreased

Bottling company case study examples.

- Sample mean can be calculated using the following formula: μ=x=1 Nxi , where xi is mass of sample.

The mean is equal

x=130i=130xi=14.87 ounces In a set of observations, median is a value of variable that have half of the number of observations below it and remaining half above it (Agarval, 43). To set median it is necessary to arrange data in ascending or descending order. As the number of samples is even (N=2p) the average of p-th and (p+1)-th is median. In our case median is equal to 14.8 ounces.

Standard deviation can be calculated as (Bajpai, 129)

σ=i=1Nxi-μ2N=0.541 ounces σN=0.54130=0.099 ounces

It is possible to find numbers –x and x, between which lies mass of soda with probability 95 % (1-α).

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This paper provides information on geographical aspects, with focus no urban environment of Frankfurt, Germany with an intention of investigating and analyzing financial and commercial patterns based on size and function of three retail centers. The analysis will involve application Reilly’s retail theory and Christaller’s model of central places (Morris, 118). An understanding of urban environmental issues in cities such as Frankfurt provides a spring board upon which spatial planning can be tailored to meet the social, economic and recreational needs of people.

Fly-Lab Part II (Assignments 1-3) Case Study Examples

Assignment #1: epistasis.

- What did you observe in the F1 generation?

The F1 generation was comprised of wild types in terms of wing size and wing vein.

Was this what you expected? Why or why not? Yes. The wing mutation and the vestigial wing size genes are recessive and hence would not be expressed.

Once you have produced an F1 generation, mate F1 flies to generate an F2 generation.

Study the results of your F2 generation and then answer the following questions.

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H0: MA - MB = 0 (the mean response time of company A does not differ from the mean response time of company B). Vs.

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For this case study the alternative hypothesis: H1 represents the claim that the mean response time of company A differs from the mean response time of company B.

Decision rule: Reject the null hypothesis; H0 if the z statistics > critical z Value (Conover 2005).

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I choose the following 3 hypothesis to test: - Marriages where the man is older than the woman will be perceived as being more satisfying than marriages where the woman is older than the man. - There will be a positive association between perceived level of relationship satisfaction and optimism. - There will be a positive association between perceived level of relationship satisfaction and relationship longevity

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The litigation involved in solving contractual disputes is dynamic and thus requires the litigant to ascertain certain facts around the alleged inducement into committing on a false belief. It is important that every party in a legal engagement act upon self-satisfaction and shear approval of the subject in question. However, there are weaknesses that certain people exhibit. The lure of missing on an opportunity can be the motivation behind poor examination of contractual facts.

Case Study On Genetics: Fly Lab Assignment

What was the phenotypic ratio for the offspring resulting from this testcross? Results for the F1 generation for monohybrid cross between a female fly with brown eye (BW) color with a male fly having ebony body (E) color are as shown below.

Fly lab Lab Notes for Steven F

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Mental health.

Introduction One of the main branches of psychology is mental assessment. This part of psychology calls for numerous observations and ability to relate a certain behavior or response to a set of responses to comprehensively understand the mental status of a person (http://yalepress.yale.edu/yupbooks/excerpts/hicks_50.pdf).

It usually involves careful observation of any possible or visible cue that might give a clue to the mental status a person, a lot of careful questioning and taking of notes as well as mental history of the person under observation. It also calls for human behavior understanding and causes of the various types of mental ailments (http://yalepress.yale.edu/yupbooks/excerpts/hicks_50.pdf).

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Profits Communicated To Investors During This Period Are Much Higher Than The Actual Profits Realized Case Study

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Many multinational corporations have a problem balancing ethics and value maximization. However, Starbucks does not have a very large problem with it because the ethics and moral responsibility is apparent in their decision making. According to their Business Ethics and compliance statement, Starbucks believes that conducting business ethically and striving to do the right thing are vital to the success of the company . Since Starbucks is traditionally known for their overpriced coffee the consumer is paying for their moral choices nonetheless. However there are some examples of questionable decisions that have been reported.

Questionable Practices

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This paper aims at providing a comprehensive and an analytical interview between the author and the ESOL student. It will discuss the steps and the strategies that are associated with the learning of language. This report paper shall contain a summary of the interview, discussion of the relevant theories and how they apply. The paper will also contain an interview journal. The paper shall be organized as follows: introduction, subject/ context of the interview, hypothesis, method, findings, discussion and finally conclusion.

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Educational research is undertaken to generate knowledge. Its five objectives are “exploration” “description,” “ explanation,” “prediction,” and “influence” (Johnson & Christensen, nd). Among the many areas of educational research are quantitative research, qualitative research, mixed methods, and action research. These four areas will be discussed in this paper as well as the research process, and specific applications of these methodologies.

The Research Process

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  • Hongjin An 1 ,
  • Min Zhong 1 ,
  • http://orcid.org/0000-0002-5736-1283 Huatian Gan 2 , 3
  • 1 Department of Gastroenterology and Hepatology, West China Hospital, Sichuan University , Chengdu , China
  • 2 Department of Geriatrics and National Clinical Research Center for Geriatrics, West China Hospital, Sichuan University , Chengdu , China
  • 3 Department of Gastroenterology and Laboratory of Inflammatory Bowel Disease, the Center for Inflammatory Bowel Disease, Clinical Institute of Inflammation and Immunology, Frontiers Science Center for Disease-related Molecular Network, West China Hospital, Sichuan University , Chengdu , China
  • Correspondence to Dr Huatian Gan, West China Hospital of Sichuan University, Chengdu, Sichuan, China; ganhuatian123{at}163.com


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We read with great interest the population-based cohort study by Abrahami D et al , 1 in which they found that the use of proton pump inhibitors (PPIs) was not associated with an increased risk of inflammatory bowel disease (IBD). However, the assessment of causality in observational studies is often challenging due to the presence of multiple confounding factors. The existence of a causal relationship between PPIs and IBD remains unclear at present. Mendelian randomisation (MR) is a method of generating more reliable evidence using exposure-related genetic variants to assess causality, limiting the bias caused by confounders. 2 Therefore, we used a two-sample MR analysis to investigate the association between the use of PPIs and IBD including Crohn’s disease (CD) and ulcerative colitis (UC).

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Here, we mainly used the inverse-variance weighted 8 method for MR analysis with weighted median, 9 MR-Egger 10 and MR-PRESSO 5 as complementary approaches. Furthermore, we applied a series of sensitivity analyses to ensure the robustness of our results, with Cochran’s Q test to assess heterogeneity and the intercept of an MR-Egger regression to assess horizontal pleiotropy. The genetic prediction of omeprazole, esomeprazole, lansoprazole and rabeprazole use, as depicted in figure 1 , demonstrated no significant association with an increased risk of IBD after excluding pleiotropic SNPs (omeprazole, OR, 1.05; 95% CI, 0.88 to 1.25; p=0.587; esomeprazole, OR, 0.99; 95% CI, 0.92 to 1.07; p=0.865; lansoprazole, OR, 1.06; 95% CI, 0.89 to 1.26; p=0.537; and rabeprazole, OR, 1.00; 95% CI, 0.95 to 1.04; p=0.862). The IBD subtype analyses also did not reveal any evidence of an increased risk of CD or UC associated with the use of PPIs ( figure 1 ). These findings were robustly confirmed through complementary approaches employing rigorous methodologies that consistently yielded similar point estimates ( figure 1 ). Further sensitivity analyses showed the absence of heterogeneity (All P heterogeneity >0.05) and pleiotropy (All P pleiotropy >0.05), again demonstrating the robustness of the conclusions ( figure 1 ).

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Mendelian randomisation estimates the associations between the use of different types of proton pump inhibitors and inflammatory bowel disease. IBD, inflammatory bowel disease; CD, Crohn’s disease; UC, ulcerative colitis; PPIs, proton pump inhibitors; IVW, inverse-variance weighted; MR, Mendelian randomisation.

In conclusion, the MR results corroborate Abrahami D et al ’s findings that PPIs were not associated with an increased risk of IBD. Nonetheless, further research is needed to elucidate the effects of more types, drug dosage, frequency and duration on IBD.

Ethics statements

Patient consent for publication.

Not applicable.

Ethics approval

  • Abrahami D ,
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Supplementary materials

Supplementary data.

This web only file has been produced by the BMJ Publishing Group from an electronic file supplied by the author(s) and has not been edited for content.

  • Data supplement 1

HA and MZ contributed equally.

Contributors All authors conceived and designed the study. HA and MZ did the statistical analyses and wrote the manuscript. HG revised the manuscript and is the guarantor. HA and MZ have contributed equally to this study.

Funding The present work was supported by the National Natural Science Foundation of China (No. 82070560) and 1.3.5 Project for Disciplines of Excellence, West China Hospital, Sichuan (No. ZYGD23013).

Competing interests None declared.

Provenance and peer review Not commissioned; externally peer reviewed.

Supplemental material This content has been supplied by the author(s). It has not been vetted by BMJ Publishing Group Limited (BMJ) and may not have been peer-reviewed. Any opinions or recommendations discussed are solely those of the author(s) and are not endorsed by BMJ. BMJ disclaims all liability and responsibility arising from any reliance placed on the content. Where the content includes any translated material, BMJ does not warrant the accuracy and reliability of the translations (including but not limited to local regulations, clinical guidelines, terminology, drug names and drug dosages), and is not responsible for any error and/or omissions arising from translation and adaptation or otherwise.

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Create a System to Grow Consistently

  • Paul Leinwand

hypothesis case study example

Delivering consistent growth is one of the hardest things a company can do. A brilliant idea or product innovation can create a burst of episodic growth, but few companies demonstrate growth year in and year out, especially amid the disruptions and uncertain economy we’ve experienced during the 2020s. Some companies have managed to sustain consistent growth, however.

Research from PwC reveals that the highest-performing organizations invest in a growth system, an integrated collection of capabilities and assets that drives both short-term and long-term growth. The authors provide a framework for building a growth system offering case examples highlighting Toast, IKEA, Vertex, Adobe, and Roblox.

Five elements can move you beyond episodic success.

Delivering sustained growth is one of the hardest things a company can do. A brilliant idea or product innovation can create a burst of episodic growth, but few companies demonstrate growth year in and year out, especially amid the disruptions and uncertain economy we’ve experienced during the 2020s. Some companies have cracked the code on sustained growth, however, while realizing the elusive goal of knowing precisely where next quarter’s revenue will come from.

Invest in prediction, adaptability, and resilience.

  • Paul Blase is a principal at PwC U.S. and leads the firm’s growth platform. He advises executives on designing systems to deliver consistent growth.
  • Paul Leinwand is a principal at PwC U.S., a global managing director at Strategy&, and an adjunct professor at Northwestern’s Kellogg School. He is a coauthor, with Mahadeva Matt Mani, of Beyond Digital: How Great Leaders Transform Their Organizations and Shape the Future (HBR Press, 2022).

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