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

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

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

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

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

Table of contents

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

• Normal distribution
• Degrees of freedom
• Null hypothesis
• Discourse analysis
• Control groups
• Mixed methods research
• Non-probability sampling
• Quantitative research
• Ecological validity

Research bias

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

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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.

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Researcher, Academic Writer, Web developer

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• Open access
• Published: 27 June 2011

The case study approach

• Sarah Crowe 1 ,
• Kathrin Cresswell 2 ,
• Ann Robertson 2 ,
• Guro Huby 3 ,
• Anthony Avery 1 &
• Aziz Sheikh 2  

BMC Medical Research Methodology volume  11 , Article number:  100 ( 2011 ) Cite this article

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

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Introduction

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

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

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

What is a case study?

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

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

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

What are case studies used for?

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

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

How are case studies conducted?

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

Defining the case

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

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

Selecting the case(s)

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

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

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

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

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

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

Collecting the data

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

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

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

Analysing, interpreting and reporting case studies

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

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

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

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

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

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

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

Conclusions

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

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Acknowledgements

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

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

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Crowe, S., Cresswell, K., Robertson, A. et al. The case study approach. BMC Med Res Methodol 11 , 100 (2011). https://doi.org/10.1186/1471-2288-11-100

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The Ultimate Guide to Qualitative Research - Part 1: The Basics

• Introduction and overview
• What is qualitative research?
• What is qualitative data?
• Examples of qualitative data
• Qualitative vs. quantitative research
• Mixed methods
• Qualitative research preparation
• Theoretical perspective
• Theoretical framework
• Literature reviews

Research question

• Conceptual framework
• Conceptual vs. theoretical framework

Data collection

• Qualitative research methods
• Focus groups
• Observational research

What is a case study?

Applications for case study research, what is a good case study, process of case study design, benefits and limitations of case studies.

• Ethnographical research
• Ethical considerations
• Confidentiality and privacy
• Power dynamics
• Reflexivity

Case studies

Case studies are essential to qualitative research , offering a lens through which researchers can investigate complex phenomena within their real-life contexts. This chapter explores the concept, purpose, applications, examples, and types of case studies and provides guidance on how to conduct case study research effectively.

Whereas quantitative methods look at phenomena at scale, case study research looks at a concept or phenomenon in considerable detail. While analyzing a single case can help understand one perspective regarding the object of research inquiry, analyzing multiple cases can help obtain a more holistic sense of the topic or issue. Let's provide a basic definition of a case study, then explore its characteristics and role in the qualitative research process.

Definition of a case study

A case study in qualitative research is a strategy of inquiry that involves an in-depth investigation of a phenomenon within its real-world context. It provides researchers with the opportunity to acquire an in-depth understanding of intricate details that might not be as apparent or accessible through other methods of research. The specific case or cases being studied can be a single person, group, or organization – demarcating what constitutes a relevant case worth studying depends on the researcher and their research question .

Among qualitative research methods , a case study relies on multiple sources of evidence, such as documents, artifacts, interviews , or observations , to present a complete and nuanced understanding of the phenomenon under investigation. The objective is to illuminate the readers' understanding of the phenomenon beyond its abstract statistical or theoretical explanations.

Characteristics of case studies

Case studies typically possess a number of distinct characteristics that set them apart from other research methods. These characteristics include a focus on holistic description and explanation, flexibility in the design and data collection methods, reliance on multiple sources of evidence, and emphasis on the context in which the phenomenon occurs.

Furthermore, case studies can often involve a longitudinal examination of the case, meaning they study the case over a period of time. These characteristics allow case studies to yield comprehensive, in-depth, and richly contextualized insights about the phenomenon of interest.

The role of case studies in research

Case studies hold a unique position in the broader landscape of research methods aimed at theory development. They are instrumental when the primary research interest is to gain an intensive, detailed understanding of a phenomenon in its real-life context.

In addition, case studies can serve different purposes within research - they can be used for exploratory, descriptive, or explanatory purposes, depending on the research question and objectives. This flexibility and depth make case studies a valuable tool in the toolkit of qualitative researchers.

Remember, a well-conducted case study can offer a rich, insightful contribution to both academic and practical knowledge through theory development or theory verification, thus enhancing our understanding of complex phenomena in their real-world contexts.

What is the purpose of a case study?

Case study research aims for a more comprehensive understanding of phenomena, requiring various research methods to gather information for qualitative analysis . Ultimately, a case study can allow the researcher to gain insight into a particular object of inquiry and develop a theoretical framework relevant to the research inquiry.

Why use case studies in qualitative research?

Using case studies as a research strategy depends mainly on the nature of the research question and the researcher's access to the data.

Conducting case study research provides a level of detail and contextual richness that other research methods might not offer. They are beneficial when there's a need to understand complex social phenomena within their natural contexts.

The explanatory, exploratory, and descriptive roles of case studies

Case studies can take on various roles depending on the research objectives. They can be exploratory when the research aims to discover new phenomena or define new research questions; they are descriptive when the objective is to depict a phenomenon within its context in a detailed manner; and they can be explanatory if the goal is to understand specific relationships within the studied context. Thus, the versatility of case studies allows researchers to approach their topic from different angles, offering multiple ways to uncover and interpret the data .

The impact of case studies on knowledge development

Case studies play a significant role in knowledge development across various disciplines. Analysis of cases provides an avenue for researchers to explore phenomena within their context based on the collected data.

This can result in the production of rich, practical insights that can be instrumental in both theory-building and practice. Case studies allow researchers to delve into the intricacies and complexities of real-life situations, uncovering insights that might otherwise remain hidden.

Types of case studies

In qualitative research , a case study is not a one-size-fits-all approach. Depending on the nature of the research question and the specific objectives of the study, researchers might choose to use different types of case studies. These types differ in their focus, methodology, and the level of detail they provide about the phenomenon under investigation.

Understanding these types is crucial for selecting the most appropriate approach for your research project and effectively achieving your research goals. Let's briefly look at the main types of case studies.

Exploratory case studies

Exploratory case studies are typically conducted to develop a theory or framework around an understudied phenomenon. They can also serve as a precursor to a larger-scale research project. Exploratory case studies are useful when a researcher wants to identify the key issues or questions which can spur more extensive study or be used to develop propositions for further research. These case studies are characterized by flexibility, allowing researchers to explore various aspects of a phenomenon as they emerge, which can also form the foundation for subsequent studies.

Descriptive case studies

Descriptive case studies aim to provide a complete and accurate representation of a phenomenon or event within its context. These case studies are often based on an established theoretical framework, which guides how data is collected and analyzed. The researcher is concerned with describing the phenomenon in detail, as it occurs naturally, without trying to influence or manipulate it.

Explanatory case studies

Explanatory case studies are focused on explanation - they seek to clarify how or why certain phenomena occur. Often used in complex, real-life situations, they can be particularly valuable in clarifying causal relationships among concepts and understanding the interplay between different factors within a specific context.

Intrinsic, instrumental, and collective case studies

These three categories of case studies focus on the nature and purpose of the study. An intrinsic case study is conducted when a researcher has an inherent interest in the case itself. Instrumental case studies are employed when the case is used to provide insight into a particular issue or phenomenon. A collective case study, on the other hand, involves studying multiple cases simultaneously to investigate some general phenomena.

Each type of case study serves a different purpose and has its own strengths and challenges. The selection of the type should be guided by the research question and objectives, as well as the context and constraints of the research.

The flexibility, depth, and contextual richness offered by case studies make this approach an excellent research method for various fields of study. They enable researchers to investigate real-world phenomena within their specific contexts, capturing nuances that other research methods might miss. Across numerous fields, case studies provide valuable insights into complex issues.

Critical information systems research

Case studies provide a detailed understanding of the role and impact of information systems in different contexts. They offer a platform to explore how information systems are designed, implemented, and used and how they interact with various social, economic, and political factors. Case studies in this field often focus on examining the intricate relationship between technology, organizational processes, and user behavior, helping to uncover insights that can inform better system design and implementation.

Health research

Health research is another field where case studies are highly valuable. They offer a way to explore patient experiences, healthcare delivery processes, and the impact of various interventions in a real-world context.

Case studies can provide a deep understanding of a patient's journey, giving insights into the intricacies of disease progression, treatment effects, and the psychosocial aspects of health and illness.

Asthma research studies

Specifically within medical research, studies on asthma often employ case studies to explore the individual and environmental factors that influence asthma development, management, and outcomes. A case study can provide rich, detailed data about individual patients' experiences, from the triggers and symptoms they experience to the effectiveness of various management strategies. This can be crucial for developing patient-centered asthma care approaches.

Other fields

Apart from the fields mentioned, case studies are also extensively used in business and management research, education research, and political sciences, among many others. They provide an opportunity to delve into the intricacies of real-world situations, allowing for a comprehensive understanding of various phenomena.

Case studies, with their depth and contextual focus, offer unique insights across these varied fields. They allow researchers to illuminate the complexities of real-life situations, contributing to both theory and practice.

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Understanding the key elements of case study design is crucial for conducting rigorous and impactful case study research. A well-structured design guides the researcher through the process, ensuring that the study is methodologically sound and its findings are reliable and valid. The main elements of case study design include the research question , propositions, units of analysis, and the logic linking the data to the propositions.

The research question is the foundation of any research study. A good research question guides the direction of the study and informs the selection of the case, the methods of collecting data, and the analysis techniques. A well-formulated research question in case study research is typically clear, focused, and complex enough to merit further detailed examination of the relevant case(s).

Propositions

Propositions, though not necessary in every case study, provide a direction by stating what we might expect to find in the data collected. They guide how data is collected and analyzed by helping researchers focus on specific aspects of the case. They are particularly important in explanatory case studies, which seek to understand the relationships among concepts within the studied phenomenon.

Units of analysis

The unit of analysis refers to the case, or the main entity or entities that are being analyzed in the study. In case study research, the unit of analysis can be an individual, a group, an organization, a decision, an event, or even a time period. It's crucial to clearly define the unit of analysis, as it shapes the qualitative data analysis process by allowing the researcher to analyze a particular case and synthesize analysis across multiple case studies to draw conclusions.

Argumentation

This refers to the inferential model that allows researchers to draw conclusions from the data. The researcher needs to ensure that there is a clear link between the data, the propositions (if any), and the conclusions drawn. This argumentation is what enables the researcher to make valid and credible inferences about the phenomenon under study.

Understanding and carefully considering these elements in the design phase of a case study can significantly enhance the quality of the research. It can help ensure that the study is methodologically sound and its findings contribute meaningful insights about the case.

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Conducting a case study involves several steps, from defining the research question and selecting the case to collecting and analyzing data . This section outlines these key stages, providing a practical guide on how to conduct case study research.

Defining the research question

The first step in case study research is defining a clear, focused research question. This question should guide the entire research process, from case selection to analysis. It's crucial to ensure that the research question is suitable for a case study approach. Typically, such questions are exploratory or descriptive in nature and focus on understanding a phenomenon within its real-life context.

Selecting and defining the case

The selection of the case should be based on the research question and the objectives of the study. It involves choosing a unique example or a set of examples that provide rich, in-depth data about the phenomenon under investigation. After selecting the case, it's crucial to define it clearly, setting the boundaries of the case, including the time period and the specific context.

Previous research can help guide the case study design. When considering a case study, an example of a case could be taken from previous case study research and used to define cases in a new research inquiry. Considering recently published examples can help understand how to select and define cases effectively.

Developing a detailed case study protocol

A case study protocol outlines the procedures and general rules to be followed during the case study. This includes the data collection methods to be used, the sources of data, and the procedures for analysis. Having a detailed case study protocol ensures consistency and reliability in the study.

The protocol should also consider how to work with the people involved in the research context to grant the research team access to collecting data. As mentioned in previous sections of this guide, establishing rapport is an essential component of qualitative research as it shapes the overall potential for collecting and analyzing data.

Collecting data

Gathering data in case study research often involves multiple sources of evidence, including documents, archival records, interviews, observations, and physical artifacts. This allows for a comprehensive understanding of the case. The process for gathering data should be systematic and carefully documented to ensure the reliability and validity of the study.

Analyzing and interpreting data

The next step is analyzing the data. This involves organizing the data , categorizing it into themes or patterns , and interpreting these patterns to answer the research question. The analysis might also involve comparing the findings with prior research or theoretical propositions.

Writing the case study report

The final step is writing the case study report . This should provide a detailed description of the case, the data, the analysis process, and the findings. The report should be clear, organized, and carefully written to ensure that the reader can understand the case and the conclusions drawn from it.

Each of these steps is crucial in ensuring that the case study research is rigorous, reliable, and provides valuable insights about the case.

The type, depth, and quality of data in your study can significantly influence the validity and utility of the study. In case study research, data is usually collected from multiple sources to provide a comprehensive and nuanced understanding of the case. This section will outline the various methods of collecting data used in case study research and discuss considerations for ensuring the quality of the data.

Interviews are a common method of gathering data in case study research. They can provide rich, in-depth data about the perspectives, experiences, and interpretations of the individuals involved in the case. Interviews can be structured , semi-structured , or unstructured , depending on the research question and the degree of flexibility needed.

Observations

Observations involve the researcher observing the case in its natural setting, providing first-hand information about the case and its context. Observations can provide data that might not be revealed in interviews or documents, such as non-verbal cues or contextual information.

Documents and artifacts

Documents and archival records provide a valuable source of data in case study research. They can include reports, letters, memos, meeting minutes, email correspondence, and various public and private documents related to the case.

These records can provide historical context, corroborate evidence from other sources, and offer insights into the case that might not be apparent from interviews or observations.

Physical artifacts refer to any physical evidence related to the case, such as tools, products, or physical environments. These artifacts can provide tangible insights into the case, complementing the data gathered from other sources.

Ensuring the quality of data collection

Determining the quality of data in case study research requires careful planning and execution. It's crucial to ensure that the data is reliable, accurate, and relevant to the research question. This involves selecting appropriate methods of collecting data, properly training interviewers or observers, and systematically recording and storing the data. It also includes considering ethical issues related to collecting and handling data, such as obtaining informed consent and ensuring the privacy and confidentiality of the participants.

Data analysis

Analyzing case study research involves making sense of the rich, detailed data to answer the research question. This process can be challenging due to the volume and complexity of case study data. However, a systematic and rigorous approach to analysis can ensure that the findings are credible and meaningful. This section outlines the main steps and considerations in analyzing data in case study research.

Organizing the data

The first step in the analysis is organizing the data. This involves sorting the data into manageable sections, often according to the data source or the theme. This step can also involve transcribing interviews, digitizing physical artifacts, or organizing observational data.

Categorizing and coding the data

Once the data is organized, the next step is to categorize or code the data. This involves identifying common themes, patterns, or concepts in the data and assigning codes to relevant data segments. Coding can be done manually or with the help of software tools, and in either case, qualitative analysis software can greatly facilitate the entire coding process. Coding helps to reduce the data to a set of themes or categories that can be more easily analyzed.

Identifying patterns and themes

After coding the data, the researcher looks for patterns or themes in the coded data. This involves comparing and contrasting the codes and looking for relationships or patterns among them. The identified patterns and themes should help answer the research question.

Interpreting the data

Once patterns and themes have been identified, the next step is to interpret these findings. This involves explaining what the patterns or themes mean in the context of the research question and the case. This interpretation should be grounded in the data, but it can also involve drawing on theoretical concepts or prior research.

Verification of the data

The last step in the analysis is verification. This involves checking the accuracy and consistency of the analysis process and confirming that the findings are supported by the data. This can involve re-checking the original data, checking the consistency of codes, or seeking feedback from research participants or peers.

Like any research method , case study research has its strengths and limitations. Researchers must be aware of these, as they can influence the design, conduct, and interpretation of the study.

Understanding the strengths and limitations of case study research can also guide researchers in deciding whether this approach is suitable for their research question . This section outlines some of the key strengths and limitations of case study research.

Benefits include the following:

• Rich, detailed data: One of the main strengths of case study research is that it can generate rich, detailed data about the case. This can provide a deep understanding of the case and its context, which can be valuable in exploring complex phenomena.
• Flexibility: Case study research is flexible in terms of design , data collection , and analysis . A sufficient degree of flexibility allows the researcher to adapt the study according to the case and the emerging findings.
• Real-world context: Case study research involves studying the case in its real-world context, which can provide valuable insights into the interplay between the case and its context.
• Multiple sources of evidence: Case study research often involves collecting data from multiple sources , which can enhance the robustness and validity of the findings.

On the other hand, researchers should consider the following limitations:

• Generalizability: A common criticism of case study research is that its findings might not be generalizable to other cases due to the specificity and uniqueness of each case.
• Time and resource intensive: Case study research can be time and resource intensive due to the depth of the investigation and the amount of collected data.
• Complexity of analysis: The rich, detailed data generated in case study research can make analyzing the data challenging.
• Subjectivity: Given the nature of case study research, there may be a higher degree of subjectivity in interpreting the data , so researchers need to reflect on this and transparently convey to audiences how the research was conducted.

Being aware of these strengths and limitations can help researchers design and conduct case study research effectively and interpret and report the findings appropriately.

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Writing a Case Study

What is a case study?

A Case study is: 

• An in-depth research design that primarily uses a qualitative methodology but sometimes​​ includes quantitative methodology.
• Used to examine an identifiable problem confirmed through research.
• Used to investigate an individual, group of people, organization, or event.
• Used to mostly answer "how" and "why" questions.

What are the different types of case studies?

Note: These are the primary case studies. As you continue to research and learn

about case studies you will begin to find a robust list of different types. 

Who are your case study participants?

What is triangulation ? 

Validity and credibility are an essential part of the case study. Therefore, the researcher should include triangulation to ensure trustworthiness while accurately reflecting what the researcher seeks to investigate.

How to write a Case Study?

When developing a case study, there are different ways you could present the information, but remember to include the five parts for your case study.

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Case Study Research Method in Psychology

Saul McLeod, PhD

Editor-in-Chief for Simply Psychology

BSc (Hons) Psychology, MRes, PhD, University of Manchester

Saul McLeod, PhD., is a qualified psychology teacher with over 18 years of experience in further and higher education. He has been published in peer-reviewed journals, including the Journal of Clinical Psychology.

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Olivia Guy-Evans, MSc

Associate Editor for Simply Psychology

BSc (Hons) Psychology, MSc Psychology of Education

Olivia Guy-Evans is a writer and associate editor for Simply Psychology. She has previously worked in healthcare and educational sectors.

On This Page:

Case studies are in-depth investigations of a person, group, event, or community. Typically, data is gathered from various sources using several methods (e.g., observations & interviews).

The case study research method originated in clinical medicine (the case history, i.e., the patient’s personal history). In psychology, case studies are often confined to the study of a particular individual.

The information is mainly biographical and relates to events in the individual’s past (i.e., retrospective), as well as to significant events that are currently occurring in his or her everyday life.

The case study is not a research method, but researchers select methods of data collection and analysis that will generate material suitable for case studies.

Freud (1909a, 1909b) conducted very detailed investigations into the private lives of his patients in an attempt to both understand and help them overcome their illnesses.

This makes it clear that the case study is a method that should only be used by a psychologist, therapist, or psychiatrist, i.e., someone with a professional qualification.

There is an ethical issue of competence. Only someone qualified to diagnose and treat a person can conduct a formal case study relating to atypical (i.e., abnormal) behavior or atypical development.

 Famous Case Studies

• Anna O – One of the most famous case studies, documenting psychoanalyst Josef Breuer’s treatment of “Anna O” (real name Bertha Pappenheim) for hysteria in the late 1800s using early psychoanalytic theory.
• Little Hans – A child psychoanalysis case study published by Sigmund Freud in 1909 analyzing his five-year-old patient Herbert Graf’s house phobia as related to the Oedipus complex.
• Bruce/Brenda – Gender identity case of the boy (Bruce) whose botched circumcision led psychologist John Money to advise gender reassignment and raise him as a girl (Brenda) in the 1960s.
• Genie Wiley – Linguistics/psychological development case of the victim of extreme isolation abuse who was studied in 1970s California for effects of early language deprivation on acquiring speech later in life.
• Phineas Gage – One of the most famous neuropsychology case studies analyzes personality changes in railroad worker Phineas Gage after an 1848 brain injury involving a tamping iron piercing his skull.

Clinical Case Studies

• Studying the effectiveness of psychotherapy approaches with an individual patient
• Assessing and treating mental illnesses like depression, anxiety disorders, PTSD
• Neuropsychological cases investigating brain injuries or disorders

Child Psychology Case Studies

• Studying psychological development from birth through adolescence
• Cases of learning disabilities, autism spectrum disorders, ADHD
• Effects of trauma, abuse, deprivation on development

Types of Case Studies

• Explanatory case studies : Used to explore causation in order to find underlying principles. Helpful for doing qualitative analysis to explain presumed causal links.
• Exploratory case studies : Used to explore situations where an intervention being evaluated has no clear set of outcomes. It helps define questions and hypotheses for future research.
• Descriptive case studies : Describe an intervention or phenomenon and the real-life context in which it occurred. It is helpful for illustrating certain topics within an evaluation.
• Multiple-case studies : Used to explore differences between cases and replicate findings across cases. Helpful for comparing and contrasting specific cases.
• Intrinsic : Used to gain a better understanding of a particular case. Helpful for capturing the complexity of a single case.
• Collective : Used to explore a general phenomenon using multiple case studies. Helpful for jointly studying a group of cases in order to inquire into the phenomenon.

Where Do You Find Data for a Case Study?

There are several places to find data for a case study. The key is to gather data from multiple sources to get a complete picture of the case and corroborate facts or findings through triangulation of evidence. Most of this information is likely qualitative (i.e., verbal description rather than measurement), but the psychologist might also collect numerical data.

1. Primary sources

• Interviews – Interviewing key people related to the case to get their perspectives and insights. The interview is an extremely effective procedure for obtaining information about an individual, and it may be used to collect comments from the person’s friends, parents, employer, workmates, and others who have a good knowledge of the person, as well as to obtain facts from the person him or herself.
• Observations – Observing behaviors, interactions, processes, etc., related to the case as they unfold in real-time.
• Documents & Records – Reviewing private documents, diaries, public records, correspondence, meeting minutes, etc., relevant to the case.

2. Secondary sources

• News/Media – News coverage of events related to the case study.
• Academic articles – Journal articles, dissertations etc. that discuss the case.
• Government reports – Official data and records related to the case context.
• Books/films – Books, documentaries or films discussing the case.

3. Archival records

Searching historical archives, museum collections and databases to find relevant documents, visual/audio records related to the case history and context.

Public archives like newspapers, organizational records, photographic collections could all include potentially relevant pieces of information to shed light on attitudes, cultural perspectives, common practices and historical contexts related to psychology.

4. Organizational records

Organizational records offer the advantage of often having large datasets collected over time that can reveal or confirm psychological insights.

Of course, privacy and ethical concerns regarding confidential data must be navigated carefully.

However, with proper protocols, organizational records can provide invaluable context and empirical depth to qualitative case studies exploring the intersection of psychology and organizations.

• Organizational/industrial psychology research : Organizational records like employee surveys, turnover/retention data, policies, incident reports etc. may provide insight into topics like job satisfaction, workplace culture and dynamics, leadership issues, employee behaviors etc.
• Clinical psychology : Therapists/hospitals may grant access to anonymized medical records to study aspects like assessments, diagnoses, treatment plans etc. This could shed light on clinical practices.
• School psychology : Studies could utilize anonymized student records like test scores, grades, disciplinary issues, and counseling referrals to study child development, learning barriers, effectiveness of support programs, and more.

How do I Write a Case Study in Psychology?

Follow specified case study guidelines provided by a journal or your psychology tutor. General components of clinical case studies include: background, symptoms, assessments, diagnosis, treatment, and outcomes. Interpreting the information means the researcher decides what to include or leave out. A good case study should always clarify which information is the factual description and which is an inference or the researcher’s opinion.

1. Introduction

• Provide background on the case context and why it is of interest, presenting background information like demographics, relevant history, and presenting problem.
• Compare briefly to similar published cases if applicable. Clearly state the focus/importance of the case.

2. Case Presentation

• Describe the presenting problem in detail, including symptoms, duration,and impact on daily life.
• Include client demographics like age and gender, information about social relationships, and mental health history.
• Describe all physical, emotional, and/or sensory symptoms reported by the client.
• Use patient quotes to describe the initial complaint verbatim. Follow with full-sentence summaries of relevant history details gathered, including key components that led to a working diagnosis.
• Summarize clinical exam results, namely orthopedic/neurological tests, imaging, lab tests, etc. Note actual results rather than subjective conclusions. Provide images if clearly reproducible/anonymized.
• Clearly state the working diagnosis or clinical impression before transitioning to management.

3. Management and Outcome

• Indicate the total duration of care and number of treatments given over what timeframe. Use specific names/descriptions for any therapies/interventions applied.
• Present the results of the intervention,including any quantitative or qualitative data collected.
• For outcomes, utilize visual analog scales for pain, medication usage logs, etc., if possible. Include patient self-reports of improvement/worsening of symptoms. Note the reason for discharge/end of care.

4. Discussion

• Analyze the case, exploring contributing factors, limitations of the study, and connections to existing research.
• Analyze the effectiveness of the intervention,considering factors like participant adherence, limitations of the study, and potential alternative explanations for the results.
• Identify any questions raised in the case analysis and relate insights to established theories and current research if applicable. Avoid definitive claims about physiological explanations.
• Offer clinical implications, and suggest future research directions.

5. Additional Items

• Thank specific assistants for writing support only. No patient acknowledgments.
• References should directly support any key claims or quotes included.
• Use tables/figures/images only if substantially informative. Include permissions and legends/explanatory notes.
• Provides detailed (rich qualitative) information.
• Provides insight for further research.
• Permitting investigation of otherwise impractical (or unethical) situations.

Case studies allow a researcher to investigate a topic in far more detail than might be possible if they were trying to deal with a large number of research participants (nomothetic approach) with the aim of ‘averaging’.

Because of their in-depth, multi-sided approach, case studies often shed light on aspects of human thinking and behavior that would be unethical or impractical to study in other ways.

Research that only looks into the measurable aspects of human behavior is not likely to give us insights into the subjective dimension of experience, which is important to psychoanalytic and humanistic psychologists.

Case studies are often used in exploratory research. They can help us generate new ideas (that might be tested by other methods). They are an important way of illustrating theories and can help show how different aspects of a person’s life are related to each other.

The method is, therefore, important for psychologists who adopt a holistic point of view (i.e., humanistic psychologists ).

Limitations

• Lacking scientific rigor and providing little basis for generalization of results to the wider population.
• Researchers’ own subjective feelings may influence the case study (researcher bias).
• Difficult to replicate.
• Time-consuming and expensive.
• The volume of data, together with the time restrictions in place, impacted the depth of analysis that was possible within the available resources.

Because a case study deals with only one person/event/group, we can never be sure if the case study investigated is representative of the wider body of “similar” instances. This means the conclusions drawn from a particular case may not be transferable to other settings.

Because case studies are based on the analysis of qualitative (i.e., descriptive) data , a lot depends on the psychologist’s interpretation of the information she has acquired.

This means that there is a lot of scope for Anna O , and it could be that the subjective opinions of the psychologist intrude in the assessment of what the data means.

For example, Freud has been criticized for producing case studies in which the information was sometimes distorted to fit particular behavioral theories (e.g., Little Hans ).

This is also true of Money’s interpretation of the Bruce/Brenda case study (Diamond, 1997) when he ignored evidence that went against his theory.

Breuer, J., & Freud, S. (1895).  Studies on hysteria . Standard Edition 2: London.

Curtiss, S. (1981). Genie: The case of a modern wild child .

Diamond, M., & Sigmundson, K. (1997). Sex Reassignment at Birth: Long-term Review and Clinical Implications. Archives of Pediatrics & Adolescent Medicine , 151(3), 298-304

Freud, S. (1909a). Analysis of a phobia of a five year old boy. In The Pelican Freud Library (1977), Vol 8, Case Histories 1, pages 169-306

Freud, S. (1909b). Bemerkungen über einen Fall von Zwangsneurose (Der “Rattenmann”). Jb. psychoanal. psychopathol. Forsch ., I, p. 357-421; GW, VII, p. 379-463; Notes upon a case of obsessional neurosis, SE , 10: 151-318.

Harlow J. M. (1848). Passage of an iron rod through the head.  Boston Medical and Surgical Journal, 39 , 389–393.

Harlow, J. M. (1868).  Recovery from the Passage of an Iron Bar through the Head .  Publications of the Massachusetts Medical Society. 2  (3), 327-347.

Money, J., & Ehrhardt, A. A. (1972).  Man & Woman, Boy & Girl : The Differentiation and Dimorphism of Gender Identity from Conception to Maturity. Baltimore, Maryland: Johns Hopkins University Press.

Money, J., & Tucker, P. (1975). Sexual signatures: On being a man or a woman.

Further Information

• Case Study Approach
• Case Study Method
• Enhancing the Quality of Case Studies in Health Services Research
• “We do things together” A case study of “couplehood” in dementia
• Using mixed methods for evaluating an integrative approach to cancer care: a case study

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• Case Study | Definition, Examples & Methods

Case Study | Definition, Examples & Methods

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

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

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

Table of contents

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

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

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

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

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.

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• DOI: 10.1177/1525822X0101300402
• Corpus ID: 41919755

A Case in Case Study Methodology

• Christine B. Meyer
• Published 1 November 2001
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What the Case Study Method Really Teaches

• Nitin Nohria

Seven meta-skills that stick even if the cases fade from memory.

It’s been 100 years since Harvard Business School began using the case study method. Beyond teaching specific subject matter, the case study method excels in instilling meta-skills in students. This article explains the importance of seven such skills: preparation, discernment, bias recognition, judgement, collaboration, curiosity, and self-confidence.

During my decade as dean of Harvard Business School, I spent hundreds of hours talking with our alumni. To enliven these conversations, I relied on a favorite question: “What was the most important thing you learned from your time in our MBA program?”

• Nitin Nohria is the George F. Baker Jr. and Distinguished Service University Professor. He served as the 10th dean of Harvard Business School, from 2010 to 2020.

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Methodologic and Data-Analysis Triangulation in Case Studies: A Scoping Review

Margarithe charlotte schlunegger.

1 Department of Health Professions, Applied Research & Development in Nursing, Bern University of Applied Sciences, Bern, Switzerland

2 Faculty of Health, School of Nursing Science, Witten/Herdecke University, Witten, Germany

Maya Zumstein-Shaha

Rebecca palm.

3 Department of Health Care Research, Carl von Ossietzky University Oldenburg, Oldenburg, Germany

Associated Data

Supplemental material, sj-docx-1-wjn-10.1177_01939459241263011 for Methodologic and Data-Analysis Triangulation in Case Studies: A Scoping Review by Margarithe Charlotte Schlunegger, Maya Zumstein-Shaha and Rebecca Palm in Western Journal of Nursing Research

We sought to explore the processes of methodologic and data-analysis triangulation in case studies using the example of research on nurse practitioners in primary health care.

Design and methods:

We conducted a scoping review within Arksey and O’Malley’s methodological framework, considering studies that defined a case study design and used 2 or more data sources, published in English or German before August 2023.

Data sources:

The databases searched were MEDLINE and CINAHL, supplemented with hand searching of relevant nursing journals. We also examined the reference list of all the included studies.

In total, 63 reports were assessed for eligibility. Ultimately, we included 8 articles. Five studies described within-method triangulation, whereas 3 provided information on between/across-method triangulation. No study reported within-method triangulation of 2 or more quantitative data-collection procedures. The data-collection procedures were interviews, observation, documentation/documents, service records, and questionnaires/assessments. The data-analysis triangulation involved various qualitative and quantitative methods of analysis. Details about comparing or contrasting results from different qualitative and mixed-methods data were lacking.

Conclusions:

Various processes for methodologic and data-analysis triangulation are described in this scoping review but lack detail, thus hampering standardization in case study research, potentially affecting research traceability. Triangulation is complicated by terminological confusion. To advance case study research in nursing, authors should reflect critically on the processes of triangulation and employ existing tools, like a protocol or mixed-methods matrix, for transparent reporting. The only existing reporting guideline should be complemented with directions on methodologic and data-analysis triangulation.

Case study research is defined as “an empirical method that investigates a contemporary phenomenon (the ‘case’) in depth and within its real-world context, especially when the boundaries between phenomenon and context may not be clearly evident. A case study relies on multiple sources of evidence, with data needing to converge in a triangulating fashion.” 1 (p15) This design is described as a stand-alone research approach equivalent to grounded theory and can entail single and multiple cases. 1 , 2 However, case study research should not be confused with single clinical case reports. “Case reports are familiar ways of sharing events of intervening with single patients with previously unreported features.” 3 (p107) As a methodology, case study research encompasses substantially more complexity than a typical clinical case report. 1 , 3

A particular characteristic of case study research is the use of various data sources, such as quantitative data originating from questionnaires as well as qualitative data emerging from interviews, observations, or documents. Therefore, a case study always draws on multiple sources of evidence, and the data must converge in a triangulating manner. 1 When using multiple data sources, a case or cases can be examined more convincingly and accurately, compensating for the weaknesses of the respective data sources. 1 Another characteristic is the interaction of various perspectives. This involves comparing or contrasting perspectives of people with different points of view, eg, patients, staff, or leaders. 4 Through triangulation, case studies contribute to the completeness of the research on complex topics, such as role implementation in clinical practice. 1 , 5 Triangulation involves a combination of researchers from various disciplines, of theories, of methods, and/or of data sources. By creating connections between these sources (ie, investigator, theories, methods, data sources, and/or data analysis), a new understanding of the phenomenon under study can be obtained. 6 , 7

This scoping review focuses on methodologic and data-analysis triangulation because concrete procedures are missing, eg, in reporting guidelines. Methodologic triangulation has been called methods, mixed methods, or multimethods. 6 It can encompass within-method triangulation and between/across-method triangulation. 7 “Researchers using within-method triangulation use at least 2 data-collection procedures from the same design approach.” 6 (p254) Within-method triangulation is either qualitative or quantitative but not both. Therefore, within-method triangulation can also be considered data source triangulation. 8 In contrast, “researchers using between/across-method triangulation employ both qualitative and quantitative data-collection methods in the same study.” 6 (p254) Hence, methodologic approaches are combined as well as various data sources. For this scoping review, the term “methodologic triangulation” is maintained to denote between/across-method triangulation. “Data-analysis triangulation is the combination of 2 or more methods of analyzing data.” 6 (p254)

Although much has been published on case studies, there is little consensus on the quality of the various data sources, the most appropriate methods, or the procedures for conducting methodologic and data-analysis triangulation. 5 According to the EQUATOR (Enhancing the QUAlity and Transparency Of health Research) clearinghouse for reporting guidelines, one standard exists for organizational case studies. 9 Organizational case studies provide insights into organizational change in health care services. 9 Rodgers et al 9 pointed out that, although high-quality studies are being funded and published, they are sometimes poorly articulated and methodologically inadequate. In the reporting checklist by Rodgers et al, 9 a description of the data collection is included, but reporting directions on methodologic and data-analysis triangulation are missing. Therefore, the purpose of this study was to examine the process of methodologic and data-analysis triangulation in case studies. Accordingly, we conducted a scoping review to elicit descriptions of and directions for triangulation methods and analysis, drawing on case studies of nurse practitioners (NPs) in primary health care as an example. Case studies are recommended to evaluate the implementation of new roles in (primary) health care, such as that of NPs. 1 , 5 Case studies on new role implementation can generate a unique and in-depth understanding of specific roles (individual), teams (smaller groups), family practices or similar institutions (organization), and social and political processes in health care systems. 1 , 10 The integration of NPs into health care systems is at different stages of progress around the world. 11 Therefore, studies are needed to evaluate this process.

The methodological framework by Arksey and O’Malley 12 guided this scoping review. We examined the current scientific literature on the use of methodologic and data-analysis triangulation in case studies on NPs in primary health care. The review process included the following stages: (1) establishing the research question; (2) identifying relevant studies; (3) selecting the studies for inclusion; (4) charting the data; (5) collating, summarizing, and reporting the results; and (6) consulting experts in the field. 12 Stage 6 was not performed due to a lack of financial resources. The reporting of the review followed the PRISMA-ScR (Preferred Reporting Items for Systematic Reviews and Meta-Analyses extension for Scoping Review) guideline by Tricco et al 13 (guidelines for reporting systematic reviews and meta-analyses [ Supplementary Table A ]). Scoping reviews are not eligible for registration in PROSPERO.

Stage 1: Establishing the Research Question

The aim of this scoping review was to examine the process of triangulating methods and analysis in case studies on NPs in primary health care to improve the reporting. We sought to answer the following question: How have methodologic and data-analysis triangulation been conducted in case studies on NPs in primary health care? To answer the research question, we examined the following elements of the selected studies: the research question, the study design, the case definition, the selected data sources, and the methodologic and data-analysis triangulation.

Stage 2: Identifying Relevant Studies

A systematic database search was performed in the MEDLINE (via PubMed) and CINAHL (via EBSCO) databases between July and September 2020 to identify relevant articles. The following terms were used as keyword search strategies: (“Advanced Practice Nursing” OR “nurse practitioners”) AND (“primary health care” OR “Primary Care Nursing”) AND (“case study” OR “case studies”). Searches were limited to English- and German-language articles. Hand searches were conducted in the journals Nursing Inquiry , BMJ Open , and BioMed Central ( BMC ). We also screened the reference lists of the studies included. The database search was updated in August 2023. The complete search strategy for all the databases is presented in Supplementary Table B .

Stage 3: Selecting the Studies

Inclusion and exclusion criteria.

We used the inclusion and exclusion criteria reported in Table 1 . We included studies of NPs who had at least a master’s degree in nursing according to the definition of the International Council of Nurses. 14 This scoping review considered studies that were conducted in primary health care practices in rural, urban, and suburban regions. We excluded reviews and study protocols in which no data collection had occurred. Articles were included without limitations on the time period or country of origin.

Inclusion and Exclusion Criteria.

Screening process

After the search, we collated and uploaded all the identified records into EndNote v.X8 (Clarivate Analytics, Philadelphia, Pennsylvania) and removed any duplicates. Two independent reviewers (MCS and SA) screened the titles and abstracts for assessment in line with the inclusion criteria. They retrieved and assessed the full texts of the selected studies while applying the inclusion criteria. Any disagreements about the eligibility of studies were resolved by discussion or, if no consensus could be reached, by involving experienced researchers (MZ-S and RP).

Stages 4 and 5: Charting the Data and Collating, Summarizing, and Reporting the Results

The first reviewer (MCS) extracted data from the selected publications. For this purpose, an extraction tool developed by the authors was used. This tool comprised the following criteria: author(s), year of publication, country, research question, design, case definition, data sources, and methodologic and data-analysis triangulation. First, we extracted and summarized information about the case study design. Second, we narratively summarized the way in which the data and methodological triangulation were described. Finally, we summarized the information on within-case or cross-case analysis. This process was performed using Microsoft Excel. One reviewer (MCS) extracted data, whereas another reviewer (SA) cross-checked the data extraction, making suggestions for additions or edits. Any disagreements between the reviewers were resolved through discussion.

A total of 149 records were identified in 2 databases. We removed 20 duplicates and screened 129 reports by title and abstract. A total of 46 reports were assessed for eligibility. Through hand searches, we identified 117 additional records. Of these, we excluded 98 reports after title and abstract screening. A total of 17 reports were assessed for eligibility. From the 2 databases and the hand search, 63 reports were assessed for eligibility. Ultimately, we included 8 articles for data extraction. No further articles were included after the reference list screening of the included studies. A PRISMA flow diagram of the study selection and inclusion process is presented in Figure 1 . As shown in Tables 2 and ​ and3, 3 , the articles included in this scoping review were published between 2010 and 2022 in Canada (n = 3), the United States (n = 2), Australia (n = 2), and Scotland (n = 1).

PRISMA flow diagram.

Characteristics of Articles Included.

Overview of Within-Method, Between/Across-Method, and Data-Analysis Triangulation.

Research Question, Case Definition, and Case Study Design

The following sections describe the research question, case definition, and case study design. Case studies are most appropriate when asking “how” or “why” questions. 1 According to Yin, 1 how and why questions are explanatory and lead to the use of case studies, histories, and experiments as the preferred research methods. In 1 study from Canada, eg, the following research question was presented: “How and why did stakeholders participate in the system change process that led to the introduction of the first nurse practitioner-led Clinic in Ontario?” (p7) 19 Once the research question has been formulated, the case should be defined and, subsequently, the case study design chosen. 1 In typical case studies with mixed methods, the 2 types of data are gathered concurrently in a convergent design and the results merged to examine a case and/or compare multiple cases. 10

Research question

“How” or “why” questions were found in 4 studies. 16 , 17 , 19 , 22 Two studies additionally asked “what” questions. Three studies described an exploratory approach, and 1 study presented an explanatory approach. Of these 4 studies, 3 studies chose a qualitative approach 17 , 19 , 22 and 1 opted for mixed methods with a convergent design. 16

In the remaining studies, either the research questions were not clearly stated or no “how” or “why” questions were formulated. For example, “what” questions were found in 1 study. 21 No information was provided on exploratory, descriptive, and explanatory approaches. Schadewaldt et al 21 chose mixed methods with a convergent design.

Case definition and case study design

A total of 5 studies defined the case as an organizational unit. 17 , 18 - 20 , 22 Of the 8 articles, 4 reported multiple-case studies. 16 , 17 , 22 , 23 Another 2 publications involved single-case studies. 19 , 20 Moreover, 2 publications did not state the case study design explicitly.

Within-Method Triangulation

This section describes within-method triangulation, which involves employing at least 2 data-collection procedures within the same design approach. 6 , 7 This can also be called data source triangulation. 8 Next, we present the single data-collection procedures in detail. In 5 studies, information on within-method triangulation was found. 15 , 17 - 19 , 22 Studies describing a quantitative approach and the triangulation of 2 or more quantitative data-collection procedures could not be included in this scoping review.

Qualitative approach

Five studies used qualitative data-collection procedures. Two studies combined face-to-face interviews and documents. 15 , 19 One study mixed in-depth interviews with observations, 18 and 1 study combined face-to-face interviews and documentation. 22 One study contained face-to-face interviews, observations, and documentation. 17 The combination of different qualitative data-collection procedures was used to present the case context in an authentic and complex way, to elicit the perspectives of the participants, and to obtain a holistic description and explanation of the cases under study.

All 5 studies used qualitative interviews as the primary data-collection procedure. 15 , 17 - 19 , 22 Face-to-face, in-depth, and semi-structured interviews were conducted. The topics covered in the interviews included processes in the introduction of new care services and experiences of barriers and facilitators to collaborative work in general practices. Two studies did not specify the type of interviews conducted and did not report sample questions. 15 , 18

Observations

In 2 studies, qualitative observations were carried out. 17 , 18 During the observations, the physical design of the clinical patients’ rooms and office spaces was examined. 17 Hungerford et al 18 did not explain what information was collected during the observations. In both studies, the type of observation was not specified. Observations were generally recorded as field notes.

Public documents

In 3 studies, various qualitative public documents were studied. 15 , 19 , 22 These documents included role description, education curriculum, governance frameworks, websites, and newspapers with information about the implementation of the role and general practice. Only 1 study failed to specify the type of document and the collected data. 15

Electronic health records

In 1 study, qualitative documentation was investigated. 17 This included a review of dashboards (eg, provider productivity reports or provider quality dashboards in the electronic health record) and quality performance reports (eg, practice-wide or co-management team-wide performance reports).

Between/Across-Method Triangulation

This section describes the between/across methods, which involve employing both qualitative and quantitative data-collection procedures in the same study. 6 , 7 This procedure can also be denoted “methodologic triangulation.” 8 Subsequently, we present the individual data-collection procedures. In 3 studies, information on between/across triangulation was found. 16 , 20 , 21

Mixed methods

Three studies used qualitative and quantitative data-collection procedures. One study combined face-to-face interviews, documentation, and self-assessments. 16 One study employed semi-structured interviews, direct observation, documents, and service records, 20 and another study combined face-to-face interviews, non-participant observation, documents, and questionnaires. 23

All 3 studies used qualitative interviews as the primary data-collection procedure. 16 , 20 , 23 Face-to-face and semi-structured interviews were conducted. In the interviews, data were collected on the introduction of new care services and experiences of barriers to and facilitators of collaborative work in general practices.

Observation

In 2 studies, direct and non-participant qualitative observations were conducted. 20 , 23 During the observations, the interaction between health professionals or the organization and the clinical context was observed. Observations were generally recorded as field notes.

In 2 studies, various qualitative public documents were examined. 20 , 23 These documents included role description, newspapers, websites, and practice documents (eg, flyers). In the documents, information on the role implementation and role description of NPs was collected.

Individual journals

In 1 study, qualitative individual journals were studied. 16 These included reflective journals from NPs, who performed the role in primary health care.

Service records

Only 1 study involved quantitative service records. 20 These service records were obtained from the primary care practices and the respective health authorities. They were collected before and after the implementation of an NP role to identify changes in patients’ access to health care, the volume of patients served, and patients’ use of acute care services.

Questionnaires/Assessment

In 2 studies, quantitative questionnaires were used to gather information about the teams’ satisfaction with collaboration. 16 , 21 In 1 study, 3 validated scales were used. The scales measured experience, satisfaction, and belief in the benefits of collaboration. 21 Psychometric performance indicators of these scales were provided. However, the time points of data collection were not specified; similarly, whether the questionnaires were completed online or by hand was not mentioned. A competency self-assessment tool was used in another study. 16 The assessment comprised 70 items and included topics such as health promotion, protection, disease prevention and treatment, the NP-patient relationship, the teaching-coaching function, the professional role, managing and negotiating health care delivery systems, monitoring and ensuring the quality of health care practice, and cultural competence. Psychometric performance indicators were provided. The assessment was completed online with 2 measurement time points (pre self-assessment and post self-assessment).

Data-Analysis Triangulation

This section describes data-analysis triangulation, which involves the combination of 2 or more methods of analyzing data. 6 Subsequently, we present within-case analysis and cross-case analysis.

Mixed-methods analysis

Three studies combined qualitative and quantitative methods of analysis. 16 , 20 , 21 Two studies involved deductive and inductive qualitative analysis, and qualitative data were analyzed thematically. 20 , 21 One used deductive qualitative analysis. 16 The method of analysis was not specified in the studies. Quantitative data were analyzed using descriptive statistics in 3 studies. 16 , 20 , 23 The descriptive statistics comprised the calculation of the mean, median, and frequencies.

Qualitative methods of analysis

Two studies combined deductive and inductive qualitative analysis, 19 , 22 and 2 studies only used deductive qualitative analysis. 15 , 18 Qualitative data were analyzed thematically in 1 study, 22 and data were treated with content analysis in the other. 19 The method of analysis was not specified in the 2 studies.

Within-case analysis

In 7 studies, a within-case analysis was performed. 15 - 20 , 22 Six studies used qualitative data for the within-case analysis, and 1 study employed qualitative and quantitative data. Data were analyzed separately, consecutively, or in parallel. The themes generated from qualitative data were compared and then summarized. The individual cases were presented mostly as a narrative description. Quantitative data were integrated into the qualitative description with tables and graphs. Qualitative and quantitative data were also presented as a narrative description.

Cross-case analyses

Of the multiple-case studies, 5 carried out cross-case analyses. 15 - 17 , 20 , 22 Three studies described the cross-case analysis using qualitative data. Two studies reported a combination of qualitative and quantitative data for the cross-case analysis. In each multiple-case study, the individual cases were contrasted to identify the differences and similarities between the cases. One study did not specify whether a within-case or a cross-case analysis was conducted. 23

Confirmation or contradiction of data

This section describes confirmation or contradiction through qualitative and quantitative data. 1 , 4 Qualitative and quantitative data were reported separately, with little connection between them. As a result, the conclusions on neither the comparisons nor the contradictions could be clearly determined.

Confirmation or contradiction among qualitative data

In 3 studies, the consistency of the results of different types of qualitative data was highlighted. 16 , 19 , 21 In particular, documentation and interviews or interviews and observations were contrasted:

• Confirmation between interviews and documentation: The data from these sources corroborated the existence of a common vision for an NP-led clinic. 19
• Confirmation among interviews and observation: NPs experienced pressure to find and maintain their position within the existing system. Nurse practitioners and general practitioners performed complete episodes of care, each without collaborative interaction. 21
• Contradiction among interviews and documentation: For example, interviewees mentioned that differentiating the scope of practice between NPs and physicians is difficult as there are too many areas of overlap. However, a clear description of the scope of practice for the 2 roles was provided. 21

Confirmation through a combination of qualitative and quantitative data

Both types of data showed that NPs and general practitioners wanted to have more time in common to discuss patient cases and engage in personal exchanges. 21 In addition, the qualitative and quantitative data confirmed the individual progression of NPs from less competent to more competent. 16 One study pointed out that qualitative and quantitative data obtained similar results for the cases. 20 For example, integrating NPs improved patient access by increasing appointment availability.

Contradiction through a combination of qualitative and quantitative data

Although questionnaire results indicated that NPs and general practitioners experienced high levels of collaboration and satisfaction with the collaborative relationship, the qualitative results drew a more ambivalent picture of NPs’ and general practitioners’ experiences with collaboration. 21

Research Question and Design

The studies included in this scoping review evidenced various research questions. The recommended formats (ie, how or why questions) were not applied consistently. Therefore, no case study design should be applied because the research question is the major guide for determining the research design. 2 Furthermore, case definitions and designs were applied variably. The lack of standardization is reflected in differences in the reporting of these case studies. Generally, case study research is viewed as allowing much more freedom and flexibility. 5 , 24 However, this flexibility and the lack of uniform specifications lead to confusion.

Methodologic Triangulation

Methodologic triangulation, as described in the literature, can be somewhat confusing as it can refer to either data-collection methods or research designs. 6 , 8 For example, methodologic triangulation can allude to qualitative and quantitative methods, indicating a paradigmatic connection. Methodologic triangulation can also point to qualitative and quantitative data-collection methods, analysis, and interpretation without specific philosophical stances. 6 , 8 Regarding “data-collection methods with no philosophical stances,” we would recommend using the wording “data source triangulation” instead. Thus, the demarcation between the method and the data-collection procedures will be clearer.

Within-Method and Between/Across-Method Triangulation

Yin 1 advocated the use of multiple sources of evidence so that a case or cases can be investigated more comprehensively and accurately. Most studies included multiple data-collection procedures. Five studies employed a variety of qualitative data-collection procedures, and 3 studies used qualitative and quantitative data-collection procedures (mixed methods). In contrast, no study contained 2 or more quantitative data-collection procedures. In particular, quantitative data-collection procedures—such as validated, reliable questionnaires, scales, or assessments—were not used exhaustively. The prerequisites for using multiple data-collection procedures are availability, the knowledge and skill of the researcher, and sufficient financial funds. 1 To meet these prerequisites, research teams consisting of members with different levels of training and experience are necessary. Multidisciplinary research teams need to be aware of the strengths and weaknesses of different data sources and collection procedures. 1

Qualitative methods of analysis and results

When using multiple data sources and analysis methods, it is necessary to present the results in a coherent manner. Although the importance of multiple data sources and analysis has been emphasized, 1 , 5 the description of triangulation has tended to be brief. Thus, traceability of the research process is not always ensured. The sparse description of the data-analysis triangulation procedure may be due to the limited number of words in publications or the complexity involved in merging the different data sources.

Only a few concrete recommendations regarding the operationalization of the data-analysis triangulation with the qualitative data process were found. 25 A total of 3 approaches have been proposed 25 : (1) the intuitive approach, in which researchers intuitively connect information from different data sources; (2) the procedural approach, in which each comparative or contrasting step in triangulation is documented to ensure transparency and replicability; and (3) the intersubjective approach, which necessitates a group of researchers agreeing on the steps in the triangulation process. For each case study, one of these 3 approaches needs to be selected, carefully carried out, and documented. Thus, in-depth examination of the data can take place. Farmer et al 25 concluded that most researchers take the intuitive approach; therefore, triangulation is not clearly articulated. This trend is also evident in our scoping review.

Mixed-methods analysis and results

Few studies in this scoping review used a combination of qualitative and quantitative analysis. However, creating a comprehensive stand-alone picture of a case from both qualitative and quantitative methods is challenging. Findings derived from different data types may not automatically coalesce into a coherent whole. 4 O’Cathain et al 26 described 3 techniques for combining the results of qualitative and quantitative methods: (1) developing a triangulation protocol; (2) following a thread by selecting a theme from 1 component and following it across the other components; and (3) developing a mixed-methods matrix.

The most detailed description of the conducting of triangulation is the triangulation protocol. The triangulation protocol takes place at the interpretation stage of the research process. 26 This protocol was developed for multiple qualitative data but can also be applied to a combination of qualitative and quantitative data. 25 , 26 It is possible to determine agreement, partial agreement, “silence,” or dissonance between the results of qualitative and quantitative data. The protocol is intended to bring together the various themes from the qualitative and quantitative results and identify overarching meta-themes. 25 , 26

The “following a thread” technique is used in the analysis stage of the research process. To begin, each data source is analyzed to identify the most important themes that need further investigation. Subsequently, the research team selects 1 theme from 1 data source and follows it up in the other data source, thereby creating a thread. The individual steps of this technique are not specified. 26 , 27

A mixed-methods matrix is used at the end of the analysis. 26 All the data collected on a defined case are examined together in 1 large matrix, paying attention to cases rather than variables or themes. In a mixed-methods matrix (eg, a table), the rows represent the cases for which both qualitative and quantitative data exist. The columns show the findings for each case. This technique allows the research team to look for congruency, surprises, and paradoxes among the findings as well as patterns across multiple cases. In our review, we identified only one of these 3 approaches in the study by Roots and MacDonald. 20 These authors mentioned that a causal network analysis was performed using a matrix. However, no further details were given, and reference was made to a later publication. We could not find this publication.

Case Studies in Nursing Research and Recommendations

Because it focused on the implementation of NPs in primary health care, the setting of this scoping review was narrow. However, triangulation is essential for research in this area. This type of research was found to provide a good basis for understanding methodologic and data-analysis triangulation. Despite the lack of traceability in the description of the data and methodological triangulation, we believe that case studies are an appropriate design for exploring new nursing roles in existing health care systems. This is evidenced by the fact that case study research is widely used in many social science disciplines as well as in professional practice. 1 To strengthen this research method and increase the traceability in the research process, we recommend using the reporting guideline and reporting checklist by Rodgers et al. 9 This reporting checklist needs to be complemented with methodologic and data-analysis triangulation. A procedural approach needs to be followed in which each comparative step of the triangulation is documented. 25 A triangulation protocol or a mixed-methods matrix can be used for this purpose. 26 If there is a word limit in a publication, the triangulation protocol or mixed-methods matrix needs to be identified. A schematic representation of methodologic and data-analysis triangulation in case studies can be found in Figure 2 .

Schematic representation of methodologic and data-analysis triangulation in case studies (own work).

Limitations

This study suffered from several limitations that must be acknowledged. Given the nature of scoping reviews, we did not analyze the evidence reported in the studies. However, 2 reviewers independently reviewed all the full-text reports with respect to the inclusion criteria. The focus on the primary care setting with NPs (master’s degree) was very narrow, and only a few studies qualified. Thus, possible important methodological aspects that would have contributed to answering the questions were omitted. Studies describing the triangulation of 2 or more quantitative data-collection procedures could not be included in this scoping review due to the inclusion and exclusion criteria.

Conclusions

Given the various processes described for methodologic and data-analysis triangulation, we can conclude that triangulation in case studies is poorly standardized. Consequently, the traceability of the research process is not always given. Triangulation is complicated by the confusion of terminology. To advance case study research in nursing, we encourage authors to reflect critically on methodologic and data-analysis triangulation and use existing tools, such as the triangulation protocol or mixed-methods matrix and the reporting guideline checklist by Rodgers et al, 9 to ensure more transparent reporting.

Supplemental Material

Acknowledgments.

The authors thank Simona Aeschlimann for her support during the screening process.

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding: The author(s) received no financial support for the research, authorship, and/or publication of this article.

Supplemental Material: Supplemental material for this article is available online.

What is the Case Study Method?

Simply put, the case method is a discussion of real-life situations that business executives have faced.

On average, you'll attend three to four different classes a day, for a total of about six hours of class time (schedules vary). To prepare, you'll work through problems with your peers.

How the Case Method Creates Value

Often, executives are surprised to discover that the objective of the case study is not to reach consensus, but to understand how different people use the same information to arrive at diverse conclusions. When you begin to understand the context, you can appreciate the reasons why those decisions were made. You can prepare for case discussions in several ways.

Case Discussion Preparation Details

In self-reflection.

The time you spend here is deeply introspective. You're not only working with case materials and assignments, but also taking on the role of the case protagonist—the person who's supposed to make those tough decisions. How would you react in those situations? We put people in a variety of contexts, and they start by addressing that specific problem.

In a small group setting

The discussion group is a critical component of the HBS experience. You're working in close quarters with a group of seven or eight very accomplished peers in diverse functions, industries, and geographies. Because they bring unique experience to play you begin to see that there are many different ways to wrestle with a problem—and that’s very enriching.

In the classroom

The faculty guides you in examining and resolving the issues—but the beauty here is that they don't provide you with the answers. You're interacting in the classroom with other executives—debating the issue, presenting new viewpoints, countering positions, and building on one another's ideas. And that leads to the next stage of learning.

Beyond the classroom

Once you leave the classroom, the learning continues and amplifies as you get to know people in different settings—over meals, at social gatherings, in the fitness center, or as you are walking to class. You begin to distill the takeaways that you want to bring back and apply in your organization to ensure that the decisions you make will create more value for your firm.

How Cases Unfold In the Classroom

Pioneered by HBS faculty, the case method puts you in the role of the chief decision maker as you explore the challenges facing leading companies across the globe. Learning to think fast on your feet with limited information sharpens your analytical skills and empowers you to make critical decisions in real time.

To get the most out of each case, it's important to read and reflect, and then meet with your discussion group to share your insights. You and your peers will explore the underlying issues, compare alternatives, and suggest various ways of resolving the problem.

How to Prepare for Case Discussions

There's more than one way to prepare for a case discussion, but these general guidelines can help you develop a method that works for you.

Preparation Guidelines

Read the professor's assignment or discussion questions.

The assignment and discussion questions help you focus on the key aspects of the case. Ask yourself: What are the most important issues being raised?

Read the first few paragraphs and then skim the case

Each case begins with a text description followed by exhibits. Ask yourself: What is the case generally about, and what information do I need to analyze?

Reread the case, underline text, and make margin notes

Put yourself in the shoes of the case protagonist, and own that person's problems. Ask yourself: What basic problem is this executive trying to resolve?

Note the key problems on a pad of paper and go through the case again

Sort out relevant considerations and do the quantitative or qualitative analysis. Ask yourself: What recommendations should I make based on my case data analysis?

Case Study Best Practices

The key to being an active listener and participant in case discussions—and to getting the most out of the learning experience—is thorough individual preparation.

We've set aside formal time for you to discuss the case with your group. These sessions will help you to become more confident about sharing your views in the classroom discussion.

Participate

Actively express your views and challenge others. Don't be afraid to share related "war stories" that will heighten the relevance and enrich the discussion.

If the content doesn't seem to relate to your business, don't tune out. You can learn a lot about marketing insurance from a case on marketing razor blades!

Actively apply what you're learning to your own specific management situations, both past and future. This will magnify the relevance to your business.

People with diverse backgrounds, experiences, skills, and styles will take away different things. Be sure to note what resonates with you, not your peers.

Being exposed to so many different approaches to a given situation will put you in a better position to enhance your management style.

Frequently Asked Questions

What can i expect on the first day, what happens in class if nobody talks, does everyone take part in "role-playing".

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Teach programming using task-driven case studies: pedagogical approach, guidelines, and implementation.

1. Introduction

1.1. task-driven teaching, 1.2. case studies, 1.3. task-driven case studies, 2. background, 2.1. problem-based learning, 2.2. case studies in teaching, 2.3. task-driven teaching methodology, 2.4. games in teaching and automatic feedback, 3. task-driven case studies’ pedagogical framework.

• Case study , a realistic project providing an opportunity to showcase most of the learned topics.
• Tasks defined in the context of the selected case study and corresponding to the learning objectives of the course.
• Written study guides , explaining the case study, leading students through the tasks, and providing enough context and explanation.

3.1. Reasons to Use Tasks

• We want to make sure that students are active during lessons. Both the teacher and the students are reminded that practical lessons should revolve around the students working and not the teacher lecturing.
• We want the student to use best practices while working. Finer-grained tasks help us to keep the student on the right track. In learning, the process is more important than the result.
• Instead of only showing the process and the students repeating after the teacher, we use task-driven case studies to make them try the process by themselves. Then it is harder to forget about the details.

3.2. Role of Written Study Guides

• A written form of the guide allows students to work at their own speed. If there is something unclear, they can get back to it anytime.
• Students can continue working at home without any impedance. If a student is unable to come to the lesson, he misses only individual consultations with a teacher. To a large degree, the lesson can be simulated by the study guide. This proved to be very useful during COVID restrictions.
• A study guide can be shared between universities or learning facilities.

3.3. Course and Case Study Relationship

3.4. task-driven case study lifecycle, 3.5. guidelines.

• Know the learning goals.
• Select a well-known domain.
• Find an interesting topic.
• Keep the project in industrial quality.
• Show the whole process.
• Prepare for incremental implementation.
• Support individual approach.
• Implement code first.
• Divide code into goals.
• Evaluate goals’ coverage.
• Find goal dependencies.
• Do the review.
• Always tell objectives.
• Describe the current state and expected increment.
• Show context and reasoning.
• Specify tasks clearly and precisely.
• Refine tasks with comments.
• Add supplementary tasks.
• Provide further reading.
• Use suitable software support.
• Verify continuity and consistency of the guide.
• Review the guide.
• Start with a minimal version and improve it.
• Monitor progress continuously.
• Favor individual achievements.
• Examine understanding.
• Get feedback from the “battlefield”.
• Update the case study.

4. Selection of the Case Study

4.1. know the learning goals.

• Students are familiar with Java language basics.
• Students can create a project and a class in the NetBeans IDE.
• Students understand the role of interfaces in object-oriented programming.
• Students can implement existing interfaces in Java.
• Students can create their own interfaces in the Java language.
• Students are familiar with the role and types of collections in the Java language.
• Students can work with the generic ArrayList collection.
• Students can use String class methods for working with strings.

4.2. Select a Well-Known Domain

• Example: You can imagine that, for example, the problem of luggage transport at an airport is not a very good choice. Most of the students never had to (or will never have to) deal with that problem, and some of them probably never even traveled by plane. That is the reason why we picked a Minesweeper game. Thanks to the Microsoft Windows operating system, it is one of the most known games. We could barely find a student in the Java technologies course who had never played Minesweeper.

4.3. Find an Interesting Topic

• Example: That is why we chose the Minesweeper game. In some of the other courses, games are used too. For example, we used the N-Puzzle game in the .NET programming course and Alien Breed clone in the object-oriented programming course.

4.4. Keep the Project in Industrial Quality

• Example: The solution to our Minesweeper case study is comparable to the professional Minesweeper game (see Figure 3 ). Students can see that they are able to implement a program comparable to the industry.

4.5. Show the Whole Process

• Example: In our Minesweeper case study, we chose the Minesweeper game because it is small enough to be implemented by a student in the time span of the course, and yet the result is a whole game that is comparable with industrial Minesweeper.

4.6. Prepare for Incremental Implementation

• Example: In the Minesweeper case study, the first case study lesson introduces the Minesweeper game. We are designing the game core together with students using standard UML notations. During this, they are led to our source code skeleton implementing best practices from object-oriented programming. In the next lesson, students implement the game logic—the game field and all its behavior. So far, their solution is not playable. However, we do not wait anymore, and in the third lesson, they start implementing a simple console user interface that would be able to present the current state of the field. Although, after the third lesson, they cannot play the game, they can already run the game and see whether their field generation works as it should. Since that moment, they are always able to run the game and see the increment they add during each particular lesson.

4.7. Support Individual Approach

• Example: In our Minesweeper case study, we suggest that students implement some additional features that the main project does not have. An example may be implementing the support for a simultaneous click of both mouse buttons to open also adjacent tiles and not merely the one that the mouse points to. We also support their own ideas on how to make the game even more interesting.

5. Solution Implementation

5.1. implement code first.

• Example: We implemented our own Minesweeper game before giving the case study to students. Before using the case study approach in the Java technologies course, the Minesweeper game was one of the examples that we used to show the students more complex examples implemented in Java. Then we decided to prepare a case study and reworked the old solution to incorporate all the topics of the course and to reflect our best knowledge.

5.2. Divide Code into Goals

• Example: To explicitly record implementation objectives in the code of the Minesweeper case study, TODO comments marked with the task identifiers were used. Each task represented an implementation objective. We started using TODO comments because of the tool support—see the automatically generated list of TODO comments in an IDE in Figure 4 . However, current IDEs have better support for source code annotations since they are first-class citizens of the language. The following code is an excerpt showing a TODO comment marking the getColumnCount() method as a part of the task identified as “getters” in the second module (lesson) of the course.
• //TODO: Task 2 - getters
• * Returns column count of the field.
• * @return column count.
• public int getColumnCount() { ...
• @Task(module = "02", id = "getters")

Click here to enlarge figure

5.3. Evaluate Goals’ Coverage

• Example: A simple help in checking the code coverage is, for example, the Action Items window in the NetBeans IDE (previously called the Tasks window). In  Figure 4 , there is a screenshot showing the list of tasks currently present in the Minesweeper teacher’s solution. It is easier to check the goals this way since the goals’ source code can be scattered throughout the whole project.    

5.4. Find Goal Dependencies

• Example: In the Java technologies course, the lectures are aligned with case study modules so that the students always have the theoretical knowledge that is needed for the current module of the case study. The alignment is depicted in Figure 6 .

5.5. Do the Review

6. writing study guide.

• Example: To get a better notion of how such a study guide looks, a specific example of one lesson from the Java technologies course can be found at https://kurzy.kpi.fei.tuke.sk/tjava-en/student/06.html (accessed on 30 August 2024).

6.1. Always Tell Objectives

• Example: Examples of learning goals are presented in Section 4 when we discussed making a list of the learning goals for the case study. However, there are also implementation objectives. These are specific to each case study. For example, in the following list, there are some implementation objectives from the Minesweeper case study.
• Students have to implement the generation of the game field.
• Students have to implement the presentation of the game field.
• Students have to implement a time-measuring feature for the game.
• Students have to implement the settings feature.
• Students have to implement a graphical user interface in Swing.

6.2. Describe the Current State and Expected Increment

• Example: We use class diagrams in each module to show the difference in the program structure before and after finishing the current lesson. In  Figure 8 , there is a class diagram of the Minesweeper case study in the fifth module. The yellow classes represent the current state, and the red ones are the increment for the fifth lesson. This helps the students to understand how the implementation goals will be projected into the program structure.

6.3. Show Context and Reasoning

• Example: In the Minesweeper case study, each step starts with an explanation of the current situation, the problem context, and the reasoning behind it. This part of the step is intertwined with the tasks that lead to solving the problem—each step of the module starts with the context and reasoning, and after that, the tasks follow.

6.4. Specify Tasks Clearly and Precisely

• Example: Following is an example of a task from our Minesweeper case study that tells the student to implement a method that will be a part of the Minesweeper marking tiles feature. This is one of the simpler tasks from earlier lessons of this introductory Java course.
• Task (id = markTile)
• Implement the void markTile(int row, int column) method in the Field class. This method allows marking/unmarking tiles specified by the row and column. In~case the tile is closed (Tile.CLOSED), its state will be marked (the state will change to Tile.MARKED). If~a tile is marked (Tile.MARKED), its state will be changed to closed (Tile.CLOSED). Rows and columns are numbered from 0.
• * Marks tile at specified indices.
• * @param row row number
• * @param column column number
• public void markTile(int row, int column) {
•     throw new UnsupportedOperationException("Method markTile not yet implemented");
•     final Tile tile = tiles[row][column];
•     if (tile.getState() == Tile.State.CLOSED) {
•         tile.setState(Tile.State.MARKED);
•     } else if (tile.getState() == Tile.State.MARKED) {
•         tile.setState(Tile.State.CLOSED);
• In the BestTimes class define a private void insertToDB(PlayerTime playerTime) method that will store a PlayTime object in the database.

6.5. Refine Tasks with Comments

• Example: The following is an example of a hint for the “markTile” task that was presented above. It advises using the implementation of the openTile(int row, int column) method for inspiration. The  openTile(int row, int column) method does a very similar job and is provided to students in the Minesweeper code skeleton at the beginning of the course. Most of the students should not have any serious problems in solving the task without this hint. However, below-average students or programming novices may struggle with it, and this hint should refer them to the right direction even before they will need to ask the teacher for help.
• When implementing the void markTile(int row, int column) method, you can use the implementation of void openTile(int row, int column) method as an inspiration.

6.6. Add Supplementary Tasks

• Example: In the Minesweeper case study, the implementation of new features is suggested, such as support for a new state in marking tile—using the question mark to signify that the user is not sure whether there is a mine or not.

6.7. Provide Further Reading

• Example: In the Java technologies course, we recommend the book Head First Java for further reading. For the advanced study, Effective Java is recommended. For particular topics, students are usually provided with links to specialized tutorials and blogs.

6.8. Use Suitable Software Support

• Example: At our university, we developed a specialized document generator for task-driven case study guides. This program transforms a set of Markdown files enriched with metadata representing the goals, tasks, etc. into a static website and possibly other formats, such as PDF. Utilizing custom software for this task also opens possibilities to check for inconsistencies, such as goals without any corresponding tasks.

6.9. Verify Continuity and Consistency of the Guide

6.10. review the guide, 6.11. start with a minimal version and improve it, 7. course execution, 7.1. monitor progress continuously, 7.2. favor individual achievements.

• Example: In the Java technologies course, we reward finishing the Minesweeper case study without any supplementary tasks by half of the maximum points available. The rest of the points can be obtained through additional tasks and custom features.

7.3. Examine Understanding

• Example: For our exams, an incomplete modified version of the Minesweeper solution is used. Students get to implement some missing part where they have to use the skills they should have acquired from the case study. The tasks are not the same as those in the case study, but they are similar in character. The following is an example of the exam task:
• Implement the processInput() method that will process input from the console using regular expressions. After~the implementation, the~game should be playable. After~each printing of the field, the~game would require typing some input. The~input is in the same format as in the case study: (X) EXIT, (MA1) MARK, (OB4) OPEN.

7.4. Get Feedback from the “Battlefield”

• Example: One of the important feedback entries we received from the students in the Java technologies course was the information that the task of implementing a method that counts adjacent mines to a tile is too difficult for many students (algorithmically). It did not look so difficult to us or our colleagues.

7.5. Update the Case Study

• Example: After finding out that the implementation of counting the adjacent mines is too difficult for the students, we decided to provide a hint to the task. If necessary, we could also include a note in the teachers’ version of the study guide about discussing the algorithm with students.

8. Experience

8.1. teachers’ view, 8.2. students’ view, 8.2.1. objective, 8.2.2. method, 8.2.3. results, 9. potential drawbacks, 10. conclusions, author contributions, institutional review board statement, informed consent statement, data availability statement, conflicts of interest.

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Porubän, J.; Nosál’, M.; Sulír, M.; Chodarev, S. Teach Programming Using Task-Driven Case Studies: Pedagogical Approach, Guidelines, and Implementation. Computers 2024 , 13 , 221. https://doi.org/10.3390/computers13090221

Porubän J, Nosál’ M, Sulír M, Chodarev S. Teach Programming Using Task-Driven Case Studies: Pedagogical Approach, Guidelines, and Implementation. Computers . 2024; 13(9):221. https://doi.org/10.3390/computers13090221

Porubän, Jaroslav, Milan Nosál’, Matúš Sulír, and Sergej Chodarev. 2024. "Teach Programming Using Task-Driven Case Studies: Pedagogical Approach, Guidelines, and Implementation" Computers 13, no. 9: 221. https://doi.org/10.3390/computers13090221

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Estimation of Rock Mass Equivalent Permeability Around Tunnel Route Using the Geostatistical Methods: A Case Study

• Research Paper
• Published: 05 September 2024

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• Sanaz Khoubani 1 ,
• Ali Aalianvari 1 &
• Saeed Soltani-Mohammadi 1  

The objective of this paper is to estimate the equivalent permeability of the rock surrounding the tailrace tunnel of the Azad Dam pumped storage power plant, using geostatistical methods. The permeability of the rock mass is a critical factor that influences the estimation of water flow rates. Since the tunnel passes through various geological units with different permeabilities, it is crucial to estimate the equivalent permeability for each unit in order to predict the water seepage from that unit into the tunnel. In order to estimate the permeability along the tunnel and underground structures, twelve exploratory boreholes were drilled, and water pressure tests were conducted. Due to the distribution of the exploratory boreholes, a study and statistical analysis are necessary to determine the permeability of the rock mass for each geological unit. Using geostatistical log kriging, multiple indicator kriging with four thresholds, and multiple indicator kriging with five thresholds, the permeability of the rock mass at the tunnel route was estimated. The results indicate that at least 40% of the rock mass has low permeability, while the remaining mass of the tunnel passes through rocks with moderate to high permeability. The accuracy of the estimated permeability values was evaluated by predicting the water inflow into the tunnel using the estimated permeability values and comparing it to the observed flow. Numerical models were generated for each geological unit to estimate the water inflow into the tunnel, based on the results of the geostatistical methods. Log kriging, multiple indicator kriging with four thresholds, and multiple indicator kriging with five thresholds were used to calculate the water inflow, resulting in 94.15, 94.15, and 127.5 L per second, respectively. The results of the modeling were compared to the observed water flow into the tunnel. Comparing the modeling results to both the statistical methods and observed values showed errors of 31.2%, 31.2%, and 6.9%, respectively. Of the three methods, the multiple indicator kriging computational method with five thresholds was found to be the most accurate, with the least amount of error and the closest approximation to the actual value. As a result, it was selected as the best method.

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No datasets were generated or analysed during the current study.

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Department of Mining Engineering, Faculty of Engineering, University of Kashan, Kashan, Islamic Republic of Iran

Sanaz Khoubani, Ali Aalianvari & Saeed Soltani-Mohammadi

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Khoubani, S., Aalianvari, A. & Soltani-Mohammadi, S. Estimation of Rock Mass Equivalent Permeability Around Tunnel Route Using the Geostatistical Methods: A Case Study. Iran J Sci Technol Trans Civ Eng (2024). https://doi.org/10.1007/s40996-024-01608-1

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Unveiling spatial variations in atmospheric CO 2 sources: a case study of metropolitan area of Naples, Italy

• Roberto M. R. Di Martino   ORCID: orcid.org/0000-0001-6435-2759 1 ,
• Sergio Gurrieri   ORCID: orcid.org/0000-0003-4085-0440 1 ,
• Antonio Paonita   ORCID: orcid.org/0000-0001-9124-5027 1 ,
• Stefano Caliro   ORCID: orcid.org/0000-0002-8522-6695 2 &
• Alessandro Santi   ORCID: orcid.org/0000-0002-1549-9786 2  

Scientific Reports volume  14 , Article number:  20483 ( 2024 ) Cite this article

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• Atmospheric chemistry
• Atmospheric science
• Climate sciences
• Environmental sciences
• Geochemistry
• Natural hazards
• Solid Earth sciences
• Volcanology

In the lower atmosphere, CO 2 emissions impact human health and ecosystems, making data at this level essential for addressing carbon-cycle and public-health questions. The atmospheric concentration of CO 2 is crucial in urban areas due to its connection with air quality, pollution, and climate change, becoming a pivotal parameter for environmental management and public safety. In volcanic zones, geogenic CO 2 profoundly affects the environment, although hydrocarbon combustion is the primary driver of increased atmospheric CO 2 and global warming. Distinguishing geogenic from anthropogenic emissions is challenging, especially through air CO 2 concentration measurements alone. This study presents survey results on the stable isotope composition of carbon and oxygen in CO 2 and airborne CO 2 concentration in Naples’ urban area, including the Campi Flegrei caldera, a widespread hydrothermal/volcanic zone in the metropolitan area. Over the past 50 years, two major volcanic unrests (1969–72 and 1982–84) were monitored using seismic, deformation, and geochemical data. Since 2005, this area has experienced ongoing unrest, involving the pressurization of the underlying hydrothermal system as a causal factor of the current uplift in the Pozzuoli area and the increased CO 2 emissions in the atmosphere. To better understand CO 2 emission dynamics and to quantify its volcanic origin a mobile laboratory was used. Results show that CO 2 levels in Naples’ urban area exceed background atmospheric levels, indicating an anthropogenic origin from fossil fuel combustion. Conversely, in Pozzuoli's urban area, the stable isotope composition reveals a volcanic origin of the airborne CO 2 . This study emphasizes the importance of monitoring stable isotopes of atmospheric CO 2 , especially in volcanic areas, contributing valuable insights for environmental and public health management.

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Introduction.

The equilibrium among natural CO 2 emissions, biotic uptake on land, and ocean absorption regulates long-term fluctuations in airborne CO 2 , establishing the greenhouse effect essential for the biosphere's existence on Earth. Human activities, particularly fossil fuel combustion, vehicle mobility, house heating, and waste management, disrupt the carbon cycle, leading to an increase in airborne CO 2 levels 1 , 2 , 3 , 4 , 5 . Disruption of this equilibrium worsens the effects of global warming and climate changes.

Global temperature data from Copernicus ( https://climate.copernicus.eu/ accessed on 2024, January 10), shows that the mean near-surface temperature in 2023 was ~ 1.4 ± 0.12 °C above the 1850–1900 average. This marked the warmest year in the 174-year observational record, surpassing the joint warmest years of 2016 and 2020. Notably, the last decade (2014–2023) encompasses the nine warmest years on record. Real-time data from specific locations reveals a continued increase in CO 2 levels in 2023, while consolidated concentration datasets of CO 2 , methane, and nitrous oxide reached their highest records in 2022.

Several causes contribute to global warming and climate change 6 . Since the eighteenth century the industrialization has led to the gradual abandonment of rural areas and the concentration of people in urbanized zones. Industries, mainly relying on electrical power generated by hydrocarbon combustion, settled in suburban areas contribute significantly to CO 2 emissions 5 , 7 . Urban growth, characterized by skyscrapers and increased vehicle mobility, results in continuous large-scale carbon dioxide release, predominantly concentrated in urban areas, significantly impacting the global atmospheric composition.

Earth degassing, driven by natural sources like soil respiration, volcanic degassing, and photosynthesis, contributes to atmospheric CO 2 concentrations 8 . Regions of active volcanism, responsible for a significant portion of natural gas emissions, release CO 2 of magmatic origin, particularly during eruptions, accounting for ~ 1% of global CO 2 emissions annually 9 , 10 , 11 . Although this percentage is modest on a global scale, locally, natural emissions may have a more substantial environmental impact, raising hazards for local populations 12 , 13 , 14 , 15 . For example, during the recent outgassing crisis at Vulcano, Italy 16 , 17 , gas hazards increased due to either diffuse degassing or crater plume emissions, though human health risk threshold value was not exceeded 18 , 19 , 20 .

Naples, with around 1 million residents, ranks third in population among Italian cities and is the most densely populated city in Europe. Its strategic location in Mediterranean shipping routes and heavy ship traffic in the harbour make it a potential major source of anthropogenic CO 2 . The city is located in a volcanic area with active volcanic and hydrothermal zones, making it an ideal study area to investigate the coexistence of human-related and natural CO 2 emissions.

This study presents the results of a spatial survey on airborne CO 2 in the metropolitan area of Naples. The survey aimed to collect measurements of airborne CO 2 concentration and stable isotopes of CO 2 to differentiate between volcanic and anthropogenic sources, identifying sources that elevate airborne CO 2 concentrations above the background. The study area includes Naples’ downtown and a broad urbanized zone extending from the western edge of Vesuvius volcano to Bacoli and Cuma in the east, and Agnano crater in the north, encompassing the active volcanic/hydrothermal zone of Campi Flegrei (Fig.  1 a). The Campi Flegrei area has experienced significant volcanic activity, including supereruptions, the oldest one dating back 40,000 years 21 , 22 . This area exhibits continuous degassing and seismic activity (i.e., Solfatara and Pisciarelli in the municipality of Pozzuoli). Anomalies in CO 2 emissions occur from soils via diffuse degassing and from fumaroles 23 , 24 , 25 , 26 , 27 , particularly in the Solfatara area (Zone A in Fig.  1 a). The most recent eruption originated from Monte Nuovo in 1538 A.D. Since then, this system has been in a state of persistent degassing and fluctuating seismic activity, leading to ground motion known as bradiseism. The study area has also increased the degassing since 2005 and is currently in unrest 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 . Human-related and geologic CO 2 emissions have distinct stable isotopic signatures, allowing differentiation in the air at the district scale through a combination of concentrations and isotopic measurements 12 , 13 , 18 , 19 , 20 , 37 , 38 , 39 . The results of the spatial survey enable a comparison between volcanic CO 2 emissions and those of anthropogenic origin in the urbanized area of Naples.

Study area, the route used during survey and dataset distribution. The survey was conducted in May 2023. ( a ) The blue line represents the route used during the survey. The selected subsets for Solfatara area (orange zone A), downtown Naples (green zone B), and airport (ice blue zone C) are shown. ( b ) Probability plot for concentration dataset. Global average value of airborne CO 2 concentration is reported as reference. (blue line indicates 423 ppm vol) for a comparison with the average CO 2 concentration over the target area (50% cumulative probability). ( c ) Histograms for both the oxygen isotope (δ 18 O–CO 2 ) and carbon isotope (δ 13 C–CO 2 ) compositions. ( d ) Three-dimensional view of the study area showing the atmospheric CO 2 concentration measurements at their respective locations. The height of the vertical bars is proportional to the concentration levels. The colour scale and bar height indicate that the highest CO 2 concentration was detected near the port. ( e ) Placement of the measurements within the study area. The colour scale is identical to that in subplot ( d ) and indicates the CO 2 concentration measured in the air. The maps ( a ), ( d ), and ( e ) were generated in Qgis 3.34 environment ( https://qgis.org/download/ ).

We developed a measurement program to detect and quantify the spatial variability of CO 2 concentration and its stable isotopes in the near-surface air of the Naples metropolitan area (Fig.  1 a). The dataset enables a better determination of the influence of meteorological factors and multiple greenhouse gas sources on the nature of the urban CO 2 dome 40 , 41 , 42 , 43 , which is considerably more challenging to identify than its mere presence. For this study, the wind direction was selected as the meteorological factor influencing CO 2 dispersal, while other meteorological factors (e.g., temperature, atmospheric pressure, relative humidity) can be averaged over the survey's completion time (11.4 h of acquisition during daytime over 24 h), as variations at the meteorological station from National Research Counsil (i.e., C.N.R. Long: 432,409; Lat: 4,520,399 UTM) are likely suitable for the entire Naples metropolitan area. Throughout the survey period, the weather remained consistently sunny. Table 1 presents the statistics of both environmental variables and atmospheric measurements.

Figure  1 b–c shows statistical distributions of measurements collected during the survey. The dataset collected in the Naples metropolitan area shows airborne CO 2 concentrations higher than 423 ppm vol (Fig.  1 b), which is the global reference for airborne CO 2 concentration for May 20, 2023 ( https://www.climate.gov/climatedashboard accessed on July 2, 2024). The probability plot 44 reveals three independent subsets of CO 2 concentrations. The 50% cumulative distribution indicates that the average value for the background CO 2 concentration in the urban area of Naples is 448.1 ± 1.0 ppm vol. The background population comprises more than 98.9% of the cumulative dataset, while the anomalous subset constitutes less than 0.1% of the cumulative dataset, with CO 2 concentrations exceeding 1300 ppm vol (Fig.  1 b).

Regarding stable isotopes, the carbon isotope composition of airborne CO 2 (reported in delta notation δ 13 C–CO 2 against the Vienna Pee Dee isotopic ratio-VPDB) shows values more 13 C-depleted than the theoretical background air (δ 13 C–CO 2  =  − 8‰ vs VPDB). This result indicates that a source of CO 2 forces airborne CO 2 concentration above background values. This gas source has a 13 C-depleted isotopic signature and establishes an urban CO 2 dome in the Naples metropolitan area. Furthermore, the statistical parameters of the data distribution (skewness =  − 2.27, kurtosis = 15.74) indicate that the dataset has a peak at δ 13 C–CO 2  =  − 10.40‰, which is more 13 C-depleted than the theoretical atmospheric CO 2 value 45 .

The range of values for δ 18 O-CO 2 is wide compared to the spatial and temporal scales of the collected measurements. The oxygen isotope composition of airborne CO 2 depends on both the hydrology of the region and oxygen isotope fractionation in plant leaves during photosynthesis 46 , 47 , 48 . These factors change over spatial and temporal scales different from those of the measurement acquisition (i.e., ~ 10 4 –10 5  m and approximately 24 h, respectively). The oxygen isotope values are almost normally distributed (skewness =  − 1.50, kurtosis = 7.3) throughout the study area (Fig.  2 b). Gaussian fitting of the oxygen values has a peak at δ 18 O–CO 2  =  − 3.16‰ versus VPDB, which is more 18 O-depleted than the expected value for a coastal area of the Mediterranean region 49 , 50 , 51 , 52 .

Spatial variations of the CO 2 measurements collected during survey throughout the target area (cell size 10 m). The maps were generated in Qgis 3.34 environment ( https://qgis.org/download/ ) using Measurement interpolation generated in SAGA GIS environment ( https://saga-gis.sourceforge.io/en/index.html ). ( a ) Spatial variation of the airborne CO 2 concentration. ( b ) Spatial variation of the oxygen isotope composition of the airborne CO 2 . ( c ) Spatial variation of the carbon isotope composition of the airborne CO 2 . Traces of the concentration profiles are reported (black lines). See text for description.

The collected dataset was utilized to investigate the spatial variation of airborne CO 2 (Fig.  2 ). These data allow investigation of whether urban CO 2 sources affect atmospheric chemistry at a district scale or over the urban area (i.e., at the local scale, ~ 10 4 –10 5  m). The results illustrate a heterogeneous distribution of airborne CO 2 concentration over the Naples metropolitan area, with a concentration gradient from the coast to the inland, likely influenced by local atmospheric circulation. Granieri et al. 14 , who conducted detailed micrometeorological studies on atmospheric circulation in the Naples area for gas dispersal simulations, noted a diurnal sea breeze blowing from SW to NE, pushing clean air inland from the seaside during morning hours. A supply of clean air from the sea would dilute CO 2 concentration at relatively low levels. However, measured CO 2 concentrations in the urban area of Naples suggest that atmospheric circulation is insufficient to reduce atmospheric CO 2 concentrations to background levels, at least on days with similar weather conditions to the ones of the day of measurements. Further research should address the issue concerning the critical atmospheric circulation conditions that help to reduce the concentration level of CO 2 . The implementation of atmospheric CO 2 monitoring programs in urban areas, particularly when integrated with stable isotope composition analyses, is posited as an effective method for detecting anthropogenic or natural forcings influencing atmospheric CO 2 levels. Elevated atmospheric CO 2 concentrations are frequently correlated with increased levels of other pollutants, suggesting that these monitoring programs can significantly enhance public health management strategies. Additionally, in urbanized regions located within volcanic zones, atmospheric CO 2 monitoring is crucial for mitigating volcanic risks associated with gas emissions (i.e., the gas hazard) 19 . Examination of the dataset reveals areas with high airborne CO 2 concentrations, notably near Naples' harbour, where the highest CO 2 concentration was measured (Fig.  1 d,e), and the district of Museo square, among others (Zone B in Fig.  1 a).

Figure  2 illustrates additional zones with high concentrations of airborne CO 2 . The airborne CO 2 concentrations achieve 572 ppm vol in a zone situated in the northeastern sector of the investigated area. While this level does not surpass any established risk threshold for human health 53 , it exceeds the reference value recorded at NOAA Global Monitoring Laboratory for the investigated time frame (424 ppm by volume) by > 33%. A land use survey in the metropolitan area of Naples reveals the presence of the airport, particularly the runways and aircraft parking areas adjacent to the route used for data collection. Another zone exhibiting elevated concentrations of airborne CO 2 is identified on the western side of downtown Naples, within the municipality of Pozzuoli (i.e., transect B–B′ in Fig.  3 b). This area is renowned for its evidence of the underlying volcanic hydrothermal system of Campi Flegrei 26 , 27 , 28 , 29 , with airborne CO 2 concentrations reaching 567 ppm vol. The spatial distribution of airborne CO 2 concentrations in this zone appears more heterogeneous compared to other areas, attributable to the presence of several high concentration nuclei near Bagnoli and Baia (Figs.  2 a and 3 a), eastward and westward of Solfatara, respectively.

Transects through selected zones of the study area to inspect lateral variations of airborne CO 2 concentration (blue line), δ 18 O–CO 2 (red line), and δ 13 C-CO 2 (blue line). ( a ) A–A′ transect (Bacoli). ( b ) B–B′ transect (Solfatara). ( c ) C–C′ transect (Downtown). ( d ) D–D′ transect (Portici).

The δ 18 O–CO 2 has been recognized as a tracer of photosynthesis and the hydrologic cycle's effects on airborne CO 2 . These processes play a pivotal role in the fractionation of oxygen in airborne CO 2 at vastly different spatiotemporal scales. While the hydrologic cycle exhibits seasonal effects at the regional scale, notable changes in vegetation (e.g., transition from C3 to C4 or CAM plant dominant types) account for variations in the oxygen isotope composition due to differences in photosynthesis. Since the survey was completed in a few hours, the spatial variations in the oxygen isotope composition resulting from these processes are expected to have negligible effects on the spatial variations of δ 18 O–CO 2 , which constitutes an ancillary factor for identifying variations in the source of CO 2 at the district scale 12 , 13 , 18 , 20 , 51 , 54 .

The kriging interpolation of the δ 18 O-CO 2 dataset reveals a zone with slightly 18 O-depleted airborne CO 2 westward of downtown Naples, where the δ 18 O–CO 2  =  ~  − 2‰. Near Baia, where high concentrations of CO 2 were measured (Fig.  2 a), the airborne CO 2 exhibits more 18 O-depleted values, reaching δ 18 O–CO 2  =  − 5.38‰ through a steep isotopic gradient (e.g., transect A–A′ in Fig.  3 a). The δ 18 O–CO 2 abruptly increases to approximately − 2‰ northwestwardly along the transect A–A′ (Fig.  3 a). Airborne CO 2 shows less 18 O-depleted values near Solfatara. A concentration profile across the Pozzuoli area (Fig.  3 b) depicts the least 18 O-depleted CO 2 in the air, having δ 18 O–CO 2  =  − 0.06‰ in the vicinity of Solfatara and toward the northeast (Fig.  3 b). The δ 18 O-CO 2 values decrease to an average of − 2.5‰ northeast of Astroni. Downtown Naples has been identified as an area where airborne CO 2 exhibits more 18 O-depleted values, although zones with δ 18 O–CO 2  <  − 6.5‰ are heterogeneously distributed between Pianura and Capodimonte, where CO 2 exhibits more 18 O-depleted CO 2 (i.e., transect C–C′ in Fig.  3 c). In this zone, heavily 18 O-depleted CO 2 (δ 18 O–CO 2  <  − 16.0‰) was measured in the harbour district.

Additionally, a wide zone elongated NW–SE exhibits δ 18 O–CO 2  <  − 5.3‰, extending from the eastern edge of downtown Naples to the west of Torre del Greco, coinciding with a densely urbanized area and a widespread industrialized area (i.e., Area Est-Centro direzionale). Figure  3 d illustrates a step gradient of δ 18 O–CO 2 that separates the coastal zone where δ 18 O–CO 2  =  ~  − 5.06‰ from the inland area where δ 18 O–CO 2  =  ~  − 2.85‰. The ∆ 18 O–CO 2  = 2.21 represents an order of magnitude greater than the accuracy of the oxygen isotope determination (± 0.25‰). In summary, the spatial variations of the measurements show strong fluctuations of δ 18 O–CO 2 in different zones. Kriging interpolation of the δ 18 O–CO 2 dataset reveals areas with slightly 18 O-depleted airborne CO 2 westward of Naples' downtown, and more 18 O-depleted values eastwards of downtown Naples. Similarly, wide variations in δ 13 C–CO 2 values correspond to spatial variations in the carbon isotopic signature of airborne CO 2 (Fig. six). Dataset statistics indicate that airborne CO 2 is 13 C-depleted compared to standard air. Cross-sections show trends indicating potential CO 2 sources with 13 C-depleted or enriched signatures in different areas, with notable variations near Baia and downtown Naples. These results suggest considerable variability in emission sources at the scale of the urbanized zone, and a dominant source of CO 2 with a 13 C-depleted signature. This expectation arises because the carbon isotope signature of airborne CO 2 can track the source of the gas 55 , 56 .

The cross-section through the urbanized areas of Bacoli (Figs.  2 a and 3 a) shows an average value of δ 13 C–CO 2  =  − 10.5‰, indicating airborne CO 2 to be more 13 C-depleted than theoretical air and global reference values recorded by NOAA ( https://www.climate.gov/climatedashboard accessed on July 2, 2024). A significant change in the carbon isotope composition of airborne CO 2 is evident at Baia, where a decrease to a value of δ 13 C–CO 2  <  − 14‰ was measured, coinciding with concentration values higher than those measured at Bacoli (Fig.  2 c). Low values of δ 13 C-CO 2 indicates that a heavily 13 C-depleted source of CO 2 is responsible for forcing airborne CO 2 above background levels and is the main contributor to increased CO 2 concentration. The carbon isotope composition increases to less 13 C-depleted values north of Cuma and achieves δ 13 C–CO 2  =  ~  − 9‰ in the northern zone of the target area. The B–B′ cross-section shows a different trend compared to the A–A′ profile (Fig.  3 a,b respectively). Specifically, δ 13 C–CO 2 decreases from approximately − 9 to − 11‰. Continuing along the Solfatara profile (Fig.  3 b), a sudden increase in δ 13 C–CO 2 value is observed, reaching values of approximately − 8‰ at the highest concentration values observed along the same profile.

This trend appears to be clearly opposite to that observed in the A–A′ profile, suggesting the presence of potential CO 2 sources with a less 13 C-depleted signature compared to those forcing airborne CO 2 concentration in adjacent areas. The alternative hypothesis, suggesting that clean air with δ 13 C–CO 2  =  − 8‰ produces the observed values, can be dismissed based on the evidence that 13 C-enrichment correlates with an increase in CO₂ concentration. This trend contradicts the expectation of a decrease in CO₂ concentration, which would be consistent with the clean air hypothesis. Furthermore, the A–A′, C–C′, and D–D′ profiles demonstrate that CO₂ concentrations exhibit opposite trends in comparison with δ 13 C–CO 2 . Specifically, these transects reveal that increases in CO₂ concentration coincide spatially with decreases in δ 13 C–CO 2 , indicating that the effective source of CO₂ in these zones is more 13 C-depleted. In the surrounding area, δ 13 C–CO 2 values average around − 10‰ regardless of CO 2 concentration in the air. These 13 C-depleted values reduce evidences of spatial 13 C-enrichment in airborne CO 2 . Therefore, the gas source which causes rise in CO 2 concentration above background levels in the area of Solfatara has a carbon isotope composition only slightly 13 C-depleted compared to the VPDB standard. Accordingly, to the northeast of the Astroni crater, δ 13 C–CO 2 decrease sharply to values ranging between − 10 and − 11‰. Moreover, zones with high airborne CO 2 concentrations near both Bagnoli and Posillipo also show heavily 13 C-depleted isotopic composition (i.e., δ 13 C–CO 2  =  − 14.69‰ and δ 13 C–CO 2  =  − 13.85‰, respectively).

The C–C′ profile (Fig.  3 c) crosses Naples’ downtown (Fig.  2 ), which is busiest by vehicle during morning hours. The airborne CO 2 has δ 13 C–CO 2 values from − 17.65 to − 8.54‰ with an average δ 13 C–CO 2  =  ~  − 11‰. High CO 2 concentrations along this profile occur at the harbour district (Fig.  3 c and Fig.  2 a), which coincides with the zone having the most 13 C-depleted values of airborne CO 2 (Fig.  2 c). A comparison with other profiles reveals that a 13 C-depleted source of CO 2 forces the airborne CO 2 concentration in downtown Naples more efficiently than in peripheral zones to the west (i.e., Bacoli, Baia, and Posillipo). This source is less effective in forcing CO 2 concentration in the zone near Pozzuoli (B–B′ profile), where the source of CO 2 has a less 13 C-depleted carbon isotope composition. This northwest-oriented profile shows a zone with less 13 C-depleted values of airborne CO 2 to northwest (Fig.  2 c), consistent with a decrease in airborne CO 2 concentrations (Fig.  2 a).

Remarkable variations in the stable isotope composition of airborne CO 2 can be identified east of the urban area of Naples (Fig.  2 c). In concordance with δ 18 O–CO 2 , δ 13 C–CO 2 shows remarkable variations along the seaside compared to the inland along the D–D′ profile (Fig.  3 d). Airborne CO 2 concentrations fluctuate, superimposed on a decrease from the seaside to the inland. According to this trend, the carbon isotope composition shows an opposite trend from the most 13 C-depleted values in the coastal zone to the less 13 C-depleted CO 2 inland, revealing that potential sources of CO 2 with heavily 13 C-depleted signatures force airborne CO 2 concentration in the coastal zone near Portici and Torre del Greco. These sources are less effective in forcing CO 2 concentration inland, near San Giorgio a Cremano.

Measurements of CO 2 concentration, combined with stable isotope compositions of airborne CO 2 , provide relevant data for distinguishing between natural and anthropogenic CO 2 emissions in the atmosphere, and potentially tracking the gas dispersal from various sources of greenhouse gases at the urban spatial scale (i.e., 10 4 –10 5  m). This method overcomes the inherent difficulty of studying CO 2 dispersion caused by its high background level and subtle spatial variations of airborne CO 2 concentration. Indeed, various sources of CO 2 have different isotopic signatures for both carbon and oxygen.

There are several methods for tracking the dispersion of gases emitted from a source into the atmosphere. The methods commonly used to track gas dispersion are based on models that require a priori knowledge of the source, the amount of gas emitted, and the geometry of the dispersion area. Isotopic studies combined with atmospheric chemistry follow a different paradigm. The data collected from field measurements underwent analysis utilizing the Keeling plot method mass balance models for oxygen and carbon isotopes 49 , 50 , 57 . The Keeling plot method facilitates the determination of the primary CO 2 source at the local level using observational data.

At the same time, the mass balance model for oxygen and carbon isotopes allows an assessment of the influences of the individual CO 2 sources on the local air composition. The mathematical expressions governing this model were developed within the framework of previous studies 20 and are expounded concisely upon in the method section dedicated to assessing additional CO 2 in the atmosphere. This method allows for detecting the forcing effects introduced by the gas sources on the composition of the atmosphere. The measurements utilized in the theoretical model results (see Eq. ( 11 ) in this study) furnish point-by-point estimates of additional CO 2 concentration (i.e., the C fs ) along the trajectory.

Subsequently, the interpolation of C fs values employing the Kriging algorithm model facilitates the simulation of CO 2 dispersion. This algorithm generates a predictive layer for δ 13 C–CO 2 , δ 18 O–CO 2 , CO 2 concentration, and C fs. This method has been successfully applied to detect chemical and isotopic effects on the air in the La Fossa caldera on the island of Vulcano, both during periods of quiescent outgassing and during the recent period of increased volcanic outgassing in 2021 20 .

The Keeling plot illustrates a correlation between the carbon isotope composition of CO 2 and the inverse of airborne CO 2 concentration. Figure  4 shows the concentration dataset normalized by the global reference for airborne CO 2 concentration (i.e., 423 ppm vol). Each straight line on this plot represents binary mixing between the atmospheric background and an additional CO 2 source. The intercept on the isotopic axis provides the carbon isotopic signatures, facilitating the identification of the CO 2 emission source.

The correlation between δ 13 C–CO 2 and the inverse of airborne CO 2 concentration (i.e., Keeling plot). Data were normalized against the Global reference values recorded by NOAA (a https://www.climate.gov/climatedashboard accessed on July 2, 2024. ( a ) Dataset collected over the target area. ( b ) Urbanized areas of Naples. Green circles distinguish the subset of measurement collected near the airport (zone C in Fig.  1 a) from those collected in downtown Naples (zone B in Fig.  1 a). ( c ) Pozzuoli–Solfatara–Agnano area (zone A in Fig.  1 a) Yellow circles distinguish the subset of magmatic origin from that of anthropogenic origin in the area (blue circles).

Figure  4 a displays several mixing lines between background air and various potential sources of CO 2 , including natural (e.g., soil and plant respiration or volcanic degassing) and anthropogenic origins (e.g., combustion of fossil fuels or natural gas and landfill CO 2 emissions), whose isotopic signatures were retrieved from previous studies 37 . A geometric mean regression is recommended for the analysis of a scattered dataset (i.e., R 2  < 0.980) in the Keeling plot due to the inherent bias associated with determining the carbon isotopic signature through the utilization of a linear regression model 58 . The line representing the isotopic signature of the forcing source can be derived by applying a standard regression and subsequently dividing by the r-coefficient. This corrective approach aims to approximate the geometric mean regression through the utilization of a standard estimate obtained from a linear regression model.

The dataset collected over the target area reveals a variety of mixing lines, highlighting the inherent complexity of identifying a single CO 2 source. The alignments of δ 13 C–CO 2 in the Keeling plot suggests that fossil fuel combustion is a significant source of greenhouse gases, resulting in airborne CO 2 concentrations ranging from > 600 to ~ 1410 ppm vol (i.e., normalized values are from 0.7 to 0.3, respectively). However, multiple CO 2 sources can influence airborne CO 2 concentrations in the target area, especially at low to intermediate values (i.e., from 423 to 600 ppm vol, corresponding to normalized values ranging 0.7–1). These results support findings that human-related activities, such as urban mobility by vehicles and household heating, predominantly based on the combustion of fossil fuels, contribute significantly to rise the airborne CO 2 concentration. Nonetheless, natural CO 2 emissions, such as those from volcanic outgassing, which is estimated on the synoptic scale to account for approximately 1% of total annual emissions, can locally play a pivotal role in the amount of CO 2 injected into the atmosphere.

A sector in Naples’ downtown (i.e., Zone B in Fig.  1 a), distinct from Zone A, which includes the Campi Flegrei volcanic/hydrothermal zone and the western suburbs of Naples (i.e., Bagnoli and Posillipo), can serve as a test site to quantify the specific contribution to increasing airborne CO 2 concentrations caused by human-related emissions. Figure  4 b illustrates δ 13 C–CO 2 against CO 2 concentrations, showing good agreement with the mixing line between background air and CO 2 produced by fossil fuel combustion, characterized by a heavily 13 C-depleted signature (i.e., δ 13 C–CO 2  =  − 29.94‰). Furthermore, data collected in the airport zone (i.e., Zone C in Fig.  1 a), where high levels of airborne CO 2 concentrations have been measured, indicate that the CO 2 source affecting both concentration and isotope composition of airborne CO 2 is of anthropogenic origin (i.e., δ 13 C–CO 2  =  − 29.31 ‰).

Figure  4 c illustrates the complex distribution of concentration and carbon isotope composition values detected in the study area, predominantly located in the urban area of Pozzuoli, in the western suburbs of Naples. Results of cluster analysis applied to a subset of measurements collected in the Zone A (Fig.  1 a) reveal that multiple CO 2 sources play an almost equivalent role in elevating the concentration of airborne CO 2 above background levels. One subset of measurements, with CO 2 concentrations in the range 423–700 ppm vol, exhibits an isotopic signature in good agreement with the mixing line between background air and CO 2 produced by the combustion of fossil fuels (i.e., δ 13 C–CO 2  =  − 32.93‰). Another subset of measurements indicates that δ 13 C–CO 2 of the air increases as CO 2 concentrations rise due to the influence of a less 13 C-depleted CO 2 source, with δ 13 C–CO 2 ≈ − 1.97‰. Although slightly lower, this value aligns with the carbon isotopic signature of CO 2 emitted from Pisciarelli and Bocca Grande fumaroles.

Those data retrieved from application of laboratory techniques to condensed fumarolic fluids have accuracy ± 0.1‰ 26 . Differences in the range Δ 13 C < 0.4‰ can be neglected because of the accuracy of the measurements with Deltaray (i.e., ± 0.25‰ according to 12 , 13 , 18 , 37 , 58 ).

Equation ( 11 ), included in the method section, facilitates the calculation of additional CO 2 in the air owing to either natural (i.e., volcanic/hydrothermal CO 2 ) or anthropogenic (i.e., produced by the combustion of fossil fuels) emissions. This calculation is based on input parameters in a theoretical model and measurements of airborne CO 2 concentration, δ 13 C–CO 2 , and δ 18 O–CO 2 in the field. C fs provides the concentration of the forcing source of CO 2 , exceeding local background levels in the atmosphere. A combination of the positioning of the endogenous sources of CO 2 and results of the Keeling plot helps distinguish the application of the mass balance model to the dispersal of volcanic CO 2 in the zone Solfatara (i.e., Zone A in Fig.  1 a) and the dispersal of CO 2 produced by the combustion of fossil fuels downtown Naples (i.e., Zone B in Fig.  1 a).

Figure  5 shows dispersions of CO 2 from anthropogenic origin in Naples’ downtown. In particular, the excess CO 2 concentrations in air produced by hydrocarbon combustion, which has a 13 C-depleted isotope composition compared to standard air (Fig.  4 b). For the calculation of the additional amount of CO 2 in the air, an anthropogenic source of CO 2 with the isotopic signature δ 13 C =  − 31.00‰ and δ 18 O =  − 16.00‰ has been adopted as the model parameters. Figure  5 a shows the fossil fuel-derived CO 2 has a heterogeneous distribution across the target area. A CO 2 dome 40 , 41 , 42 , 43 appears irregular and has numerous lobulations. The dome encloses islands where hydrocarbon combustion forces the CO 2 above the atmospheric background and generates concentration peaks even greater than + 300 ppm above the airborne CO 2 background (Fig.  5 b). One such island of high CO 2 concentration is well delineated in the harbour area, which is renowned for being among the Mediterranean's major harbours. In fact, the burning of hydrocarbons sustains the majority of the ship traffic in these areas. Another area with high CO 2 concentrations is located in the western downtown, near one of the most densely populated areas of Naples.

Dispersal of anthropogenic CO 2 in downtown Naples (cell size 10 m). The maps were generated in Qgis 3.34 environment ( https://qgis.org/download/ ) using Measurement interpolation generated in SAGA GIS environment ( https://saga-gis.sourceforge.io/en/index.html ). ( a ) CO 2 concentration map that shows the CO 2 concentration excess above the reference background. The concentration excess value of 83 ppm vol has been set as the threshold for transparency. ( b ) Vertical profile (black line in subplot a) of the excess CO 2 concentration across downtown Naples. ( c ) Wind vectors and speed recorded at C.N.R. station. ( d ) Wind direction frequency during survey.

The results of isotopic investigations prove the anthropogenic origin of atmospheric CO 2 . It is reasonable to assume that most of the anthropogenic CO 2 found in downtown Naples is the result of hydrocarbon combustion produced by urban mobility, given that the average air temperature during measurement collection was 22 °C (with an air temperature range of 19–23 °C). Within the one-day measurement acquisition timescale, variations in wind intensity and direction affecting the dispersion of CO 2 cannot be ruled out. This is particularly expected in Zone B, where the wind can influence the dispersion of emitted plumes near Naples' harbour. However, the data on wind direction (Fig.  5 c) and speed indicate that during the acquisition time window, the atmospheric circulation brought in SSW air, which is generally less enriched in anthropogenic CO 2 . Given the morphology of the study area and the local effects of densely built environments (Fig.  5 d), it is reasonable to assume a dilution effect of anthropogenic CO 2 due to the influence of less CO 2 —rich air from the sea. Accordingly, the anthropogenic CO 2 concentration along the C–C′ profile (Fig.  5 c) shows a notable increase in airborne CO 2 near the harbour and above a pedestrian area, suggesting that proximal sources of greenhouse gas emissions in the nearby areas are responsible for the increase in CO 2 above background levels.

Measurements collected at Pozzuoli (Zone A in Fig.  1 a) reveal multiple origins for CO 2 present in the air, namely volcanic and anthropogenic. Although human-related activities cause high concentrations of airborne CO 2 , a comparison with downtown can be made concerning the dispersal of geogenic CO 2 in the Pozzuoli area because the Campi Flegrei volcanic/hydrothermal system was in a state of unrest at the time of measurement collection 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 . Results of the cluster analysis provide a subset for calculating the amount of geogenic CO 2 that the main degassing zones at Campi Flegrei discharge into the atmosphere. The isotope composition and the airborne CO 2 concentration values of this subset were used in Eq. ( 11 ), with the values for the isotopic signatures of both carbon and oxygen for CO 2 emitted at Solfatara and Pisciarelli in May 2023 serving as model parameters (i.e., δ 13 C–CO 2  =  − 1.67‰ vs VPDB and δ 18 O–CO 2  =  − 7.85‰ vs VPDB) to obtain point-to-point calculations of volcanic CO 2 dispersal. These values provide insight into the dispersal of volcanic CO 2 from the main degassing vents at Campi Flegrei based on direct measurements and model parameters (Fig.  6 a). A comparison with the downtown map (Fig.  5 a) shows a more homogeneous dispersal of volcanic CO 2 along an N–S oriented dispersal zone. Furthermore, the volcanic CO 2 concentration is higher than 124 ppm vol above background levels in the area lying between Pozzuoli and Pisciarelli alone. Considering a background air CO 2 concentration of 423 ppm vol and the volcanic input calculated in the present study, this result is in good agreement with dispersal simulations averaged over a whole diurnal cycle obtained using the DISGAS software 14 . Measurements of concentration, corroborated by isotopic determinations, reveal volcanic CO 2 dispersion in the area of Bagnoli and eastward towards the urbanized area of Naples. In this area, measurements of airborne CO 2 concentrations alone are not able to track the dispersal of volcanic CO 2 because comparable absolute concentration values are found throughout the urban areas, where the additional CO 2 has anthropogenic origins. According to Granieri et al. 14 , inland air circulation prevails during nighttime in the Gulf of Naples, when volcanic CO 2 dispersal occurs towards the sea.

Dispersal of volcanic CO 2 in Pozzuoli-Solfatara zone (cell size 10 m). The maps were generated in Qgis 3.34 environment ( https://qgis.org/download/ ) using Measurement interpolation generated in SAGA GIS environment ( https://saga-gis.sourceforge.io/en/index.html ). ( a ) CO 2 concentration map that shows the CO 2 concentration excess above the reference background. The concentration excess value of 75 ppm vol has been set as the threshold for transparency. ( b ) Wind vectors and speed recorded at C.N.R. station. ( c ) Wind direction frequency during survey. ( d ) Vertical profile (black line in subplot a) of the excess CO 2 concentration across Pozzuoli-Solfatara area.

At the time of the survey, weather datasets reveal that NW winds blew from Solfatara towards the sea, even during the early morning (i.e., by ~ 8:00 UTC), after which sea breeze dominated air circulation from the SE throughout the daytime hours (Figura 6b,c). Arguably, the dispersal of volcanic CO 2 results from a combination of volcanic CO 2 dispersal and the residual layer that develops during nighttime and has not yet been disrupted by diurnal atmospheric turbulence. These results show that spatial surveys for studying airborne CO 2 helps in identifying multiple sources of greenhouse gases at the district scale of urban areas. Furthermore, stable isotope measurements allow an assessment of the impact of either volcanic degassing or anthropogenic emissions on airborne CO 2 concentrations.

The results of this study illustrate that integrating measurements of carbon and oxygen isotopic composition with those of CO 2 concentration aids in elucidating the genesis and development of CO 2 dome in urbanized areas. This represents a step forward in evaluating the impact of specific carbon dioxide sources, whether anthropogenic or natural, on the progression of climate change, as it facilitates the discernment of the underlying causes of urban domes through direct investigations.

The findings of this study also suggest that surveys conducted in urban areas such as Naples can be utilized to identify the primary regions for continuous monitoring of both natural and anthropogenic CO 2 emissions against global warming. Climate change has reached a global scale and threatens the stability of various vital sectors, including infrastructure, the economy, electricity production, international relations, biodiversity, and freshwater and food resources. Climate change affects all regions of the world, and its macroscopic effects manifest through extreme weather events, producing vast damage in cities and rural areas.

The international community is implementing a series of measures to combat ongoing climate change, which significantly impacts economic and social systems globally. For instance, several ambitious plans aim to reduce greenhouse gas emissions by 2050, mainly CO 2 . To achieve such ambitious goals, it is crucial to estimate and monitor CO 2 emissions, especially in urban areas where most CO 2 is produced through hydrocarbon combustion. Currently, no monitoring tools are available to detect near-real-time CO 2 emissions for individual countries. Therefore, efforts to monitor CO 2 in the air on a regional scale (synoptic ~ 10 6  m) with low latency (through the publication of hourly, daily, weekly, and annual data) via networks of stations installed in densely urbanized areas are becoming increasingly relevant. However, monitoring CO₂ in the atmosphere is not straightforward due to the high background concentration (approximately 400 ppm vol), which limits the potential for spatial variability. Consequently, monitoring the concentration alone may not always provide sufficient data for real-time estimation. Various studies demonstrate that integrating isotopic and concentration data provides information on the origin of CO 2 emissions 12 , 13 , 16 , 18 , 20 , 37 , 38 , 39 , 58 , 59 , 60 .

The δ 18 O–CO 2 largely depends on the CO 2 partitioning among the atmosphere, hydrosphere, lithosphere, and biosphere and can be deciphered through isotopic fractionation processes. Recent studies 12 , 18 , 19 , 20 show that it is possible to quantify atmospheric CO 2 emissions from natural and anthropogenic sources, isotopically characterized by δ 13 C–CO 2 and δ 18 O–CO 2 values, through integrated monitoring of atmospheric CO 2 concentration, isotopic composition, and meteorological data (direct investigations).

Therefore, the implementation of an active monitoring system is urgent and represents a paradigm shift in quantifying atmospheric CO 2 emissions at the scale of individual urbanized areas, compared to the currently applied methods based on statistical data at the national level for countries that are signatories to the United Nations Framework Convention on Climate Change 61 .

Instrument setup

The instrument employed for data acquisition in this study is a Delta Ray–Thermo Fisher Scientific. It measures the concentration of the isotopologues 13 COO, 12 COO, and CO 18 O based on the adsorption strength of light in the mid-infrared region (~ 4.3 μm) following the Lambert–Beer law. The 13 C/ 12 C and 18 O/ 16 O ratios are calculated using different concentration ratios of the isotopologues, while the total CO 2 concentration is determined by summing the concentrations of the three CO 2 isotopologues. Stable isotope ratios are expressed in agreement with the VPDB scale using the δ-notation (i.e., δ 13 C–CO 2 and δ 18 O–CO 2 , respectively) within the CO 2 concentration range of 200–3500 ppm vol.

The Delta Ray instrument is equipped with the QTegra software. A specially designed template includes protocols for recording δ 13 C–CO 2 , δ 18 O–CO 2 , and CO 2 concentration values, along with information on the sample list, acquisition parameters, referencing, evaluation settings, and sample definition. Instrument calibration and referencing against two working standards ensure an accuracy of ± 0.25‰ for isotope determinations and ± 1 ppm vol for CO 2 concentration measurements.

The instrument records each measurement of δ 13 C–CO 2 and δ 18 O–CO 2 at a frequency of 1 Hz. Before data acquisition, the instrument conducts isotope ratio referencing on the working standards at a fixed CO 2 concentration (i.e., CO 2  = 400 ppm vol) approximating background airborne CO 2 . After purging the unknown air sample for 60 s, the instrument skips the purge and measures the concentration of CO 2 isotopologues in the air. Once the air has purged the gas inlet, the instrument calculates δ 13 C–CO 2 and δ 18 O–CO 2 , as well as CO 2 concentration.

Measurement strategies

An off-road vehicle housed the instrument, and the equipment for measuring δ 13 C–CO 2 , δ 18 O–CO 2 , and airborne CO 2 concentrations during the studies across the urbanized zone of Naples. The positioning of the vehicle was recorded by a global positioning system device (GARMIN GPSMAP® 64 s), time-synchronized with the Delta Ray's internal clock. In specific urban environments 12 , 37 , 38 , 39 , 55 , 56 , 62 and, more recently, in volcanic regions 18 , 20 , investigations have been conducted utilizing mobile laboratories to analyze the spatial variability of CO 2 .

An inverter (12 V input–output, pure sine wave) was connected to the car's electrical system, supplying power to the instrument (~ 300 W). A stainless-steel capillary (1/16 in.; Swagelok-typeTM, 3 m long) was connected to the instrument's inlet, with the other end attached to the front of the car roof (~ 2.3 m above the ground) to avoid potential contamination from the gasoline engine exhaust. The air passed through a filter (2 μm, 1/16 in, capillary aperture) to prevent contamination from dust on the roads. Considering the volume of the sampling capillary, the instrument's flow rate (approximately 100–110 ml min −1 ), and the average speed of the mobile laboratory (approximately 3.5 m s −1 ), the delay between measurements and their corresponding positions is approximately 25 m. This delay is comparable to the GPS positioning.

A route of approximately 170 km (Table 1 ) was designed in the laboratory to obtain a continuous, non-overlapping path, covering various environments in the wide urbanized area of Naples (Fig.  1 a). The route includes Miseno, Bacoli, Agnano, Campi Flegrei caldera, Pozzuoli, Capodimonte, Bagnoli, Posillipo to the east of Naples' downtown, and Portici, Ercolano, Torre del Greco, and San Giorgio a Cremano to the west, respectively. The route was planned to ensure that segments did not overlap, preventing an increase in the statistical weight of some route segments over others. The route was meticulously followed using a routing application (e.g., Google Maps). The survey was completed in thirteen hours at an average speed of 13 km h −1 , with the spatial density of measurements corresponding to the metric order (~ 4 m average distance between measurements). The dataset encompasses ~ 41,000 georeferenced measurements for δ 13 C–CO 2 , δ 18 O–CO 2 , and CO 2 concentration, respectively 63 . This method was already employed for a simultaneous airborne CO 2 spatial survey at Vulcano and revealed the dispersion of volcanic CO 2 through direct measurements 18 , 20 .

Data processing approach

The data acquired from onsite measurements underwent processing utilizing the Keeling plot approach and mass balance models for oxygen and carbon isotopes. The Keeling plot enables the identification of the predominant CO 2 source at the local scale through observational data. The mass balance model for oxygen and carbon isotopes aims to quantify the impact of the CO 2 source on the local air. The algebraic equations for the model were developed as part of a previous study 18 and are detailed in the following paragraph of this paper, addressing the assessment of either volcanic or anthropogenic CO 2 in the air at Naples’ urban area. This methodology integrates measurements of stable CO 2 isotopes in the air with isotopic signatures of both the local CO 2 source, determined through the Keeling plot method 49 , 50 , and CO 2 in the background air. The theoretical outcomes of the model facilitate the partitioning of CO 2 in the air between the local background air and the CO 2 source.

The Keeling plot 49 , 50 , is the method broadly used to identify the isotopic signature of the gas source that increases CO 2 concentrations at the atmospheric background. The Keeling plot method facilitates the examination of the primary origin of atmospheric CO 2 by analyzing the δ 13 C–CO 2 against the reciprocal of CO 2 concentration. This method relies on mass balance principles, wherein a local CO 2 source alters the concentration from the atmospheric baseline. Mathematically, this is expressed by equations:

where C and δ 13 C denote CO 2 concentration and δ 13 C–CO 2 , respectively. Subscripts denote measured values (m), atmospheric background (a), and local source (fs). The linear combination of these equations generates a straight line in the δ 13 C versus 1/C plot 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 as delineated by equation

Equation ( 3 ) provides insight into the carbon isotope composition of the local CO 2 source under constant background and CO 2 source conditions.

To identify the main CO 2 source downtown Naples, a subset of measurements was selected. This subset encompasses measurements collected in an area of 24.60 km 2 centred in the Plebiscito square district of Naples (436,676.0 E and 4,520,817.0 N). Another subset, with its centre in the Pozzuoli area (Lat: 428,058.0 E; Long: 4,520,131.0 N, UTM), was selected for comparative purposes with data collected in Naples’ downtown. Specifically focusing on Pozzuoli (Zone A), the assessment focused on volcanic CO 2 as the primary source of CO 2 in the air. The measurements used in the theoretical model results (Eq. ( 11 ) reported below in this study) provide the concentration of the isotopically marked CO 2 source (e.g., volcanic or anthropogenic), causing the airborne CO 2 concentration to exceed the background concentration, point by point within the area. In the case of the Solfatara-Pisciarelli degassing area (Zone A in Fig.  1 ), the circular area is 47.28 km 2 , and the theoretical model provides the concentration of volcanic CO 2 (C V ). Following this calculation, the interpolation of C V values using the Kriging algorithm generates simulations of CO 2 from the forcing source (volcanic or anthropogenic for Solfatara-Pisciarelli and Naples' downtown, respectively). This algorithm produces the prediction layer for δ 13 C–CO 2 , δ 18 O–CO 2 , CO 2 concentration, and concentration (C V or C F , respectively) based on the assumption that each interpolating variable changes linearly with the distance between adjacent measurements. This assumption aligns with the expected homogeneity of spatial variations in atmospheric variables at the local scale 7 . Kriging interpolation is a geostatistical method used to estimate unknown values of each spatial variable based on known measurements of δ 13 C–CO 2 , δ 18 O–CO 2 , and CO 2 concentration at specific measurement points. The spatial correlation of the data is modeled using a Gaussian variogram, a standard variogram model defined by the equation:

where γ(h) is the semivariance at lag distance h, C 0 is the nugget, C is the partial sill, and a is the range. The kriging system of equations is set up using the Gaussian variogram model to determine the weights assigned to each known data point. These weights are calculated to minimize the estimation variance for the unknown points. The Gaussian model ensures smooth interpolation with continuous and differentiable transitions between estimated values, reflecting the assumed autocorrelation structure of the data.

Based on variogram analysis, CO 2 concentration measurements (Supplementary Fig. S1 online) are spatially dependent up to 700 m (i.e., the range), beyond which they become substantially independent. The range for δ 13 C–CO 2 , indicating the distance at which spatial correlation between carbon isotope measurements becomes negligible, has also been set to 700 m for kriging interpolation. For δ 18 O–CO 2 measurements, the range was determined to be 800 m. The partial sill was calculated as 1780 for CO₂ concentration, 1.62 for δ 13 C–CO 2 , and 1.65 for δ 18 O–CO 2 , indicating the variance attributable to the spatial structure for each variable. Simulations of stable isotope variables, airborne CO 2 concentration, and volcanic CO 2 dispersion were executed using the SAGA GIS software package ( https://saga-gis.sourceforge.io/en/index.html ).

Quantification of the CO 2 input in the atmosphere

An appropriate mass balance model for airborne CO 2 incorporates both isotopic parameters and concentration. Utilizing literature values for δ 13 C–CO 2 and δ 18 O–CO 2 of standard air (e.g., δ 13 C–CO 2  =  − 8‰ and δ 18 O–CO 2  =  − 0.1‰ 50 ) alongside values specific to CO 2 of external sources (e.g., either volcanic/hydrothermal or fossil fuel derived CO 2 ), an isotopic mass balance model incorporates four unknowns: background air CO 2 concentration, CO 2 concentration in the forcing source of gas, air CO 2 mixing fraction, and volcanic CO 2 mixing fraction.

The model is expressed by Eq. ( 5 ), which represents the CO 2 concentration in the air:

where C represents the CO 2 concentration and X denotes the mixing fraction between forcing source and atmospheric CO 2 , with subscripts m, a, and fs referring to measured, background, and local forcing source of CO 2 , respectively. This model operates under the assumptions that external source (i.e., volcanic or fossil fuel derived CO 2 ) significantly elevates CO 2 concentration relative to background levels.

The binary mixing equation to determine the relative weights of CO 2 from volcanic and atmospheric sources is given by Eq. ( 6 ):

Similarly, Eqs. ( 7 )

describe the isotopic mass balance models for carbon and oxygen isotopes of CO 2 , respectively. The combination of Eq. ( 6 ) and ( 7 ) provides Eq. ( 9 ), which allows for the calculation of X a

Using Eq. ( 9 ) in Eq. ( 8 ) yields Eq. ( 10 ), enabling the determination of X FS

By employing both Eqs. ( 9 ) and ( 10 ) and rearranging Eq. ( 5 ), we derive Eq. ( 11 )

which provides the concentration of CO 2 produced by the local effective gas source in the air C fs .

Airborne CO 2 partitioning of between volcanic and human related components

Cluster analysis was conducted to explore the relationships between airborne CO 2 concentrations and carbon isotope composition. Cluster analysis facilitates the classification of observational datasets into distinct classes based on specified similarity criteria. The objective of this analysis is to discern several groups of data that exhibit internal homogeneity (i.e., similarity criteria) while displaying heterogeneity among themselves concerning both CO 2 concentration and stable isotope compositions (i.e., δ 13 C–CO 2 and δ 18 O–CO 2 values). Various clustering methods are available for partitioning datasets (e.g., k-means, hierarchical, and two-way clustering), each differing in the requirement of preselecting the number of clusters, statistical properties of the dataset, or computational complexity.

Hierarchical clustering enables the grouping of objects such that those within a group are similar to each other and distinct from objects in other groups. Hierarchical clustering holds an advantage over alternative methods as it obviates the necessity of specifying the number of clusters a priori. The hierarchical structure of clusters can be formed using partitioning algorithms, initially considering all objects as individual clusters. Subsequently, through an iterative process, objects are assigned to different clusters based on principles maximizing the inter-cluster distances. One variant of hierarchical clustering is agglomerative clustering, where each object begins as its own cluster, and pairs of smaller clusters are successively merged until all data is encompassed within a single cluster. Essentially, hierarchical clustering assesses object similarity (i.e., distance) to form new clusters. Cluster merging is predicated on the Euclidean distance metric, reflecting the sum of squares of object coordinates in Euclidean space. Calculation of Euclidean distances leads to the updating of the distance matrix, with the iterative process culminating in the merging of the last two clusters into a final cluster encompassing the entire dataset.

Multiple approaches exist for computing inter-cluster distances and updating the proximity matrix, with some (e.g., single linkage or complete linkage) assessing minimum or maximum distances between objects from different clusters. In the cluster analysis of our dataset, we employed the Ward approach, which evaluates cluster variance rather than directly measuring distances, aiming to minimize variance among clusters. In Ward's method, the distance between two clusters is contingent upon the increase in the sum of squares when the clusters are combined. Ward's method implementation seeks to minimize the sum of squares distances of points from cluster centroids. In contrast to other distance-based methods, Ward's method exhibits less susceptibility to noise and outliers. Hence, in this paper, the Ward method is preferred over alternative methods for clustering.

Conclusions

This study presents findings from a spatial survey conducted in the metropolitan area of Naples, Italy, aimed at examining potential variations in atmospheric CO 2 sources. The urban zone of Naples was chosen due to its diverse CO 2 sources, including those from both geological (e.g., volcanic/hydrothermal emissions) and anthropogenic (e.g., combustion-related) origins. Situated within the extensive volcanic zone hosting Vesuvius, Campi Flegrei, and active volcano on Ischia, Naples provides a compelling location for such investigation owing to its dense urban population compared to other urban areas in the European continent.

Identification of CO 2 sources was facilitated through a combination of stable isotopic analysis and concentration measurements. Stable isotopic composition (i.e., carbon and oxygen isotopic ratios) and airborne CO 2 concentration were measured using a high-precision laser-based analyzer installed in an SUV vehicle. Measurements, recorded at 1 Hz, were synchronized with GPS data to ascertain spatial positioning, achieving a spatial resolution on a metric scale.

Spatial variations in both isotopic composition and concentration were derived from the dataset using the kriging algorithm with Gaussian autocorrelation. Resulting maps delineated three zones characterized by elevated CO 2 concentrations exhibiting distinct stable isotopic signatures. The zone with the highest CO 2 concentration encompassed Naples’ downtown and harbour district, while intermediate concentrations were observed inland across the urban area. Spatial simulations indicated lower CO 2 concentrations along the seaside to the west of downtown, consistent with local morning atmospheric circulation patterns oriented from SW to NE. Additional zones of heightened CO 2 concentrations were identified near the airport, situated northeast of downtown, and in proximity to inhabited areas such as Pozzuoli and Pisciarelli, near Solfatara to the west. These last areas (Pozzuoli and Pisciarelli) exhibit manifestations of a broad hydrothermal/magmatic system beneath the Campi Flegrei, constituting a geological source of airborne CO 2 . Anthropogenic CO 2 emissions, primarily from vehicular engine combustion, were found to elevate CO 2 concentrations above background levels in downtown Naples, near the airport, and in the vicinity of Solfatara.

A mixing model incorporating stable isotope composition and airborne CO 2 concentration allowed quantification of CO 2 contributions from different sources. Geochemical modeling based on this approach revealed spatial dispersal patterns of additional CO 2 near Solfatara and downtown Naples, with volcanic CO 2 dispersing northeastward under prevailing morning winds northeast oriented. This volcanic CO 2 extends beyond the hydrothermal zone, supplementing anthropogenic CO 2 emissions from vehicular traffic.

This study underscores the utility of combining isotopic and CO 2 concentration data for discerning the dispersion of both endogenous greenhouse CO 2 and emissions from anthropogenic activities. Particularly relevant in densely populated volcanic/hydrothermal regions, this methodology effectively distinguishes between natural and anthropogenic gas emissions in the atmosphere, overcoming challenges associated with high background levels and subtle spatial variations of the airborne CO 2 . Measurements in Naples were collected within a single day, during the diurnal phase of the planetary boundary layer (PBL) evolution, under turbulent conditions and mixing of the atmospheric layer closest to the ground. Consequently, the CO 2 dispersal maps represent average conditions for the urban area of Naples. Establishing monitoring programs for the concentration and isotopic composition of airborne CO 2 in Naples and other cities is crucial for studying the impact of the daily evolution of the PBL on potential variations in airborne CO 2 . This is particularly important in areas where geogenic sources (i.e., volcanic or hydrothermal) coexist with anthropogenic CO 2 emissions (e.g., from fossil fuel combustion) resulting from high population density.

Data availability

The datasets generated during and/or analyzed during the current study are available in the ZENODO repository, https://zenodo.org/records/11300873 .

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Di Martino, R.M.R., Gurrieri, S., Paonita, A. et al. Unveiling spatial variations in atmospheric CO 2 sources: a case study of metropolitan area of Naples, Italy. Sci Rep 14 , 20483 (2024). https://doi.org/10.1038/s41598-024-71348-9

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DOI : https://doi.org/10.1038/s41598-024-71348-9

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