example of case study hypothesis

An official website of the United States government

The .gov means it’s official. Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

The site is secure. The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

• Publications
• Account settings

Preview improvements coming to the PMC website in October 2024. Learn More or Try it out now .

• Advanced Search
• Journal List
• J Korean Med Sci
• v.36(50); 2021 Dec 27

Formulating Hypotheses for Different Study Designs

Durga prasanna misra.

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

Armen Yuri Gasparyan

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

Olena Zimba

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

Marlen Yessirkepov

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

Vikas Agarwal

George d. kitas.

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

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

Graphical Abstract

DEFINING WORKING AND STANDALONE SCIENTIFIC HYPOTHESES

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

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

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

DO WE NEED HYPOTHESES FOR ALL STUDY DESIGNS?

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

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

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

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

STANDARDS OF WORKING AND SCIENTIFIC HYPOTHESES

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

Evidence-based data

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

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

Supported by pilot studies

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

Testable by ethical studies

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

Balance between scientific temper and controversy

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

DISTINGUISHING THE MOST INFLUENTIAL HYPOTHESES

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

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

LESSONS LEARNED FROM HYPOTHESES AMIDST THE COVID-19 PANDEMIC

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

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

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

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

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

SUGGESTIONS ON GENERATING AND PUBLISHING HYPOTHESES

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

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

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

Author Contributions:

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

Have a language expert improve your writing

Run a free plagiarism check in 10 minutes, automatically generate references for free.

• Knowledge Base
• Methodology
• Case Study | Definition, Examples & Methods

Case Study | Definition, Examples & Methods

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

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

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

Table of contents

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

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

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

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

Prevent plagiarism, run a free check.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Cite this Scribbr article

If you want to cite this source, you can copy and paste the citation or click the ‘Cite this Scribbr article’ button to automatically add the citation to our free Reference Generator.

McCombes, S. (2023, January 30). Case Study | Definition, Examples & Methods. Scribbr. Retrieved 14 May 2024, from https://www.scribbr.co.uk/research-methods/case-studies/

Is this article helpful?

Shona McCombes

Other students also liked, correlational research | guide, design & examples, a quick guide to experimental design | 5 steps & examples, descriptive research design | definition, methods & examples.

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.

Introduction

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.

• << Previous: Reviewing Collected Works
• Next: Writing a Case Study >>
• Last Updated: May 7, 2024 9:45 AM
• URL: https://libguides.usc.edu/writingguide/assignments

• Bipolar Disorder
• Therapy Center
• When To See a Therapist
• Types of Therapy
• Best Online Therapy
• Best Couples Therapy
• Best Family Therapy
• Managing Stress
• Sleep and Dreaming
• Understanding Emotions
• Self-Improvement
• Healthy Relationships
• Student Resources
• Personality Types
• Guided Meditations
• Verywell Mind Insights
• 2024 Verywell Mind 25
• Mental Health in the Classroom
• Editorial Process
• Meet Our Review Board
• Crisis Support

What Is a Case Study?

Weighing the pros and cons of this method of research

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

Cara Lustik is a fact-checker and copywriter.

Verywell / Colleen Tighe

• Pros and Cons

What Types of Case Studies Are Out There?

Where do you find data for a case study, how do i write a psychology case study.

A case study is an in-depth study of one person, group, or event. In a case study, nearly every aspect of the subject's life and history is analyzed to seek patterns and causes of behavior. Case studies can be used in many different fields, including psychology, medicine, education, anthropology, political science, and social work.

The point of a case study is to learn as much as possible about an individual or group so that the information can be generalized to many others. Unfortunately, case studies tend to be highly subjective, and it is sometimes difficult to generalize results to a larger population.

While case studies focus on a single individual or group, they follow a format similar to other types of psychology writing. If you are writing a case study, we got you—here are some rules of APA format to reference.  

At a Glance

A case study, or an in-depth study of a person, group, or event, can be a useful research tool when used wisely. In many cases, case studies are best used in situations where it would be difficult or impossible for you to conduct an experiment. They are helpful for looking at unique situations and allow researchers to gather a lot of˜ information about a specific individual or group of people. However, it's important to be cautious of any bias we draw from them as they are highly subjective.

What Are the Benefits and Limitations of Case Studies?

A case study can have its strengths and weaknesses. Researchers must consider these pros and cons before deciding if this type of study is appropriate for their needs.

One of the greatest advantages of a case study is that it allows researchers to investigate things that are often difficult or impossible to replicate in a lab. Some other benefits of a case study:

• Allows researchers to capture information on the 'how,' 'what,' and 'why,' of something that's implemented
• Gives researchers the chance to collect information on why one strategy might be chosen over another
• Permits researchers to develop hypotheses that can be explored in experimental research

On the other hand, a case study can have some drawbacks:

• It cannot necessarily be generalized to the larger population
• Cannot demonstrate cause and effect
• It may not be scientifically rigorous
• It can lead to bias

Researchers may choose to perform a case study if they want to explore a unique or recently discovered phenomenon. Through their insights, researchers develop additional ideas and study questions that might be explored in future studies.

It's important to remember that the insights from case studies cannot be used to determine cause-and-effect relationships between variables. However, case studies may be used to develop hypotheses that can then be addressed in experimental research.

Case Study Examples

There have been a number of notable case studies in the history of psychology. Much of  Freud's work and theories were developed through individual case studies. Some great examples of case studies in psychology include:

• Anna O : Anna O. was a pseudonym of a woman named Bertha Pappenheim, a patient of a physician named Josef Breuer. While she was never a patient of Freud's, Freud and Breuer discussed her case extensively. The woman was experiencing symptoms of a condition that was then known as hysteria and found that talking about her problems helped relieve her symptoms. Her case played an important part in the development of talk therapy as an approach to mental health treatment.
• Phineas Gage : Phineas Gage was a railroad employee who experienced a terrible accident in which an explosion sent a metal rod through his skull, damaging important portions of his brain. Gage recovered from his accident but was left with serious changes in both personality and behavior.
• Genie : Genie was a young girl subjected to horrific abuse and isolation. The case study of Genie allowed researchers to study whether language learning was possible, even after missing critical periods for language development. Her case also served as an example of how scientific research may interfere with treatment and lead to further abuse of vulnerable individuals.

Such cases demonstrate how case research can be used to study things that researchers could not replicate in experimental settings. In Genie's case, her horrific abuse denied her the opportunity to learn a language at critical points in her development.

This is clearly not something researchers could ethically replicate, but conducting a case study on Genie allowed researchers to study phenomena that are otherwise impossible to reproduce.

There are a few different types of case studies that psychologists and other researchers might use:

• Collective case studies : These involve studying a group of individuals. Researchers might study a group of people in a certain setting or look at an entire community. For example, psychologists might explore how access to resources in a community has affected the collective mental well-being of those who live there.
• Descriptive case studies : These involve starting with a descriptive theory. The subjects are then observed, and the information gathered is compared to the pre-existing theory.
• Explanatory case studies : These   are often used to do causal investigations. In other words, researchers are interested in looking at factors that may have caused certain things to occur.
• Exploratory case studies : These are sometimes used as a prelude to further, more in-depth research. This allows researchers to gather more information before developing their research questions and hypotheses .
• Instrumental case studies : These occur when the individual or group allows researchers to understand more than what is initially obvious to observers.
• Intrinsic case studies : This type of case study is when the researcher has a personal interest in the case. Jean Piaget's observations of his own children are good examples of how an intrinsic case study can contribute to the development of a psychological theory.

The three main case study types often used are intrinsic, instrumental, and collective. Intrinsic case studies are useful for learning about unique cases. Instrumental case studies help look at an individual to learn more about a broader issue. A collective case study can be useful for looking at several cases simultaneously.

The type of case study that psychology researchers use depends on the unique characteristics of the situation and the case itself.

There are a number of different sources and methods that researchers can use to gather information about an individual or group. Six major sources that have been identified by researchers are:

• Archival records : Census records, survey records, and name lists are examples of archival records.
• Direct observation : This strategy involves observing the subject, often in a natural setting . While an individual observer is sometimes used, it is more common to utilize a group of observers.
• Documents : Letters, newspaper articles, administrative records, etc., are the types of documents often used as sources.
• Interviews : Interviews are one of the most important methods for gathering information in case studies. An interview can involve structured survey questions or more open-ended questions.
• Participant observation : When the researcher serves as a participant in events and observes the actions and outcomes, it is called participant observation.
• Physical artifacts : Tools, objects, instruments, and other artifacts are often observed during a direct observation of the subject.

If you have been directed to write a case study for a psychology course, be sure to check with your instructor for any specific guidelines you need to follow. If you are writing your case study for a professional publication, check with the publisher for their specific guidelines for submitting a case study.

Here is a general outline of what should be included in a case study.

Section 1: A Case History

This section will have the following structure and content:

Background information : The first section of your paper will present your client's background. Include factors such as age, gender, work, health status, family mental health history, family and social relationships, drug and alcohol history, life difficulties, goals, and coping skills and weaknesses.

Description of the presenting problem : In the next section of your case study, you will describe the problem or symptoms that the client presented with.

Describe any physical, emotional, or sensory symptoms reported by the client. Thoughts, feelings, and perceptions related to the symptoms should also be noted. Any screening or diagnostic assessments that are used should also be described in detail and all scores reported.

Your diagnosis : Provide your diagnosis and give the appropriate Diagnostic and Statistical Manual code. Explain how you reached your diagnosis, how the client's symptoms fit the diagnostic criteria for the disorder(s), or any possible difficulties in reaching a diagnosis.

Section 2: Treatment Plan

This portion of the paper will address the chosen treatment for the condition. This might also include the theoretical basis for the chosen treatment or any other evidence that might exist to support why this approach was chosen.

• Cognitive behavioral approach : Explain how a cognitive behavioral therapist would approach treatment. Offer background information on cognitive behavioral therapy and describe the treatment sessions, client response, and outcome of this type of treatment. Make note of any difficulties or successes encountered by your client during treatment.
• Humanistic approach : Describe a humanistic approach that could be used to treat your client, such as client-centered therapy . Provide information on the type of treatment you chose, the client's reaction to the treatment, and the end result of this approach. Explain why the treatment was successful or unsuccessful.
• Psychoanalytic approach : Describe how a psychoanalytic therapist would view the client's problem. Provide some background on the psychoanalytic approach and cite relevant references. Explain how psychoanalytic therapy would be used to treat the client, how the client would respond to therapy, and the effectiveness of this treatment approach.
• Pharmacological approach : If treatment primarily involves the use of medications, explain which medications were used and why. Provide background on the effectiveness of these medications and how monotherapy may compare with an approach that combines medications with therapy or other treatments.

This section of a case study should also include information about the treatment goals, process, and outcomes.

When you are writing a case study, you should also include a section where you discuss the case study itself, including the strengths and limitiations of the study. You should note how the findings of your case study might support previous research. 

In your discussion section, you should also describe some of the implications of your case study. What ideas or findings might require further exploration? How might researchers go about exploring some of these questions in additional studies?

Need More Tips?

Here are a few additional pointers to keep in mind when formatting your case study:

• Never refer to the subject of your case study as "the client." Instead, use their name or a pseudonym.
• Read examples of case studies to gain an idea about the style and format.
• Remember to use APA format when citing references .

Crowe S, Cresswell K, Robertson A, Huby G, Avery A, Sheikh A. The case study approach .  BMC Med Res Methodol . 2011;11:100.

Crowe S, Cresswell K, Robertson A, Huby G, Avery A, Sheikh A. The case study approach . BMC Med Res Methodol . 2011 Jun 27;11:100. doi:10.1186/1471-2288-11-100

Gagnon, Yves-Chantal.  The Case Study as Research Method: A Practical Handbook . Canada, Chicago Review Press Incorporated DBA Independent Pub Group, 2010.

Yin, Robert K. Case Study Research and Applications: Design and Methods . United States, SAGE Publications, 2017.

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

• Privacy Policy

Home » Case Study – Methods, Examples and Guide

Case Study – Methods, Examples and Guide

Table of Contents

A case study is a research method that involves an in-depth examination and analysis of a particular phenomenon or case, such as an individual, organization, community, event, or situation.

It is a qualitative research approach that aims to provide a detailed and comprehensive understanding of the case being studied. Case studies typically involve multiple sources of data, including interviews, observations, documents, and artifacts, which are analyzed using various techniques, such as content analysis, thematic analysis, and grounded theory. The findings of a case study are often used to develop theories, inform policy or practice, or generate new research questions.

Types of Case Study

Types and Methods of Case Study are as follows:

Single-Case Study

A single-case study is an in-depth analysis of a single case. This type of case study is useful when the researcher wants to understand a specific phenomenon in detail.

For Example , A researcher might conduct a single-case study on a particular individual to understand their experiences with a particular health condition or a specific organization to explore their management practices. The researcher collects data from multiple sources, such as interviews, observations, and documents, and uses various techniques to analyze the data, such as content analysis or thematic analysis. The findings of a single-case study are often used to generate new research questions, develop theories, or inform policy or practice.

Multiple-Case Study

A multiple-case study involves the analysis of several cases that are similar in nature. This type of case study is useful when the researcher wants to identify similarities and differences between the cases.

For Example, a researcher might conduct a multiple-case study on several companies to explore the factors that contribute to their success or failure. The researcher collects data from each case, compares and contrasts the findings, and uses various techniques to analyze the data, such as comparative analysis or pattern-matching. The findings of a multiple-case study can be used to develop theories, inform policy or practice, or generate new research questions.

Exploratory Case Study

An exploratory case study is used to explore a new or understudied phenomenon. This type of case study is useful when the researcher wants to generate hypotheses or theories about the phenomenon.

For Example, a researcher might conduct an exploratory case study on a new technology to understand its potential impact on society. The researcher collects data from multiple sources, such as interviews, observations, and documents, and uses various techniques to analyze the data, such as grounded theory or content analysis. The findings of an exploratory case study can be used to generate new research questions, develop theories, or inform policy or practice.

Descriptive Case Study

A descriptive case study is used to describe a particular phenomenon in detail. This type of case study is useful when the researcher wants to provide a comprehensive account of the phenomenon.

For Example, a researcher might conduct a descriptive case study on a particular community to understand its social and economic characteristics. The researcher collects data from multiple sources, such as interviews, observations, and documents, and uses various techniques to analyze the data, such as content analysis or thematic analysis. The findings of a descriptive case study can be used to inform policy or practice or generate new research questions.

Instrumental Case Study

An instrumental case study is used to understand a particular phenomenon that is instrumental in achieving a particular goal. This type of case study is useful when the researcher wants to understand the role of the phenomenon in achieving the goal.

For Example, a researcher might conduct an instrumental case study on a particular policy to understand its impact on achieving a particular goal, such as reducing poverty. The researcher collects data from multiple sources, such as interviews, observations, and documents, and uses various techniques to analyze the data, such as content analysis or thematic analysis. The findings of an instrumental case study can be used to inform policy or practice or generate new research questions.

Case Study Data Collection Methods

Here are some common data collection methods for case studies:

Interviews involve asking questions to individuals who have knowledge or experience relevant to the case study. Interviews can be structured (where the same questions are asked to all participants) or unstructured (where the interviewer follows up on the responses with further questions). Interviews can be conducted in person, over the phone, or through video conferencing.

Observations

Observations involve watching and recording the behavior and activities of individuals or groups relevant to the case study. Observations can be participant (where the researcher actively participates in the activities) or non-participant (where the researcher observes from a distance). Observations can be recorded using notes, audio or video recordings, or photographs.

Documents can be used as a source of information for case studies. Documents can include reports, memos, emails, letters, and other written materials related to the case study. Documents can be collected from the case study participants or from public sources.

Surveys involve asking a set of questions to a sample of individuals relevant to the case study. Surveys can be administered in person, over the phone, through mail or email, or online. Surveys can be used to gather information on attitudes, opinions, or behaviors related to the case study.

Artifacts are physical objects relevant to the case study. Artifacts can include tools, equipment, products, or other objects that provide insights into the case study phenomenon.

How to conduct Case Study Research

Conducting a case study research involves several steps that need to be followed to ensure the quality and rigor of the study. Here are the steps to conduct case study research:

• Define the research questions: The first step in conducting a case study research is to define the research questions. The research questions should be specific, measurable, and relevant to the case study phenomenon under investigation.
• Select the case: The next step is to select the case or cases to be studied. The case should be relevant to the research questions and should provide rich and diverse data that can be used to answer the research questions.
• Collect data: Data can be collected using various methods, such as interviews, observations, documents, surveys, and artifacts. The data collection method should be selected based on the research questions and the nature of the case study phenomenon.
• Analyze the data: The data collected from the case study should be analyzed using various techniques, such as content analysis, thematic analysis, or grounded theory. The analysis should be guided by the research questions and should aim to provide insights and conclusions relevant to the research questions.
• Draw conclusions: The conclusions drawn from the case study should be based on the data analysis and should be relevant to the research questions. The conclusions should be supported by evidence and should be clearly stated.
• Validate the findings: The findings of the case study should be validated by reviewing the data and the analysis with participants or other experts in the field. This helps to ensure the validity and reliability of the findings.
• Write the report: The final step is to write the report of the case study research. The report should provide a clear description of the case study phenomenon, the research questions, the data collection methods, the data analysis, the findings, and the conclusions. The report should be written in a clear and concise manner and should follow the guidelines for academic writing.

Examples of Case Study

Here are some examples of case study research:

• The Hawthorne Studies : Conducted between 1924 and 1932, the Hawthorne Studies were a series of case studies conducted by Elton Mayo and his colleagues to examine the impact of work environment on employee productivity. The studies were conducted at the Hawthorne Works plant of the Western Electric Company in Chicago and included interviews, observations, and experiments.
• The Stanford Prison Experiment: Conducted in 1971, the Stanford Prison Experiment was a case study conducted by Philip Zimbardo to examine the psychological effects of power and authority. The study involved simulating a prison environment and assigning participants to the role of guards or prisoners. The study was controversial due to the ethical issues it raised.
• The Challenger Disaster: The Challenger Disaster was a case study conducted to examine the causes of the Space Shuttle Challenger explosion in 1986. The study included interviews, observations, and analysis of data to identify the technical, organizational, and cultural factors that contributed to the disaster.
• The Enron Scandal: The Enron Scandal was a case study conducted to examine the causes of the Enron Corporation’s bankruptcy in 2001. The study included interviews, analysis of financial data, and review of documents to identify the accounting practices, corporate culture, and ethical issues that led to the company’s downfall.
• The Fukushima Nuclear Disaster : The Fukushima Nuclear Disaster was a case study conducted to examine the causes of the nuclear accident that occurred at the Fukushima Daiichi Nuclear Power Plant in Japan in 2011. The study included interviews, analysis of data, and review of documents to identify the technical, organizational, and cultural factors that contributed to the disaster.

Application of Case Study

Case studies have a wide range of applications across various fields and industries. Here are some examples:

Business and Management

Case studies are widely used in business and management to examine real-life situations and develop problem-solving skills. Case studies can help students and professionals to develop a deep understanding of business concepts, theories, and best practices.

Case studies are used in healthcare to examine patient care, treatment options, and outcomes. Case studies can help healthcare professionals to develop critical thinking skills, diagnose complex medical conditions, and develop effective treatment plans.

Case studies are used in education to examine teaching and learning practices. Case studies can help educators to develop effective teaching strategies, evaluate student progress, and identify areas for improvement.

Social Sciences

Case studies are widely used in social sciences to examine human behavior, social phenomena, and cultural practices. Case studies can help researchers to develop theories, test hypotheses, and gain insights into complex social issues.

Law and Ethics

Case studies are used in law and ethics to examine legal and ethical dilemmas. Case studies can help lawyers, policymakers, and ethical professionals to develop critical thinking skills, analyze complex cases, and make informed decisions.

Purpose of Case Study

The purpose of a case study is to provide a detailed analysis of a specific phenomenon, issue, or problem in its real-life context. A case study is a qualitative research method that involves the in-depth exploration and analysis of a particular case, which can be an individual, group, organization, event, or community.

The primary purpose of a case study is to generate a comprehensive and nuanced understanding of the case, including its history, context, and dynamics. Case studies can help researchers to identify and examine the underlying factors, processes, and mechanisms that contribute to the case and its outcomes. This can help to develop a more accurate and detailed understanding of the case, which can inform future research, practice, or policy.

Case studies can also serve other purposes, including:

• Illustrating a theory or concept: Case studies can be used to illustrate and explain theoretical concepts and frameworks, providing concrete examples of how they can be applied in real-life situations.
• Developing hypotheses: Case studies can help to generate hypotheses about the causal relationships between different factors and outcomes, which can be tested through further research.
• Providing insight into complex issues: Case studies can provide insights into complex and multifaceted issues, which may be difficult to understand through other research methods.
• Informing practice or policy: Case studies can be used to inform practice or policy by identifying best practices, lessons learned, or areas for improvement.

Advantages of Case Study Research

There are several advantages of case study research, including:

• In-depth exploration: Case study research allows for a detailed exploration and analysis of a specific phenomenon, issue, or problem in its real-life context. This can provide a comprehensive understanding of the case and its dynamics, which may not be possible through other research methods.
• Rich data: Case study research can generate rich and detailed data, including qualitative data such as interviews, observations, and documents. This can provide a nuanced understanding of the case and its complexity.
• Holistic perspective: Case study research allows for a holistic perspective of the case, taking into account the various factors, processes, and mechanisms that contribute to the case and its outcomes. This can help to develop a more accurate and comprehensive understanding of the case.
• Theory development: Case study research can help to develop and refine theories and concepts by providing empirical evidence and concrete examples of how they can be applied in real-life situations.
• Practical application: Case study research can inform practice or policy by identifying best practices, lessons learned, or areas for improvement.
• Contextualization: Case study research takes into account the specific context in which the case is situated, which can help to understand how the case is influenced by the social, cultural, and historical factors of its environment.

Limitations of Case Study Research

There are several limitations of case study research, including:

• Limited generalizability : Case studies are typically focused on a single case or a small number of cases, which limits the generalizability of the findings. The unique characteristics of the case may not be applicable to other contexts or populations, which may limit the external validity of the research.
• Biased sampling: Case studies may rely on purposive or convenience sampling, which can introduce bias into the sample selection process. This may limit the representativeness of the sample and the generalizability of the findings.
• Subjectivity: Case studies rely on the interpretation of the researcher, which can introduce subjectivity into the analysis. The researcher’s own biases, assumptions, and perspectives may influence the findings, which may limit the objectivity of the research.
• Limited control: Case studies are typically conducted in naturalistic settings, which limits the control that the researcher has over the environment and the variables being studied. This may limit the ability to establish causal relationships between variables.
• Time-consuming: Case studies can be time-consuming to conduct, as they typically involve a detailed exploration and analysis of a specific case. This may limit the feasibility of conducting multiple case studies or conducting case studies in a timely manner.
• Resource-intensive: Case studies may require significant resources, including time, funding, and expertise. This may limit the ability of researchers to conduct case studies in resource-constrained settings.

About the author

Muhammad Hassan

Researcher, Academic Writer, Web developer

You may also like

Questionnaire – Definition, Types, and Examples

Observational Research – Methods and Guide

Quantitative Research – Methods, Types and...

Qualitative Research Methods

Explanatory Research – Types, Methods, Guide

Survey Research – Types, Methods, Examples

Snapsolve any problem by taking a picture. Try it in the Numerade app?

Seeing Through Statistics

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

Chapter Questions

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

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.

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

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

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?

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.

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?

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

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 $t .$ )

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)?

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.

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.

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.

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.

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," $z=-1.75$

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.

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?

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.

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?

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).

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.

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.

All Courses

• Interview Questions
• Free Courses
• Career Guide
• PGP in Data Science and Business Analytics
• PG Program in Data Science and Business Analytics Classroom
• PGP in Data Science and Engineering (Data Science Specialization)
• PGP in Data Science and Engineering (Bootcamp)
• PGP in Data Science & Engineering (Data Engineering Specialization)
• Master of Data Science (Global) – Deakin University
• MIT Data Science and Machine Learning Course Online
• Master’s (MS) in Data Science Online Degree Programme
• MTech in Data Science & Machine Learning by PES University
• Data Analytics Essentials by UT Austin
• Data Science & Business Analytics Program by McCombs School of Business
• MTech In Big Data Analytics by SRM
• M.Tech in Data Engineering Specialization by SRM University
• M.Tech in Big Data Analytics by SRM University
• PG in AI & Machine Learning Course
• Weekend Classroom PG Program For AI & ML
• AI for Leaders & Managers (PG Certificate Course)
• Artificial Intelligence Course for School Students
• IIIT Delhi: PG Diploma in Artificial Intelligence
• Machine Learning PG Program
• MIT No-Code AI and Machine Learning Course
• Study Abroad: Masters Programs
• MS in Information Science: Machine Learning From University of Arizon
• SRM M Tech in AI and ML for Working Professionals Program
• UT Austin Artificial Intelligence (AI) for Leaders & Managers
• UT Austin Artificial Intelligence and Machine Learning Program Online
• MS in Machine Learning
• IIT Roorkee Full Stack Developer Course
• IIT Madras Blockchain Course (Online Software Engineering)
• IIIT Hyderabad Software Engg for Data Science Course (Comprehensive)
• IIIT Hyderabad Software Engg for Data Science Course (Accelerated)
• IIT Bombay UX Design Course – Online PG Certificate Program
• Online MCA Degree Course by JAIN (Deemed-to-be University)
• Cybersecurity PG Course
• Online Post Graduate Executive Management Program
• Product Management Course Online in India
• NUS Future Leadership Program for Business Managers and Leaders
• PES Executive MBA Degree Program for Working Professionals
• Online BBA Degree Course by JAIN (Deemed-to-be University)
• MBA in Digital Marketing or Data Science by JAIN (Deemed-to-be University)
• Master of Business Administration- Shiva Nadar University
• Post Graduate Diploma in Management (Online) by Great Lakes
• Online MBA Programs
• Cloud Computing PG Program by Great Lakes
• University Programs
• Stanford Design Thinking Course Online
• Design Thinking : From Insights to Viability
• PGP In Strategic Digital Marketing
• Post Graduate Diploma in Management
• Master of Business Administration Degree Program
• MS in Business Analytics in USA
• MS in Machine Learning in USA
• Study MBA in Germany at FOM University
• M.Sc in Big Data & Business Analytics in Germany
• Study MBA in USA at Walsh College
• MS Data Analytics
• MS Artificial Intelligence and Machine Learning
• MS in Data Analytics
• Master of Business Administration (MBA)
• MS in Information Science: Machine Learning
• MS in Machine Learning Online
• MIT Data Science Program
• AI For Leaders Course
• Data Science and Business Analytics Course
• Cyber Security Course
• PG Program Online Artificial Intelligence Machine Learning
• PG Program Online Cloud Computing Course
• Data Analytics Essentials Online Course
• MIT Programa Ciencia De Dados Machine Learning
• MIT Programa Ciencia De Datos Aprendizaje Automatico
• Program PG Ciencia Datos Analitica Empresarial Curso Online
• Mit Programa Ciencia De Datos Aprendizaje Automatico
• Online Data Science Business Analytics Course
• Online Ai Machine Learning Course
• Online Full Stack Software Development Course
• Online Cloud Computing Course
• Cybersecurity Course Online
• Online Data Analytics Essentials Course
• Ai for Business Leaders Course
• Mit Data Science Program
• No Code Artificial Intelligence Machine Learning Program
• MS Information Science Machine Learning University Arizona
• Wharton Online Advanced Digital Marketing Program
• Introduction to Hypothesis Testing in R
• Testing of Hypothesis in R
• p-value: An Alternative way of Hypothesis Testing:
• t-test: Hypothesis Testing of Population Mean when Population Standard Deviation is Unknown:
• Two Samples Tests: Hypothesis Testing for the difference between two population means
• Hypothesis Testing for Equality of Population Variances
• Let’s Look at some Case studies:
• References:

Hypothesis Testing in R- Introduction Examples and Case Study

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

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

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

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

Parameter and Statistic

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

Sampling Distribution

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

Standard Error

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

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

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

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

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

Statistical Inference

Statistical Inference encompasses two different but related problems:

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

There are two types of estimation:

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

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

One Sample Tests

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

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

Hypothesis may be classified as: 

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

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

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

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

The Five Steps Process of Hypothesis Testing

Here, we take an example of Testing of Mean:

1. Setting up the Hypothesis:

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

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

Here the hypothesis may be:

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

H 1 : µ > µ 0 or

H 1 : µ < µ 0 or

H 1 : µ ≠ µ 0 

(Here, all three variants are Composite Hypothesis )

2. Defining Test and Test Statistic:

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

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

H 0 : µ = 75

H 1 : µ < 75.

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

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

Type I and Type II Error:

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

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

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

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

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

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

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

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

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

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

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

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

One Tailed and Two Tailed Tests of Hypothesis:

H 0 : µ ≤ µ 0  

H 1 : µ > µ 0 

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

H 0 : µ ≥ µ 0

H 1 : µ < µ 0 

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

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

H 0 : µ = µ 0

H 1 : µ ≠ µ 0

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

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

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

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

3.Deciding the Criteria for Rejection or otherwise:

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

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

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

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

5. Taking the Decision to reject or otherwise:

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

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

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

If p-value < α       : Reject H 0

If p-value ≥ α : Fails to Reject H 0

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

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

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

Hence the corresponding test statistic: 

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

Everything else in the testing process remains the same. 

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

t-distribution:

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

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

Independent Samples and Dependent (Paired Samples):

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

Testing the Difference Between Means: Independent Samples

Two samples z test:.

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

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

Alternative hypothesis:

H 1 : µ 1 – µ 2 > θ or

H 0 : µ 1 – µ 2 < θ or

H 1 : µ 1 – µ 2 ≠ θ 

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

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

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

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

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

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

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

Here, two situations are possible:

(a) Population Standard Deviations are unknown but equal:

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

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

So, the corresponding Test Statistics will be: 

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

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

(b) Population Standard Deviations are unknown but unequal:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

t-Test in SPSS:

One sample t-test.

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

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

Null Hypothesis H 0 : µ=75  

Alternative Hypothesis H 1 : µ≠75

One-Sample Statistics

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

One-Sample Test

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

Two Independent Samples t-Test

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

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

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

H 1 : µ 1 < µ 2  

Group Statistics

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

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

Independent Samples Test

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

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

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

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

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

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

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

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

Paired Samples Statistics

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

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

Paired Samples Test   

t-Test Application One Sample

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

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

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

Solution In R

[1] 1.224674

[1] 0.2305533

[1] “Accepted”

Independent t-test two sample

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

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

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

Case Study- Titan Insurance Company

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

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

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

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

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

Data preparation

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

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

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

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

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

Graphically,

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

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

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

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

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

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

Top Free Courses

What is Time Complexity And Why Is It Essential?

Top 30 Python Libraries To Know

Python Dictionary Append: How To Add Key/Value Pair?

¿Qué es la Ciencia de Datos? – Una Guía Completa [2024]

What is Data Science? – The Complete Guide

Python NumPy Tutorial – 2024

Leave a comment cancel reply.

Your email address will not be published. Required fields are marked *

Save my name, email, and website in this browser for the next time I comment.

Table of contents

A .gov website belongs to an official government organization in the United States.

A lock ( ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

• Contact Information
• Guidelines for Examining Unusual Patterns of Cancer and Environmental Concerns
• Resources and Tools

Phased Approach to Respond to Community Inquiries: Phase 3

• Conduct a feasibility assessment to determine whether an epidemiologic study would provide meaningful answers.
• Establish a community advisory committee (CAC) to create a link back to the community for valuable information.
• Consider different aspects to include in the study design and protocol development.

Phase 3: Considerations for epidemiologic studies

Feasibility assessment.

The feasibility of designing and conducting an epidemiologic study is dependent upon a variety of factors. For that reason, a feasibility assessment should be conducted to determine whether it is practical to conduct a study that would provide meaningful answers. The feasibility assessment should address multiple issues, including, but not limited to, data availability, adequate sample size to detect meaningful differences or associations, staff capacity, and other resources. In addition, to support studies and investigations it may be important for STLT health departments to consider all sources of funding and resources that may be available to them, including funding at the federal and state or local level, as well as nontraditional sources of funding.

When it has been determined that an epidemiologic study is feasible, do the following:

• Schedule meetings to discuss the initial findings and proposed approach for further assessment with the initial inquirer and other community members.
• Provide a detailed description of the next steps for evaluation. These next steps should be based on summary findings from the analysis of the 10 criteria in Phase 2 .
• Develop a summary that includes a rationale for continuing the investigation. For example, the assessment identified a potential spatial cluster or environmental factors that warrant further exploration.

Establish a community advisory committee

A community advisory committee (CAC) can contribute valuable sources of information and liaise with other community members. A CAC can provide specific details on the community, including help with cultural sensitivities or knowledge of current and/or historical environmental concerns in the area. A CAC can serve as a communication link back to the community at large.

Open communication will be needed to set goals, establish timelines, and discuss other issues (e.g., possible study limitations) so that expectations are clear. As previously mentioned, it may be important to also discuss issues related to resource requirements and other barriers that may impact conducting an epidemiologic study. Every community is different; however, agencies may be able to work with some existing organizations (e.g., neighborhood or religious organizations) to establish a CAC.

CAC and other community members can provide important insight and assist investigations:

• Help promote participation in studies and conduct outreach
• Identify specific tasks for community members that would contribute to the success of the investigation
• Identify additional data sources within the community (e.g., local lists that may be maintained which would identify previous residents)
• Identify population mobility patterns and housing development considerations

Consider the following for study design and protocol development

The following sections highlight the most important considerations for study design and protocol development. Consider developing a peer review committee with external partners to assess study design issues. Committee members should have a breadth of related skill sets in epidemiology, cancer, biostatistics, toxicology, and environmental health. The final draft of the protocol should be shared with the CAC in advance of initiating the study.

Case definition

Generate a formal case definition ahead of further analyses. Include the type of cancer, the population, the geographic area of concern, and the time period of interest. Review the study area and revise (if necessary) before starting additional analyses. For example, early assessments may have indicated that a particular contaminant was of concern and that more populations were found to be at potential risk for exposure to this contaminant. Thus, the study area would be expanded to include the other populations who were at potential risk for the exposure of concern.

A hypothesis regarding cancer cases or potential environmental contaminants was likely already generated during the assessment phase. However, hypotheses can evolve during an investigation, particularly if a potential exposure source has not been identified 1 . Re-review and update hypotheses regarding the cancer cases and contaminant(s) of interest (i.e., based on observations within the assessment phase to formulate analyses a priori). The hypothesis helps to guide the collection of data, the analysis plan, and interpretation of results.

Study population

Define the population of interest for the study. Ask the following questions to help define the study population as well as the time period of interest:

• How are the boundaries defined for the geographic area of interest?
• What are the characteristics of the population? Are there specific characteristics that are noted for the people with cancer (i.e., age group, race/ethnicity)?
• What is the latency period for the particular cancers of interest? What years of residence would need to be included to reflect the latency/development period assumed for the cancers of concern?
• How long have the residents lived in the area? What is the mobility and migration of former residents?
• Is there a potential for in utero exposures for the cancer(s) of concern based on where the mother lived during pregnancy?

Latency and change of residence add to the complexity of these investigations. Because residential history data are generally not available, collecting such data is critical as part of any epidemiologic study. Given the long latency period associated with cancers in adults, behaviors and exposures that might have contributed to the development of cancer in a person typically occur years to decades before the diagnosis. For example, malignant mesothelioma, a tumor of the lining of the lung, is associated with asbestos exposure, and the latency period between first exposure to asbestos and death from mesothelioma is often 30 years or longer 2 .

Latency in an epidemiologic investigation influences the exposure period relevant to the investigation. For example, if a person with cancer did not live in the suspected area of cancer concern during the relevant exposure period, then that person's cancer would not likely be related to an exposure in the area of concern. Conversely, the latency period might limit the ability to detect unusual patterns of cancer or identify cancers related to an environmental exposure that occurred in the past. In a mobile population, patterns resulting from an environmental contamination occurring years or even decades earlier might go undetected because exposed residents may have moved away from the community before the cancer developed. Thus, as persons move in and out of different communities, their cumulative exposure profile will change.

Because childhood cancers generally have shorter latency periods than cancers in adults, changes of residence might be less of an issue in the investigation of unusual patterns of childhood cancers. However, childhood cancer investigations may have the same limitations as adult counterparts. For example, in one California study of 380 children with a diagnosis of leukemia, approximately 65% of the study participants changed residence between birth and diagnosis 3 , indicating that even among cancers with short latency periods, migration might be an important factor. Account for latency when designing any additional analyses or studies.

Additional environmental data

If additional environmental data are needed, partner with state or local environmental regulatory agencies. ATSDR, including the regional offices, can also provide technical assistance, such as review of environmental sampling plans. Outline the types of sampling needed and resources available or necessary to conduct such sampling. Also, consider the following:

• Potential sources and routes of exposure (e.g., through air inhalation, water ingestion, in utero )
• Contaminant transport (e.g., if exposure occurs via ambient air, meteorological factors such as wind direction and speed are important)
• Other contributing sources of exposure
• Boundaries of potential spread/movement (important to understand the potential at-risk population)
• Any prior or ongoing remediation or reduction activities related to the environmental concern of interest
• Role of participating agencies in data collection and identification of resources to support the collection of environmental data.

Existing health data for case finding

Primarily, cases of cancer among the study population are identified from a state’s cancer registry, using the case definition. Consider multiple existing data sources for use to help identify cases. Forming partnerships with health information exchange or network entities may help with identifying other existing data sources. For additional support and guidance, CDC/ATSDR can provide technical assistance.

Contributing risk factors

An environmental factor may have been identified as a potential risk factor for the cancer of interest; however, cancers may be caused by several different risk factors or through multiple causal mechanisms 4 . Review additional risk factors for the type(s) of cancer under investigation, such as social determinants of health, behavioral risks, occupational exposures, and in some cases genetic factors.

Types of epidemiologic studies to consider

Methods used in environmental epidemiology are observational, not experimental. This makes the process of identifying a causative agent more difficult because researchers may not have access to information about other exposures or other variables that can create bias in the analysis 1 5 6 . However, additional studies can potentially help make inferences about cancer cases and potential associations. Consider the following types of descriptive or analytical studies:

• Case-series study : A case-series study is a descriptive analysis of persons with a similar cancer diagnosis. This study can be particularly helpful when there are small numbers of cases and it is not feasible to pursue other studies (e.g., statistical challenges associated with a small number of individuals diagnosed with the disease). Case-series studies are often designed to collect more information about each person to identify any commonalities. For these studies, identify as many relevant cases as possible to avoid selection bias. Depending on the findings, a further analytical study may be possible or warranted (see case-control or cohort below).
• Ecological study : An ecological study compares aggregated environmental data to aggregated cancer data to examine general associations. Exposures and outcomes are generally grouped to a geographic area, such as a census tract, for comparison. Individual exposures are not included in an ecological analysis. Ecological studies are most often done initially to explore potential associations but alone cannot determine causality. Epidemiologists must use caution when interpreting this type of analysis because the association with a particular environmental contaminant might not be true for individual cases, especially if there is heterogeneous distribution of the exposure over the geographic area. The related bias is known as ecological inference fallacy and could result in exposure misclassification.
• Cross-sectional study : A cross-sectional study is another descriptive study that measures health outcomes and exposure factors during a specific point in time. This type of study is helpful in describing the frequency of different characteristics in a study population during the time frame of interest. However, it may not be the ideal study design for investigating unusual patterns of cancer because this type of study design only looks at data distributions in a specific time frame, and temporal patterns cannot be established. In instances when biomarker data are available, a cross-sectional study may provide insights about key exposures among the population.
• Case-control study : Consider a case-control study when the etiology of the cancer is unknown. This type of analytical study can also be used to assess the association between cancer and a presumed exposure while being able to control for confounding factors. A case-control study collects information from cancer cases meeting the case-definition and controls within the same study area. Exposures and risk factors are compared between the two groups, for example using regression analysis methods. Case-control studies are suggested for rare cancer outcomes. Unlike the ecological study, case-control studies allow for the collection of individual-level data and risk factors to assess within the analyses. The primary disadvantages of a case-control study are the inability for individuals to recall historic events (e.g., exposures) and the difficulty of providing a direct estimate of risk. Risk is often estimated as an odds ratio, showing the odds for a particular cancer to have occurred given a particular exposure, compared to odds of the same cancer without the exposure. For this type of study, the sample size needed should be calculated ahead of time considering the power needed to detect statistical differences between the populations ( Appendix A ).
• Cohort (retrospective or prospective) : Consider a cohort study when the exposure source is known or being investigated. Select people who have varying levels of exposure for the study. Prospective cohort studies, while one of the strongest types of studies to examine exposure-disease relationships, are very time consuming and expensive. Depending on the latency of the cancer(s) of concern, a prospective cohort study may need to be 10–20 years or longer to collect enough data for analyses. The length of time needed often must account for study attrition and thus require a very large sample size. A retrospective cohort study may be feasible, but also is reliant on time-related information. For example, a cohort study may want to compare a population exposed to chemicals from Factory X, which was operating in the early 1990s. To establish a study cohort, a population within that community would have to have been in the study area ~30 years previously. Because of the length of time needed for these studies, some challenges may arise that need to be accounted for within the study design. For example, a community may have experienced a substantial percentage of movement or migration. Also, as previously mentioned, the latency of the cancer will also need to be accounted for within the study design. For example, the average latency for mesothelioma is generally thought to be decades 7 . More recently, data from the World Trade Center Health Program suggests that the minimum latency for mesothelioma is about 11 years and the minimum latency for thyroid cancer is 2.5 years 4 . Studies assessing these types of cancers would have to account for the number of years that specific types of cancers develop following exposures. Additionally, limitations exist with quantifying historic exposures for retrospective cohort studies.

Ongoing technical and scientific advancements in areas such as data science, analytic and geospatial methods, and cancer genomics may be available in the future (e.g., genomic research, gene-environment interaction).

Other considerations for your study

When evaluating the feasibility of different epidemiologic studies, consider the following:

• Funding : Funding may be needed to help with the investigation. Seek state and federal opportunities to assist with funding the investigation or with providing technical assistance. In addition, academic partnerships may help to support the investigation.
• Outreach : For more robust analyses, reach out to other states to discuss case-finding and/or environmental sampling activities, specifically in neighboring states if suspected environmental contaminants cross state borders.
• Communication : Ultimately, the goal of an epidemiologic investigation of unusual patterns or excesses of cancer is to understand the potential relationship between environmental and other risk factors identified and observed cases of cancer. Some epidemiologic investigations have identified potential associations between certain cancers and risk factors including exposures to certain chemicals 8 9 10 . However, methodological limitations and data limitations (such as unknown levels of exposure) often limit the ability to demonstrate that such relationships exist. Regardless of the outcome of an epidemiologic investigation, continuing to communicate with individuals most concerned about exposures and health outcomes is important.
• Merrill R. Environmental Epidemiology, Principles and Methods. Sudbury, MA: Jones and Bartlett Publishers, Inc.; 2008.
• Lanphear B, Buncher C. Latent period for malignant mesothelioma of occupational origin – PubMed. J Occup Med [Internet]. 1992 [cited 2022 Jan 7];34(7):718–21. Available from: https://pubmed.ncbi.nlm.nih.gov/1494965/
• Urayama KY, Von Behren J, Reynolds P, Hertz A, Does M, Buffler PA. Factors associated with residential mobility in children with leukemia: implications for assigning exposures. Ann Epidemiol [Internet]. 2009 Nov [cited 2022 Jan 7];19(11):834–40. Available from: https://pubmed.ncbi.nlm.nih.gov/19364662/
• CDC. World Trade Center Health Program [Internet]. Available from: https://www.cdc.gov/wtc/pdfs/policies/WTCHP-Minimum-Cancer-Latency-PP-01062015-508.pdf
• Gordis L. Epidemiology. Philadelphia, PA: Elsevier Saunders; 2014.
• Dicker R, Coronado F, Koo D, Parrish R. Principles of Epidemiology in Public Health Practice: An Introduction to Applied Epidemiology and Biostatics. CDC Office of Workforce and Career Development; 2006.
• Frost G. The latency period of mesothelioma among a cohort of British asbestos workers (1978–2005). Br J Cancer. 2013 Oct 29;109(7):1965–73.
• Costas K, Knorr RS, Condon SK. A case-control study of childhood leukemia in Woburn, Massachusetts: The relationship between leukemia incidence and exposure to public drinking water. Sci Total Environ. 2002;300(1–3):23–35.
• Massachusetts Department of Public Health. The Wilmington Childhood Cancer Study: An Epidemiologic Investigation of Childhood Cancer from 1990–2000. 2021.
• Vieira VM, Hoffman K, Shin HM, Weinberg JM, Webster TF, Fletcher T. Perfluorooctanoic acid exposure and cancer outcomes in a contaminated community: A geographic analysis. Environ Health Perspect. 2013;121(3):318–23.

Unusual Cancer Patterns

Guidelines and resources for examining unusual patterns of cancer and environmental concerns.

For Everyone

Public health.

Artificial intelligence in strategy

Can machines automate strategy development? The short answer is no. However, there are numerous aspects of strategists’ work where AI and advanced analytics tools can already bring enormous value. Yuval Atsmon is a senior partner who leads the new McKinsey Center for Strategy Innovation, which studies ways new technologies can augment the timeless principles of strategy. In this episode of the Inside the Strategy Room podcast, he explains how artificial intelligence is already transforming strategy and what’s on the horizon. This is an edited transcript of the discussion. For more conversations on the strategy issues that matter, follow the series on your preferred podcast platform .

Joanna Pachner: What does artificial intelligence mean in the context of strategy?

Yuval Atsmon: When people talk about artificial intelligence, they include everything to do with analytics, automation, and data analysis. Marvin Minsky, the pioneer of artificial intelligence research in the 1960s, talked about AI as a “suitcase word”—a term into which you can stuff whatever you want—and that still seems to be the case. We are comfortable with that because we think companies should use all the capabilities of more traditional analysis while increasing automation in strategy that can free up management or analyst time and, gradually, introducing tools that can augment human thinking.

Joanna Pachner: AI has been embraced by many business functions, but strategy seems to be largely immune to its charms. Why do you think that is?

Subscribe to the Inside the Strategy Room podcast

Yuval Atsmon: You’re right about the limited adoption. Only 7 percent of respondents to our survey about the use of AI say they use it in strategy or even financial planning, whereas in areas like marketing, supply chain, and service operations, it’s 25 or 30 percent. One reason adoption is lagging is that strategy is one of the most integrative conceptual practices. When executives think about strategy automation, many are looking too far ahead—at AI capabilities that would decide, in place of the business leader, what the right strategy is. They are missing opportunities to use AI in the building blocks of strategy that could significantly improve outcomes.

I like to use the analogy to virtual assistants. Many of us use Alexa or Siri but very few people use these tools to do more than dictate a text message or shut off the lights. We don’t feel comfortable with the technology’s ability to understand the context in more sophisticated applications. AI in strategy is similar: it’s hard for AI to know everything an executive knows, but it can help executives with certain tasks.

When executives think about strategy automation, many are looking too far ahead—at AI deciding the right strategy. They are missing opportunities to use AI in the building blocks of strategy.

Joanna Pachner: What kind of tasks can AI help strategists execute today?

Yuval Atsmon: We talk about six stages of AI development. The earliest is simple analytics, which we refer to as descriptive intelligence. Companies use dashboards for competitive analysis or to study performance in different parts of the business that are automatically updated. Some have interactive capabilities for refinement and testing.

The second level is diagnostic intelligence, which is the ability to look backward at the business and understand root causes and drivers of performance. The level after that is predictive intelligence: being able to anticipate certain scenarios or options and the value of things in the future based on momentum from the past as well as signals picked in the market. Both diagnostics and prediction are areas that AI can greatly improve today. The tools can augment executives’ analysis and become areas where you develop capabilities. For example, on diagnostic intelligence, you can organize your portfolio into segments to understand granularly where performance is coming from and do it in a much more continuous way than analysts could. You can try 20 different ways in an hour versus deploying one hundred analysts to tackle the problem.

Predictive AI is both more difficult and more risky. Executives shouldn’t fully rely on predictive AI, but it provides another systematic viewpoint in the room. Because strategic decisions have significant consequences, a key consideration is to use AI transparently in the sense of understanding why it is making a certain prediction and what extrapolations it is making from which information. You can then assess if you trust the prediction or not. You can even use AI to track the evolution of the assumptions for that prediction.

Those are the levels available today. The next three levels will take time to develop. There are some early examples of AI advising actions for executives’ consideration that would be value-creating based on the analysis. From there, you go to delegating certain decision authority to AI, with constraints and supervision. Eventually, there is the point where fully autonomous AI analyzes and decides with no human interaction.

Because strategic decisions have significant consequences, you need to understand why AI is making a certain prediction and what extrapolations it’s making from which information.

Joanna Pachner: What kind of businesses or industries could gain the greatest benefits from embracing AI at its current level of sophistication?

Yuval Atsmon: Every business probably has some opportunity to use AI more than it does today. The first thing to look at is the availability of data. Do you have performance data that can be organized in a systematic way? Companies that have deep data on their portfolios down to business line, SKU, inventory, and raw ingredients have the biggest opportunities to use machines to gain granular insights that humans could not.

Companies whose strategies rely on a few big decisions with limited data would get less from AI. Likewise, those facing a lot of volatility and vulnerability to external events would benefit less than companies with controlled and systematic portfolios, although they could deploy AI to better predict those external events and identify what they can and cannot control.

Third, the velocity of decisions matters. Most companies develop strategies every three to five years, which then become annual budgets. If you think about strategy in that way, the role of AI is relatively limited other than potentially accelerating analyses that are inputs into the strategy. However, some companies regularly revisit big decisions they made based on assumptions about the world that may have since changed, affecting the projected ROI of initiatives. Such shifts would affect how you deploy talent and executive time, how you spend money and focus sales efforts, and AI can be valuable in guiding that. The value of AI is even bigger when you can make decisions close to the time of deploying resources, because AI can signal that your previous assumptions have changed from when you made your plan.

Joanna Pachner: Can you provide any examples of companies employing AI to address specific strategic challenges?

Yuval Atsmon: Some of the most innovative users of AI, not coincidentally, are AI- and digital-native companies. Some of these companies have seen massive benefits from AI and have increased its usage in other areas of the business. One mobility player adjusts its financial planning based on pricing patterns it observes in the market. Its business has relatively high flexibility to demand but less so to supply, so the company uses AI to continuously signal back when pricing dynamics are trending in a way that would affect profitability or where demand is rising. This allows the company to quickly react to create more capacity because its profitability is highly sensitive to keeping demand and supply in equilibrium.

Joanna Pachner: Given how quickly things change today, doesn’t AI seem to be more a tactical than a strategic tool, providing time-sensitive input on isolated elements of strategy?

Yuval Atsmon: It’s interesting that you make the distinction between strategic and tactical. Of course, every decision can be broken down into smaller ones, and where AI can be affordably used in strategy today is for building blocks of the strategy. It might feel tactical, but it can make a massive difference. One of the world’s leading investment firms, for example, has started to use AI to scan for certain patterns rather than scanning individual companies directly. AI looks for consumer mobile usage that suggests a company’s technology is catching on quickly, giving the firm an opportunity to invest in that company before others do. That created a significant strategic edge for them, even though the tool itself may be relatively tactical.

Joanna Pachner: McKinsey has written a lot about cognitive biases  and social dynamics that can skew decision making. Can AI help with these challenges?

Yuval Atsmon: When we talk to executives about using AI in strategy development, the first reaction we get is, “Those are really big decisions; what if AI gets them wrong?” The first answer is that humans also get them wrong—a lot. [Amos] Tversky, [Daniel] Kahneman, and others have proven that some of those errors are systemic, observable, and predictable. The first thing AI can do is spot situations likely to give rise to biases. For example, imagine that AI is listening in on a strategy session where the CEO proposes something and everyone says “Aye” without debate and discussion. AI could inform the room, “We might have a sunflower bias here,” which could trigger more conversation and remind the CEO that it’s in their own interest to encourage some devil’s advocacy.

We also often see confirmation bias, where people focus their analysis on proving the wisdom of what they already want to do, as opposed to looking for a fact-based reality. Just having AI perform a default analysis that doesn’t aim to satisfy the boss is useful, and the team can then try to understand why that is different than the management hypothesis, triggering a much richer debate.

In terms of social dynamics, agency problems can create conflicts of interest. Every business unit [BU] leader thinks that their BU should get the most resources and will deliver the most value, or at least they feel they should advocate for their business. AI provides a neutral way based on systematic data to manage those debates. It’s also useful for executives with decision authority, since we all know that short-term pressures and the need to make the quarterly and annual numbers lead people to make different decisions on the 31st of December than they do on January 1st or October 1st. Like the story of Ulysses and the sirens, you can use AI to remind you that you wanted something different three months earlier. The CEO still decides; AI can just provide that extra nudge.

Joanna Pachner: It’s like you have Spock next to you, who is dispassionate and purely analytical.

Yuval Atsmon: That is not a bad analogy—for Star Trek fans anyway.

Joanna Pachner: Do you have a favorite application of AI in strategy?

Yuval Atsmon: I have worked a lot on resource allocation, and one of the challenges, which we call the hockey stick phenomenon, is that executives are always overly optimistic about what will happen. They know that resource allocation will inevitably be defined by what you believe about the future, not necessarily by past performance. AI can provide an objective prediction of performance starting from a default momentum case: based on everything that happened in the past and some indicators about the future, what is the forecast of performance if we do nothing? This is before we say, “But I will hire these people and develop this new product and improve my marketing”— things that every executive thinks will help them overdeliver relative to the past. The neutral momentum case, which AI can calculate in a cold, Spock-like manner, can change the dynamics of the resource allocation discussion. It’s a form of predictive intelligence accessible today and while it’s not meant to be definitive, it provides a basis for better decisions.

Joanna Pachner: Do you see access to technology talent as one of the obstacles to the adoption of AI in strategy, especially at large companies?

Yuval Atsmon: I would make a distinction. If you mean machine-learning and data science talent or software engineers who build the digital tools, they are definitely not easy to get. However, companies can increasingly use platforms that provide access to AI tools and require less from individual companies. Also, this domain of strategy is exciting—it’s cutting-edge, so it’s probably easier to get technology talent for that than it might be for manufacturing work.

The bigger challenge, ironically, is finding strategists or people with business expertise to contribute to the effort. You will not solve strategy problems with AI without the involvement of people who understand the customer experience and what you are trying to achieve. Those who know best, like senior executives, don’t have time to be product managers for the AI team. An even bigger constraint is that, in some cases, you are asking people to get involved in an initiative that may make their jobs less important. There could be plenty of opportunities for incorpo­rating AI into existing jobs, but it’s something companies need to reflect on. The best approach may be to create a digital factory where a different team tests and builds AI applications, with oversight from senior stakeholders.

The big challenge is finding strategists to contribute to the AI effort. You are asking people to get involved in an initiative that may make their jobs less important.

Joanna Pachner: Do you think this worry about job security and the potential that AI will automate strategy is realistic?

Yuval Atsmon: The question of whether AI will replace human judgment and put humanity out of its job is a big one that I would leave for other experts.

The pertinent question is shorter-term automation. Because of its complexity, strategy would be one of the later domains to be affected by automation, but we are seeing it in many other domains. However, the trend for more than two hundred years has been that automation creates new jobs, although ones requiring different skills. That doesn’t take away the fear some people have of a machine exposing their mistakes or doing their job better than they do it.

Joanna Pachner: We recently published an article about strategic courage in an age of volatility  that talked about three types of edge business leaders need to develop. One of them is an edge in insights. Do you think AI has a role to play in furnishing a proprietary insight edge?

Yuval Atsmon: One of the challenges most strategists face is the overwhelming complexity of the world we operate in—the number of unknowns, the information overload. At one level, it may seem that AI will provide another layer of complexity. In reality, it can be a sharp knife that cuts through some of the clutter. The question to ask is, Can AI simplify my life by giving me sharper, more timely insights more easily?

Joanna Pachner: You have been working in strategy for a long time. What sparked your interest in exploring this intersection of strategy and new technology?

Yuval Atsmon: I have always been intrigued by things at the boundaries of what seems possible. Science fiction writer Arthur C. Clarke’s second law is that to discover the limits of the possible, you have to venture a little past them into the impossible, and I find that particularly alluring in this arena.

AI in strategy is in very nascent stages but could be very consequential for companies and for the profession. For a top executive, strategic decisions are the biggest way to influence the business, other than maybe building the top team, and it is amazing how little technology is leveraged in that process today. It’s conceivable that competitive advantage will increasingly rest in having executives who know how to apply AI well. In some domains, like investment, that is already happening, and the difference in returns can be staggering. I find helping companies be part of that evolution very exciting.

Explore a career with us

Related articles.

Strategic courage in an age of volatility

Bias Busters Collection