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Research Design – Types, Methods and Examples

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Research Design

Definition:

Research design refers to the overall strategy or plan for conducting a research study. It outlines the methods and procedures that will be used to collect and analyze data, as well as the goals and objectives of the study. Research design is important because it guides the entire research process and ensures that the study is conducted in a systematic and rigorous manner.

Types of Research Design

Types of Research Design are as follows:

Descriptive Research Design

This type of research design is used to describe a phenomenon or situation. It involves collecting data through surveys, questionnaires, interviews, and observations. The aim of descriptive research is to provide an accurate and detailed portrayal of a particular group, event, or situation. It can be useful in identifying patterns, trends, and relationships in the data.

Correlational Research Design

Correlational research design is used to determine if there is a relationship between two or more variables. This type of research design involves collecting data from participants and analyzing the relationship between the variables using statistical methods. The aim of correlational research is to identify the strength and direction of the relationship between the variables.

Experimental Research Design

Experimental research design is used to investigate cause-and-effect relationships between variables. This type of research design involves manipulating one variable and measuring the effect on another variable. It usually involves randomly assigning participants to groups and manipulating an independent variable to determine its effect on a dependent variable. The aim of experimental research is to establish causality.

Quasi-experimental Research Design

Quasi-experimental research design is similar to experimental research design, but it lacks one or more of the features of a true experiment. For example, there may not be random assignment to groups or a control group. This type of research design is used when it is not feasible or ethical to conduct a true experiment.

Case Study Research Design

Case study research design is used to investigate a single case or a small number of cases in depth. It involves collecting data through various methods, such as interviews, observations, and document analysis. The aim of case study research is to provide an in-depth understanding of a particular case or situation.

Longitudinal Research Design

Longitudinal research design is used to study changes in a particular phenomenon over time. It involves collecting data at multiple time points and analyzing the changes that occur. The aim of longitudinal research is to provide insights into the development, growth, or decline of a particular phenomenon over time.

Structure of Research Design

The format of a research design typically includes the following sections:

• Introduction : This section provides an overview of the research problem, the research questions, and the importance of the study. It also includes a brief literature review that summarizes previous research on the topic and identifies gaps in the existing knowledge.
• Research Questions or Hypotheses: This section identifies the specific research questions or hypotheses that the study will address. These questions should be clear, specific, and testable.
• Research Methods : This section describes the methods that will be used to collect and analyze data. It includes details about the study design, the sampling strategy, the data collection instruments, and the data analysis techniques.
• Data Collection: This section describes how the data will be collected, including the sample size, data collection procedures, and any ethical considerations.
• Data Analysis: This section describes how the data will be analyzed, including the statistical techniques that will be used to test the research questions or hypotheses.
• Results : This section presents the findings of the study, including descriptive statistics and statistical tests.
• Discussion and Conclusion : This section summarizes the key findings of the study, interprets the results, and discusses the implications of the findings. It also includes recommendations for future research.
• References : This section lists the sources cited in the research design.

Example of Research Design

An Example of Research Design could be:

Research question: Does the use of social media affect the academic performance of high school students?

Research design:

• Research approach : The research approach will be quantitative as it involves collecting numerical data to test the hypothesis.
• Research design : The research design will be a quasi-experimental design, with a pretest-posttest control group design.
• Sample : The sample will be 200 high school students from two schools, with 100 students in the experimental group and 100 students in the control group.
• Data collection : The data will be collected through surveys administered to the students at the beginning and end of the academic year. The surveys will include questions about their social media usage and academic performance.
• Data analysis : The data collected will be analyzed using statistical software. The mean scores of the experimental and control groups will be compared to determine whether there is a significant difference in academic performance between the two groups.
• Limitations : The limitations of the study will be acknowledged, including the fact that social media usage can vary greatly among individuals, and the study only focuses on two schools, which may not be representative of the entire population.
• Ethical considerations: Ethical considerations will be taken into account, such as obtaining informed consent from the participants and ensuring their anonymity and confidentiality.

How to Write Research Design

Writing a research design involves planning and outlining the methodology and approach that will be used to answer a research question or hypothesis. Here are some steps to help you write a research design:

• Define the research question or hypothesis : Before beginning your research design, you should clearly define your research question or hypothesis. This will guide your research design and help you select appropriate methods.
• Select a research design: There are many different research designs to choose from, including experimental, survey, case study, and qualitative designs. Choose a design that best fits your research question and objectives.
• Develop a sampling plan : If your research involves collecting data from a sample, you will need to develop a sampling plan. This should outline how you will select participants and how many participants you will include.
• Define variables: Clearly define the variables you will be measuring or manipulating in your study. This will help ensure that your results are meaningful and relevant to your research question.
• Choose data collection methods : Decide on the data collection methods you will use to gather information. This may include surveys, interviews, observations, experiments, or secondary data sources.
• Create a data analysis plan: Develop a plan for analyzing your data, including the statistical or qualitative techniques you will use.
• Consider ethical concerns : Finally, be sure to consider any ethical concerns related to your research, such as participant confidentiality or potential harm.

When to Write Research Design

Research design should be written before conducting any research study. It is an important planning phase that outlines the research methodology, data collection methods, and data analysis techniques that will be used to investigate a research question or problem. The research design helps to ensure that the research is conducted in a systematic and logical manner, and that the data collected is relevant and reliable.

Ideally, the research design should be developed as early as possible in the research process, before any data is collected. This allows the researcher to carefully consider the research question, identify the most appropriate research methodology, and plan the data collection and analysis procedures in advance. By doing so, the research can be conducted in a more efficient and effective manner, and the results are more likely to be valid and reliable.

Purpose of Research Design

The purpose of research design is to plan and structure a research study in a way that enables the researcher to achieve the desired research goals with accuracy, validity, and reliability. Research design is the blueprint or the framework for conducting a study that outlines the methods, procedures, techniques, and tools for data collection and analysis.

Some of the key purposes of research design include:

• Providing a clear and concise plan of action for the research study.
• Ensuring that the research is conducted ethically and with rigor.
• Maximizing the accuracy and reliability of the research findings.
• Minimizing the possibility of errors, biases, or confounding variables.
• Ensuring that the research is feasible, practical, and cost-effective.
• Determining the appropriate research methodology to answer the research question(s).
• Identifying the sample size, sampling method, and data collection techniques.
• Determining the data analysis method and statistical tests to be used.
• Facilitating the replication of the study by other researchers.
• Enhancing the validity and generalizability of the research findings.

Applications of Research Design

There are numerous applications of research design in various fields, some of which are:

• Social sciences: In fields such as psychology, sociology, and anthropology, research design is used to investigate human behavior and social phenomena. Researchers use various research designs, such as experimental, quasi-experimental, and correlational designs, to study different aspects of social behavior.
• Education : Research design is essential in the field of education to investigate the effectiveness of different teaching methods and learning strategies. Researchers use various designs such as experimental, quasi-experimental, and case study designs to understand how students learn and how to improve teaching practices.
• Health sciences : In the health sciences, research design is used to investigate the causes, prevention, and treatment of diseases. Researchers use various designs, such as randomized controlled trials, cohort studies, and case-control studies, to study different aspects of health and healthcare.
• Business : Research design is used in the field of business to investigate consumer behavior, marketing strategies, and the impact of different business practices. Researchers use various designs, such as survey research, experimental research, and case studies, to study different aspects of the business world.
• Engineering : In the field of engineering, research design is used to investigate the development and implementation of new technologies. Researchers use various designs, such as experimental research and case studies, to study the effectiveness of new technologies and to identify areas for improvement.

Advantages of Research Design

Here are some advantages of research design:

• Systematic and organized approach : A well-designed research plan ensures that the research is conducted in a systematic and organized manner, which makes it easier to manage and analyze the data.
• Clear objectives: The research design helps to clarify the objectives of the study, which makes it easier to identify the variables that need to be measured, and the methods that need to be used to collect and analyze data.
• Minimizes bias: A well-designed research plan minimizes the chances of bias, by ensuring that the data is collected and analyzed objectively, and that the results are not influenced by the researcher’s personal biases or preferences.
• Efficient use of resources: A well-designed research plan helps to ensure that the resources (time, money, and personnel) are used efficiently and effectively, by focusing on the most important variables and methods.
• Replicability: A well-designed research plan makes it easier for other researchers to replicate the study, which enhances the credibility and reliability of the findings.
• Validity: A well-designed research plan helps to ensure that the findings are valid, by ensuring that the methods used to collect and analyze data are appropriate for the research question.
• Generalizability : A well-designed research plan helps to ensure that the findings can be generalized to other populations, settings, or situations, which increases the external validity of the study.

Research Design Vs Research Methodology

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Muhammad Hassan

Researcher, Academic Writer, Web developer

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Study designs: Part 1 – An overview and classification

Priya ranganathan.

Department of Anaesthesiology, Tata Memorial Centre, Mumbai, Maharashtra, India

Rakesh Aggarwal

1 Department of Gastroenterology, Sanjay Gandhi Postgraduate Institute of Medical Sciences, Lucknow, Uttar Pradesh, India

There are several types of research study designs, each with its inherent strengths and flaws. The study design used to answer a particular research question depends on the nature of the question and the availability of resources. In this article, which is the first part of a series on “study designs,” we provide an overview of research study designs and their classification. The subsequent articles will focus on individual designs.

INTRODUCTION

Research study design is a framework, or the set of methods and procedures used to collect and analyze data on variables specified in a particular research problem.

Research study designs are of many types, each with its advantages and limitations. The type of study design used to answer a particular research question is determined by the nature of question, the goal of research, and the availability of resources. Since the design of a study can affect the validity of its results, it is important to understand the different types of study designs and their strengths and limitations.

There are some terms that are used frequently while classifying study designs which are described in the following sections.

A variable represents a measurable attribute that varies across study units, for example, individual participants in a study, or at times even when measured in an individual person over time. Some examples of variables include age, sex, weight, height, health status, alive/dead, diseased/healthy, annual income, smoking yes/no, and treated/untreated.

Exposure (or intervention) and outcome variables

A large proportion of research studies assess the relationship between two variables. Here, the question is whether one variable is associated with or responsible for change in the value of the other variable. Exposure (or intervention) refers to the risk factor whose effect is being studied. It is also referred to as the independent or the predictor variable. The outcome (or predicted or dependent) variable develops as a consequence of the exposure (or intervention). Typically, the term “exposure” is used when the “causative” variable is naturally determined (as in observational studies – examples include age, sex, smoking, and educational status), and the term “intervention” is preferred where the researcher assigns some or all participants to receive a particular treatment for the purpose of the study (experimental studies – e.g., administration of a drug). If a drug had been started in some individuals but not in the others, before the study started, this counts as exposure, and not as intervention – since the drug was not started specifically for the study.

Observational versus interventional (or experimental) studies

Observational studies are those where the researcher is documenting a naturally occurring relationship between the exposure and the outcome that he/she is studying. The researcher does not do any active intervention in any individual, and the exposure has already been decided naturally or by some other factor. For example, looking at the incidence of lung cancer in smokers versus nonsmokers, or comparing the antenatal dietary habits of mothers with normal and low-birth babies. In these studies, the investigator did not play any role in determining the smoking or dietary habit in individuals.

For an exposure to determine the outcome, it must precede the latter. Any variable that occurs simultaneously with or following the outcome cannot be causative, and hence is not considered as an “exposure.”

Observational studies can be either descriptive (nonanalytical) or analytical (inferential) – this is discussed later in this article.

Interventional studies are experiments where the researcher actively performs an intervention in some or all members of a group of participants. This intervention could take many forms – for example, administration of a drug or vaccine, performance of a diagnostic or therapeutic procedure, and introduction of an educational tool. For example, a study could randomly assign persons to receive aspirin or placebo for a specific duration and assess the effect on the risk of developing cerebrovascular events.

Descriptive versus analytical studies

Descriptive (or nonanalytical) studies, as the name suggests, merely try to describe the data on one or more characteristics of a group of individuals. These do not try to answer questions or establish relationships between variables. Examples of descriptive studies include case reports, case series, and cross-sectional surveys (please note that cross-sectional surveys may be analytical studies as well – this will be discussed in the next article in this series). Examples of descriptive studies include a survey of dietary habits among pregnant women or a case series of patients with an unusual reaction to a drug.

Analytical studies attempt to test a hypothesis and establish causal relationships between variables. In these studies, the researcher assesses the effect of an exposure (or intervention) on an outcome. As described earlier, analytical studies can be observational (if the exposure is naturally determined) or interventional (if the researcher actively administers the intervention).

Directionality of study designs

Based on the direction of inquiry, study designs may be classified as forward-direction or backward-direction. In forward-direction studies, the researcher starts with determining the exposure to a risk factor and then assesses whether the outcome occurs at a future time point. This design is known as a cohort study. For example, a researcher can follow a group of smokers and a group of nonsmokers to determine the incidence of lung cancer in each. In backward-direction studies, the researcher begins by determining whether the outcome is present (cases vs. noncases [also called controls]) and then traces the presence of prior exposure to a risk factor. These are known as case–control studies. For example, a researcher identifies a group of normal-weight babies and a group of low-birth weight babies and then asks the mothers about their dietary habits during the index pregnancy.

Prospective versus retrospective study designs

The terms “prospective” and “retrospective” refer to the timing of the research in relation to the development of the outcome. In retrospective studies, the outcome of interest has already occurred (or not occurred – e.g., in controls) in each individual by the time s/he is enrolled, and the data are collected either from records or by asking participants to recall exposures. There is no follow-up of participants. By contrast, in prospective studies, the outcome (and sometimes even the exposure or intervention) has not occurred when the study starts and participants are followed up over a period of time to determine the occurrence of outcomes. Typically, most cohort studies are prospective studies (though there may be retrospective cohorts), whereas case–control studies are retrospective studies. An interventional study has to be, by definition, a prospective study since the investigator determines the exposure for each study participant and then follows them to observe outcomes.

The terms “prospective” versus “retrospective” studies can be confusing. Let us think of an investigator who starts a case–control study. To him/her, the process of enrolling cases and controls over a period of several months appears prospective. Hence, the use of these terms is best avoided. Or, at the very least, one must be clear that the terms relate to work flow for each individual study participant, and not to the study as a whole.

Classification of study designs

Figure 1 depicts a simple classification of research study designs. The Centre for Evidence-based Medicine has put forward a useful three-point algorithm which can help determine the design of a research study from its methods section:[ 1 ]

Classification of research study designs

• Does the study describe the characteristics of a sample or does it attempt to analyze (or draw inferences about) the relationship between two variables? – If no, then it is a descriptive study, and if yes, it is an analytical (inferential) study
• If analytical, did the investigator determine the exposure? – If no, it is an observational study, and if yes, it is an experimental study
• If observational, when was the outcome determined? – at the start of the study (case–control study), at the end of a period of follow-up (cohort study), or simultaneously (cross sectional).

In the next few pieces in the series, we will discuss various study designs in greater detail.

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The Research Problem & Statement

What they are & how to write them (with examples)

By: Derek Jansen (MBA) | Expert Reviewed By: Eunice Rautenbach (DTech) | March 2023

If you’re new to academic research, you’re bound to encounter the concept of a “ research problem ” or “ problem statement ” fairly early in your learning journey. Having a good research problem is essential, as it provides a foundation for developing high-quality research, from relatively small research papers to a full-length PhD dissertations and theses.

In this post, we’ll unpack what a research problem is and how it’s related to a problem statement . We’ll also share some examples and provide a step-by-step process you can follow to identify and evaluate study-worthy research problems for your own project.

Overview: Research Problem 101

What is a research problem.

• What is a problem statement?

Where do research problems come from?

• How to find a suitable research problem
• Key takeaways

A research problem is, at the simplest level, the core issue that a study will try to solve or (at least) examine. In other words, it’s an explicit declaration about the problem that your dissertation, thesis or research paper will address. More technically, it identifies the research gap that the study will attempt to fill (more on that later).

Let’s look at an example to make the research problem a little more tangible.

To justify a hypothetical study, you might argue that there’s currently a lack of research regarding the challenges experienced by first-generation college students when writing their dissertations [ PROBLEM ] . As a result, these students struggle to successfully complete their dissertations, leading to higher-than-average dropout rates [ CONSEQUENCE ]. Therefore, your study will aim to address this lack of research – i.e., this research problem [ SOLUTION ].

A research problem can be theoretical in nature, focusing on an area of academic research that is lacking in some way. Alternatively, a research problem can be more applied in nature, focused on finding a practical solution to an established problem within an industry or an organisation. In other words, theoretical research problems are motivated by the desire to grow the overall body of knowledge , while applied research problems are motivated by the need to find practical solutions to current real-world problems (such as the one in the example above).

As you can probably see, the research problem acts as the driving force behind any study , as it directly shapes the research aims, objectives and research questions , as well as the research approach. Therefore, it’s really important to develop a very clearly articulated research problem before you even start your research proposal . A vague research problem will lead to unfocused, potentially conflicting research aims, objectives and research questions .

What is a research problem statement?

As the name suggests, a problem statement (within a research context, at least) is an explicit statement that clearly and concisely articulates the specific research problem your study will address. While your research problem can span over multiple paragraphs, your problem statement should be brief , ideally no longer than one paragraph . Importantly, it must clearly state what the problem is (whether theoretical or practical in nature) and how the study will address it.

Here’s an example of a statement of the problem in a research context:

Rural communities across Ghana lack access to clean water, leading to high rates of waterborne illnesses and infant mortality. Despite this, there is little research investigating the effectiveness of community-led water supply projects within the Ghanaian context. Therefore, this study aims to investigate the effectiveness of such projects in improving access to clean water and reducing rates of waterborne illnesses in these communities.

As you can see, this problem statement clearly and concisely identifies the issue that needs to be addressed (i.e., a lack of research regarding the effectiveness of community-led water supply projects) and the research question that the study aims to answer (i.e., are community-led water supply projects effective in reducing waterborne illnesses?), all within one short paragraph.

Need a helping hand?

Wherever there is a lack of well-established and agreed-upon academic literature , there is an opportunity for research problems to arise, since there is a paucity of (credible) knowledge. In other words, research problems are derived from research gaps . These gaps can arise from various sources, including the emergence of new frontiers or new contexts, as well as disagreements within the existing research.

Let’s look at each of these scenarios:

New frontiers – new technologies, discoveries or breakthroughs can open up entirely new frontiers where there is very little existing research, thereby creating fresh research gaps. For example, as generative AI technology became accessible to the general public in 2023, the full implications and knock-on effects of this were (or perhaps, still are) largely unknown and therefore present multiple avenues for researchers to explore.

New contexts – very often, existing research tends to be concentrated on specific contexts and geographies. Therefore, even within well-studied fields, there is often a lack of research within niche contexts. For example, just because a study finds certain results within a western context doesn’t mean that it would necessarily find the same within an eastern context. If there’s reason to believe that results may vary across these geographies, a potential research gap emerges.

Disagreements – within many areas of existing research, there are (quite naturally) conflicting views between researchers, where each side presents strong points that pull in opposing directions. In such cases, it’s still somewhat uncertain as to which viewpoint (if any) is more accurate. As a result, there is room for further research in an attempt to “settle” the debate.

Of course, many other potential scenarios can give rise to research gaps, and consequently, research problems, but these common ones are a useful starting point. If you’re interested in research gaps, you can learn more here .

How to find a research problem

Given that research problems flow from research gaps , finding a strong research problem for your research project means that you’ll need to first identify a clear research gap. Below, we’ll present a four-step process to help you find and evaluate potential research problems.

If you’ve read our other articles about finding a research topic , you’ll find the process below very familiar as the research problem is the foundation of any study . In other words, finding a research problem is much the same as finding a research topic.

Step 1 – Identify your area of interest

Naturally, the starting point is to first identify a general area of interest . Chances are you already have something in mind, but if not, have a look at past dissertations and theses within your institution to get some inspiration. These present a goldmine of information as they’ll not only give you ideas for your own research, but they’ll also help you see exactly what the norms and expectations are for these types of projects.

At this stage, you don’t need to get super specific. The objective is simply to identify a couple of potential research areas that interest you. For example, if you’re undertaking research as part of a business degree, you may be interested in social media marketing strategies for small businesses, leadership strategies for multinational companies, etc.

Depending on the type of project you’re undertaking, there may also be restrictions or requirements regarding what topic areas you’re allowed to investigate, what type of methodology you can utilise, etc. So, be sure to first familiarise yourself with your institution’s specific requirements and keep these front of mind as you explore potential research ideas.

Step 2 – Review the literature and develop a shortlist

Once you’ve decided on an area that interests you, it’s time to sink your teeth into the literature . In other words, you’ll need to familiarise yourself with the existing research regarding your interest area. Google Scholar is a good starting point for this, as you can simply enter a few keywords and quickly get a feel for what’s out there. Keep an eye out for recent literature reviews and systematic review-type journal articles, as these will provide a good overview of the current state of research.

At this stage, you don’t need to read every journal article from start to finish . A good strategy is to pay attention to the abstract, intro and conclusion , as together these provide a snapshot of the key takeaways. As you work your way through the literature, keep an eye out for what’s missing – in other words, what questions does the current research not answer adequately (or at all)? Importantly, pay attention to the section titled “ further research is needed ”, typically found towards the very end of each journal article. This section will specifically outline potential research gaps that you can explore, based on the current state of knowledge (provided the article you’re looking at is recent).

Take the time to engage with the literature and develop a big-picture understanding of the current state of knowledge. Reviewing the literature takes time and is an iterative process , but it’s an essential part of the research process, so don’t cut corners at this stage.

As you work through the review process, take note of any potential research gaps that are of interest to you. From there, develop a shortlist of potential research gaps (and resultant research problems) – ideally 3 – 5 options that interest you.

Step 3 – Evaluate your potential options

Once you’ve developed your shortlist, you’ll need to evaluate your options to identify a winner. There are many potential evaluation criteria that you can use, but we’ll outline three common ones here: value, practicality and personal appeal.

Value – a good research problem needs to create value when successfully addressed. Ask yourself:

• Who will this study benefit (e.g., practitioners, researchers, academia)?
• How will it benefit them specifically?
• How much will it benefit them?

Practicality – a good research problem needs to be manageable in light of your resources. Ask yourself:

• What data will I need access to?
• What knowledge and skills will I need to undertake the analysis?
• What equipment or software will I need to process and/or analyse the data?
• How much time will I need?
• What costs might I incur?

Personal appeal – a research project is a commitment, so the research problem that you choose needs to be genuinely attractive and interesting to you. Ask yourself:

• How appealing is the prospect of solving this research problem (on a scale of 1 – 10)?
• Why, specifically, is it attractive (or unattractive) to me?
• Does the research align with my longer-term goals (e.g., career goals, educational path, etc)?

Depending on how many potential options you have, you may want to consider creating a spreadsheet where you numerically rate each of the options in terms of these criteria. Remember to also include any criteria specified by your institution . From there, tally up the numbers and pick a winner.

Step 4 – Craft your problem statement

Once you’ve selected your research problem, the final step is to craft a problem statement. Remember, your problem statement needs to be a concise outline of what the core issue is and how your study will address it. Aim to fit this within one paragraph – don’t waffle on. Have a look at the problem statement example we mentioned earlier if you need some inspiration.

Key Takeaways

We’ve covered a lot of ground. Let’s do a quick recap of the key takeaways:

• A research problem is an explanation of the issue that your study will try to solve. This explanation needs to highlight the problem , the consequence and the solution or response.
• A problem statement is a clear and concise summary of the research problem , typically contained within one paragraph.
• Research problems emerge from research gaps , which themselves can emerge from multiple potential sources, including new frontiers, new contexts or disagreements within the existing literature.
• To find a research problem, you need to first identify your area of interest , then review the literature and develop a shortlist, after which you’ll evaluate your options, select a winner and craft a problem statement .

Psst... there’s more!

This post was based on one of our popular Research Bootcamps . If you're working on a research project, you'll definitely want to check this out ...

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I APPRECIATE YOUR CONCISE AND MIND-CAPTIVATING INSIGHTS ON THE STATEMENT OF PROBLEMS. PLEASE I STILL NEED SOME SAMPLES RELATED TO SUICIDES.

Very pleased and appreciate clear information.

Your videos and information have been a life saver for me throughout my dissertation journey. I wish I’d discovered them sooner. Thank you!

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Research Design: What it is, Elements & Types

Can you imagine doing research without a plan? Probably not. When we discuss a strategy to collect, study, and evaluate data, we talk about research design. This design addresses problems and creates a consistent and logical model for data analysis. Let’s learn more about it.

What is Research Design?

Research design is the framework of research methods and techniques chosen by a researcher to conduct a study. The design allows researchers to sharpen the research methods suitable for the subject matter and set up their studies for success.

Creating a research topic explains the type of research (experimental,  survey research ,  correlational , semi-experimental, review) and its sub-type (experimental design, research problem , descriptive case-study). 

There are three main types of designs for research:

• Data collection
• Measurement
• Data Analysis

The research problem an organization faces will determine the design, not vice-versa. The design phase of a study determines which tools to use and how they are used.

The Process of Research Design

The research design process is a systematic and structured approach to conducting research. The process is essential to ensure that the study is valid, reliable, and produces meaningful results.

• Consider your aims and approaches: Determine the research questions and objectives, and identify the theoretical framework and methodology for the study.
• Choose a type of Research Design: Select the appropriate research design, such as experimental, correlational, survey, case study, or ethnographic, based on the research questions and objectives.
• Identify your population and sampling method: Determine the target population and sample size, and choose the sampling method, such as random , stratified random sampling , or convenience sampling.
• Choose your data collection methods: Decide on the data collection methods , such as surveys, interviews, observations, or experiments, and select the appropriate instruments or tools for collecting data.
• Plan your data collection procedures: Develop a plan for data collection, including the timeframe, location, and personnel involved, and ensure ethical considerations.
• Decide on your data analysis strategies: Select the appropriate data analysis techniques, such as statistical analysis , content analysis, or discourse analysis, and plan how to interpret the results.

The process of research design is a critical step in conducting research. By following the steps of research design, researchers can ensure that their study is well-planned, ethical, and rigorous.

Research Design Elements

Impactful research usually creates a minimum bias in data and increases trust in the accuracy of collected data. A design that produces the slightest margin of error in experimental research is generally considered the desired outcome. The essential elements are:

• Accurate purpose statement
• Techniques to be implemented for collecting and analyzing research
• The method applied for analyzing collected details
• Type of research methodology
• Probable objections to research
• Settings for the research study
• Measurement of analysis

Characteristics of Research Design

A proper design sets your study up for success. Successful research studies provide insights that are accurate and unbiased. You’ll need to create a survey that meets all of the main characteristics of a design. There are four key characteristics:

• Neutrality: When you set up your study, you may have to make assumptions about the data you expect to collect. The results projected in the research should be free from research bias and neutral. Understand opinions about the final evaluated scores and conclusions from multiple individuals and consider those who agree with the results.
• Reliability: With regularly conducted research, the researcher expects similar results every time. You’ll only be able to reach the desired results if your design is reliable. Your plan should indicate how to form research questions to ensure the standard of results.
• Validity: There are multiple measuring tools available. However, the only correct measuring tools are those which help a researcher in gauging results according to the objective of the research. The  questionnaire  developed from this design will then be valid.
• Generalization:  The outcome of your design should apply to a population and not just a restricted sample . A generalized method implies that your survey can be conducted on any part of a population with similar accuracy.

The above factors affect how respondents answer the research questions, so they should balance all the above characteristics in a good design. If you want, you can also learn about Selection Bias through our blog.

Research Design Types

A researcher must clearly understand the various types to select which model to implement for a study. Like the research itself, the design of your analysis can be broadly classified into quantitative and qualitative.

Qualitative research

Qualitative research determines relationships between collected data and observations based on mathematical calculations. Statistical methods can prove or disprove theories related to a naturally existing phenomenon. Researchers rely on qualitative observation research methods that conclude “why” a particular theory exists and “what” respondents have to say about it.

Quantitative research

Quantitative research is for cases where statistical conclusions to collect actionable insights are essential. Numbers provide a better perspective for making critical business decisions. Quantitative research methods are necessary for the growth of any organization. Insights drawn from complex numerical data and analysis prove to be highly effective when making decisions about the business’s future.

Qualitative Research vs Quantitative Research

Here is a chart that highlights the major differences between qualitative and quantitative research:

In summary or analysis , the step of qualitative research is more exploratory and focuses on understanding the subjective experiences of individuals, while quantitative research is more focused on objective data and statistical analysis.

You can further break down the types of research design into five categories:

1. Descriptive: In a descriptive composition, a researcher is solely interested in describing the situation or case under their research study. It is a theory-based design method created by gathering, analyzing, and presenting collected data. This allows a researcher to provide insights into the why and how of research. Descriptive design helps others better understand the need for the research. If the problem statement is not clear, you can conduct exploratory research. 

2. Experimental: Experimental research establishes a relationship between the cause and effect of a situation. It is a causal research design where one observes the impact caused by the independent variable on the dependent variable. For example, one monitors the influence of an independent variable such as a price on a dependent variable such as customer satisfaction or brand loyalty. It is an efficient research method as it contributes to solving a problem.

The independent variables are manipulated to monitor the change it has on the dependent variable. Social sciences often use it to observe human behavior by analyzing two groups. Researchers can have participants change their actions and study how the people around them react to understand social psychology better.

3. Correlational research: Correlational research  is a non-experimental research technique. It helps researchers establish a relationship between two closely connected variables. There is no assumption while evaluating a relationship between two other variables, and statistical analysis techniques calculate the relationship between them. This type of research requires two different groups.

A correlation coefficient determines the correlation between two variables whose values range between -1 and +1. If the correlation coefficient is towards +1, it indicates a positive relationship between the variables, and -1 means a negative relationship between the two variables. 

4. Diagnostic research: In diagnostic design, the researcher is looking to evaluate the underlying cause of a specific topic or phenomenon. This method helps one learn more about the factors that create troublesome situations. 

This design has three parts of the research:

• Inception of the issue
• Diagnosis of the issue
• Solution for the issue

5. Explanatory research : Explanatory design uses a researcher’s ideas and thoughts on a subject to further explore their theories. The study explains unexplored aspects of a subject and details the research questions’ what, how, and why.

Benefits of Research Design

There are several benefits of having a well-designed research plan. Including:

• Clarity of research objectives: Research design provides a clear understanding of the research objectives and the desired outcomes.
• Increased validity and reliability: To ensure the validity and reliability of results, research design help to minimize the risk of bias and helps to control extraneous variables.
• Improved data collection: Research design helps to ensure that the proper data is collected and data is collected systematically and consistently.
• Better data analysis: Research design helps ensure that the collected data can be analyzed effectively, providing meaningful insights and conclusions.
• Improved communication: A well-designed research helps ensure the results are clean and influential within the research team and external stakeholders.
• Efficient use of resources: reducing the risk of waste and maximizing the impact of the research, research design helps to ensure that resources are used efficiently.

A well-designed research plan is essential for successful research, providing clear and meaningful insights and ensuring that resources are practical.

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5 Research design

Research design is a comprehensive plan for data collection in an empirical research project. It is a ‘blueprint’ for empirical research aimed at answering specific research questions or testing specific hypotheses, and must specify at least three processes: the data collection process, the instrument development process, and the sampling process. The instrument development and sampling processes are described in the next two chapters, and the data collection process—which is often loosely called ‘research design’—is introduced in this chapter and is described in further detail in Chapters 9–12.

Broadly speaking, data collection methods can be grouped into two categories: positivist and interpretive. Positivist methods , such as laboratory experiments and survey research, are aimed at theory (or hypotheses) testing, while interpretive methods, such as action research and ethnography, are aimed at theory building. Positivist methods employ a deductive approach to research, starting with a theory and testing theoretical postulates using empirical data. In contrast, interpretive methods employ an inductive approach that starts with data and tries to derive a theory about the phenomenon of interest from the observed data. Often times, these methods are incorrectly equated with quantitative and qualitative research. Quantitative and qualitative methods refers to the type of data being collected—quantitative data involve numeric scores, metrics, and so on, while qualitative data includes interviews, observations, and so forth—and analysed (i.e., using quantitative techniques such as regression or qualitative techniques such as coding). Positivist research uses predominantly quantitative data, but can also use qualitative data. Interpretive research relies heavily on qualitative data, but can sometimes benefit from including quantitative data as well. Sometimes, joint use of qualitative and quantitative data may help generate unique insight into a complex social phenomenon that is not available from either type of data alone, and hence, mixed-mode designs that combine qualitative and quantitative data are often highly desirable.

Key attributes of a research design

The quality of research designs can be defined in terms of four key design attributes: internal validity, external validity, construct validity, and statistical conclusion validity.

Internal validity , also called causality, examines whether the observed change in a dependent variable is indeed caused by a corresponding change in a hypothesised independent variable, and not by variables extraneous to the research context. Causality requires three conditions: covariation of cause and effect (i.e., if cause happens, then effect also happens; if cause does not happen, effect does not happen), temporal precedence (cause must precede effect in time), and spurious correlation, or there is no plausible alternative explanation for the change. Certain research designs, such as laboratory experiments, are strong in internal validity by virtue of their ability to manipulate the independent variable (cause) via a treatment and observe the effect (dependent variable) of that treatment after a certain point in time, while controlling for the effects of extraneous variables. Other designs, such as field surveys, are poor in internal validity because of their inability to manipulate the independent variable (cause), and because cause and effect are measured at the same point in time which defeats temporal precedence making it equally likely that the expected effect might have influenced the expected cause rather than the reverse. Although higher in internal validity compared to other methods, laboratory experiments are by no means immune to threats of internal validity, and are susceptible to history, testing, instrumentation, regression, and other threats that are discussed later in the chapter on experimental designs. Nonetheless, different research designs vary considerably in their respective level of internal validity.

External validity or generalisability refers to whether the observed associations can be generalised from the sample to the population (population validity), or to other people, organisations, contexts, or time (ecological validity). For instance, can results drawn from a sample of financial firms in the United States be generalised to the population of financial firms (population validity) or to other firms within the United States (ecological validity)? Survey research, where data is sourced from a wide variety of individuals, firms, or other units of analysis, tends to have broader generalisability than laboratory experiments where treatments and extraneous variables are more controlled. The variation in internal and external validity for a wide range of research designs is shown in Figure 5.1.

Some researchers claim that there is a trade-off between internal and external validity—higher external validity can come only at the cost of internal validity and vice versa. But this is not always the case. Research designs such as field experiments, longitudinal field surveys, and multiple case studies have higher degrees of both internal and external validities. Personally, I prefer research designs that have reasonable degrees of both internal and external validities, i.e., those that fall within the cone of validity shown in Figure 5.1. But this should not suggest that designs outside this cone are any less useful or valuable. Researchers’ choice of designs are ultimately a matter of their personal preference and competence, and the level of internal and external validity they desire.

Construct validity examines how well a given measurement scale is measuring the theoretical construct that it is expected to measure. Many constructs used in social science research such as empathy, resistance to change, and organisational learning are difficult to define, much less measure. For instance, construct validity must ensure that a measure of empathy is indeed measuring empathy and not compassion, which may be difficult since these constructs are somewhat similar in meaning. Construct validity is assessed in positivist research based on correlational or factor analysis of pilot test data, as described in the next chapter.

Statistical conclusion validity examines the extent to which conclusions derived using a statistical procedure are valid. For example, it examines whether the right statistical method was used for hypotheses testing, whether the variables used meet the assumptions of that statistical test (such as sample size or distributional requirements), and so forth. Because interpretive research designs do not employ statistical tests, statistical conclusion validity is not applicable for such analysis. The different kinds of validity and where they exist at the theoretical/empirical levels are illustrated in Figure 5.2.

Improving internal and external validity

The best research designs are those that can ensure high levels of internal and external validity. Such designs would guard against spurious correlations, inspire greater faith in the hypotheses testing, and ensure that the results drawn from a small sample are generalisable to the population at large. Controls are required to ensure internal validity (causality) of research designs, and can be accomplished in five ways: manipulation, elimination, inclusion, and statistical control, and randomisation.

In manipulation , the researcher manipulates the independent variables in one or more levels (called ‘treatments’), and compares the effects of the treatments against a control group where subjects do not receive the treatment. Treatments may include a new drug or different dosage of drug (for treating a medical condition), a teaching style (for students), and so forth. This type of control is achieved in experimental or quasi-experimental designs, but not in non-experimental designs such as surveys. Note that if subjects cannot distinguish adequately between different levels of treatment manipulations, their responses across treatments may not be different, and manipulation would fail.

The elimination technique relies on eliminating extraneous variables by holding them constant across treatments, such as by restricting the study to a single gender or a single socioeconomic status. In the inclusion technique, the role of extraneous variables is considered by including them in the research design and separately estimating their effects on the dependent variable, such as via factorial designs where one factor is gender (male versus female). Such technique allows for greater generalisability, but also requires substantially larger samples. In statistical control , extraneous variables are measured and used as covariates during the statistical testing process.

Finally, the randomisation technique is aimed at cancelling out the effects of extraneous variables through a process of random sampling, if it can be assured that these effects are of a random (non-systematic) nature. Two types of randomisation are: random selection , where a sample is selected randomly from a population, and random assignment , where subjects selected in a non-random manner are randomly assigned to treatment groups.

Randomisation also ensures external validity, allowing inferences drawn from the sample to be generalised to the population from which the sample is drawn. Note that random assignment is mandatory when random selection is not possible because of resource or access constraints. However, generalisability across populations is harder to ascertain since populations may differ on multiple dimensions and you can only control for a few of those dimensions.

Popular research designs

As noted earlier, research designs can be classified into two categories—positivist and interpretive—depending on the goal of the research. Positivist designs are meant for theory testing, while interpretive designs are meant for theory building. Positivist designs seek generalised patterns based on an objective view of reality, while interpretive designs seek subjective interpretations of social phenomena from the perspectives of the subjects involved. Some popular examples of positivist designs include laboratory experiments, field experiments, field surveys, secondary data analysis, and case research, while examples of interpretive designs include case research, phenomenology, and ethnography. Note that case research can be used for theory building or theory testing, though not at the same time. Not all techniques are suited for all kinds of scientific research. Some techniques such as focus groups are best suited for exploratory research, others such as ethnography are best for descriptive research, and still others such as laboratory experiments are ideal for explanatory research. Following are brief descriptions of some of these designs. Additional details are provided in Chapters 9–12.

Experimental studies are those that are intended to test cause-effect relationships (hypotheses) in a tightly controlled setting by separating the cause from the effect in time, administering the cause to one group of subjects (the ‘treatment group’) but not to another group (‘control group’), and observing how the mean effects vary between subjects in these two groups. For instance, if we design a laboratory experiment to test the efficacy of a new drug in treating a certain ailment, we can get a random sample of people afflicted with that ailment, randomly assign them to one of two groups (treatment and control groups), administer the drug to subjects in the treatment group, but only give a placebo (e.g., a sugar pill with no medicinal value) to subjects in the control group. More complex designs may include multiple treatment groups, such as low versus high dosage of the drug or combining drug administration with dietary interventions. In a true experimental design , subjects must be randomly assigned to each group. If random assignment is not followed, then the design becomes quasi-experimental . Experiments can be conducted in an artificial or laboratory setting such as at a university (laboratory experiments) or in field settings such as in an organisation where the phenomenon of interest is actually occurring (field experiments). Laboratory experiments allow the researcher to isolate the variables of interest and control for extraneous variables, which may not be possible in field experiments. Hence, inferences drawn from laboratory experiments tend to be stronger in internal validity, but those from field experiments tend to be stronger in external validity. Experimental data is analysed using quantitative statistical techniques. The primary strength of the experimental design is its strong internal validity due to its ability to isolate, control, and intensively examine a small number of variables, while its primary weakness is limited external generalisability since real life is often more complex (i.e., involving more extraneous variables) than contrived lab settings. Furthermore, if the research does not identify ex ante relevant extraneous variables and control for such variables, such lack of controls may hurt internal validity and may lead to spurious correlations.

Field surveys are non-experimental designs that do not control for or manipulate independent variables or treatments, but measure these variables and test their effects using statistical methods. Field surveys capture snapshots of practices, beliefs, or situations from a random sample of subjects in field settings through a survey questionnaire or less frequently, through a structured interview. In cross-sectional field surveys , independent and dependent variables are measured at the same point in time (e.g., using a single questionnaire), while in longitudinal field surveys , dependent variables are measured at a later point in time than the independent variables. The strengths of field surveys are their external validity (since data is collected in field settings), their ability to capture and control for a large number of variables, and their ability to study a problem from multiple perspectives or using multiple theories. However, because of their non-temporal nature, internal validity (cause-effect relationships) are difficult to infer, and surveys may be subject to respondent biases (e.g., subjects may provide a ‘socially desirable’ response rather than their true response) which further hurts internal validity.

Secondary data analysis is an analysis of data that has previously been collected and tabulated by other sources. Such data may include data from government agencies such as employment statistics from the U.S. Bureau of Labor Services or development statistics by countries from the United Nations Development Program, data collected by other researchers (often used in meta-analytic studies), or publicly available third-party data, such as financial data from stock markets or real-time auction data from eBay. This is in contrast to most other research designs where collecting primary data for research is part of the researcher’s job. Secondary data analysis may be an effective means of research where primary data collection is too costly or infeasible, and secondary data is available at a level of analysis suitable for answering the researcher’s questions. The limitations of this design are that the data might not have been collected in a systematic or scientific manner and hence unsuitable for scientific research, since the data was collected for a presumably different purpose, they may not adequately address the research questions of interest to the researcher, and interval validity is problematic if the temporal precedence between cause and effect is unclear.

Case research is an in-depth investigation of a problem in one or more real-life settings (case sites) over an extended period of time. Data may be collected using a combination of interviews, personal observations, and internal or external documents. Case studies can be positivist in nature (for hypotheses testing) or interpretive (for theory building). The strength of this research method is its ability to discover a wide variety of social, cultural, and political factors potentially related to the phenomenon of interest that may not be known in advance. Analysis tends to be qualitative in nature, but heavily contextualised and nuanced. However, interpretation of findings may depend on the observational and integrative ability of the researcher, lack of control may make it difficult to establish causality, and findings from a single case site may not be readily generalised to other case sites. Generalisability can be improved by replicating and comparing the analysis in other case sites in a multiple case design .

Focus group research is a type of research that involves bringing in a small group of subjects (typically six to ten people) at one location, and having them discuss a phenomenon of interest for a period of one and a half to two hours. The discussion is moderated and led by a trained facilitator, who sets the agenda and poses an initial set of questions for participants, makes sure that the ideas and experiences of all participants are represented, and attempts to build a holistic understanding of the problem situation based on participants’ comments and experiences. Internal validity cannot be established due to lack of controls and the findings may not be generalised to other settings because of the small sample size. Hence, focus groups are not generally used for explanatory or descriptive research, but are more suited for exploratory research.

Action research assumes that complex social phenomena are best understood by introducing interventions or ‘actions’ into those phenomena and observing the effects of those actions. In this method, the researcher is embedded within a social context such as an organisation and initiates an action—such as new organisational procedures or new technologies—in response to a real problem such as declining profitability or operational bottlenecks. The researcher’s choice of actions must be based on theory, which should explain why and how such actions may cause the desired change. The researcher then observes the results of that action, modifying it as necessary, while simultaneously learning from the action and generating theoretical insights about the target problem and interventions. The initial theory is validated by the extent to which the chosen action successfully solves the target problem. Simultaneous problem solving and insight generation is the central feature that distinguishes action research from all other research methods, and hence, action research is an excellent method for bridging research and practice. This method is also suited for studying unique social problems that cannot be replicated outside that context, but it is also subject to researcher bias and subjectivity, and the generalisability of findings is often restricted to the context where the study was conducted.

Ethnography is an interpretive research design inspired by anthropology that emphasises that research phenomenon must be studied within the context of its culture. The researcher is deeply immersed in a certain culture over an extended period of time—eight months to two years—and during that period, engages, observes, and records the daily life of the studied culture, and theorises about the evolution and behaviours in that culture. Data is collected primarily via observational techniques, formal and informal interaction with participants in that culture, and personal field notes, while data analysis involves ‘sense-making’. The researcher must narrate her experience in great detail so that readers may experience that same culture without necessarily being there. The advantages of this approach are its sensitiveness to the context, the rich and nuanced understanding it generates, and minimal respondent bias. However, this is also an extremely time and resource-intensive approach, and findings are specific to a given culture and less generalisable to other cultures.

Selecting research designs

Given the above multitude of research designs, which design should researchers choose for their research? Generally speaking, researchers tend to select those research designs that they are most comfortable with and feel most competent to handle, but ideally, the choice should depend on the nature of the research phenomenon being studied. In the preliminary phases of research, when the research problem is unclear and the researcher wants to scope out the nature and extent of a certain research problem, a focus group (for an individual unit of analysis) or a case study (for an organisational unit of analysis) is an ideal strategy for exploratory research. As one delves further into the research domain, but finds that there are no good theories to explain the phenomenon of interest and wants to build a theory to fill in the unmet gap in that area, interpretive designs such as case research or ethnography may be useful designs. If competing theories exist and the researcher wishes to test these different theories or integrate them into a larger theory, positivist designs such as experimental design, survey research, or secondary data analysis are more appropriate.

Regardless of the specific research design chosen, the researcher should strive to collect quantitative and qualitative data using a combination of techniques such as questionnaires, interviews, observations, documents, or secondary data. For instance, even in a highly structured survey questionnaire, intended to collect quantitative data, the researcher may leave some room for a few open-ended questions to collect qualitative data that may generate unexpected insights not otherwise available from structured quantitative data alone. Likewise, while case research employ mostly face-to-face interviews to collect most qualitative data, the potential and value of collecting quantitative data should not be ignored. As an example, in a study of organisational decision-making processes, the case interviewer can record numeric quantities such as how many months it took to make certain organisational decisions, how many people were involved in that decision process, and how many decision alternatives were considered, which can provide valuable insights not otherwise available from interviewees’ narrative responses. Irrespective of the specific research design employed, the goal of the researcher should be to collect as much and as diverse data as possible that can help generate the best possible insights about the phenomenon of interest.

Social Science Research: Principles, Methods and Practices (Revised edition) Copyright © 2019 by Anol Bhattacherjee is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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Organizing Your Social Sciences Research Paper

• The Research Problem/Question
• Purpose of Guide
• Design Flaws to Avoid
• Independent and Dependent Variables
• Glossary of Research Terms
• Reading Research Effectively
• Narrowing a Topic Idea
• Broadening a Topic Idea
• Extending the Timeliness of a Topic Idea
• Academic Writing Style
• Applying Critical Thinking
• Choosing a Title
• Making an Outline
• Paragraph Development
• Research Process Video Series
• Executive Summary
• The C.A.R.S. Model
• Background Information
• Theoretical Framework
• Citation Tracking
• Content Alert Services
• Evaluating Sources
• Primary Sources
• Secondary Sources
• Tiertiary Sources
• Scholarly vs. Popular Publications
• Qualitative Methods
• Quantitative Methods
• Insiderness
• Using Non-Textual Elements
• Limitations of the Study
• Common Grammar Mistakes
• Writing Concisely
• Avoiding Plagiarism
• Footnotes or Endnotes?
• Further Readings
• Generative AI and Writing
• USC Libraries Tutorials and Other Guides
• Bibliography

A research problem is a definite or clear expression [statement] about an area of concern, a condition to be improved upon, a difficulty to be eliminated, or a troubling question that exists in scholarly literature, in theory, or within existing practice that points to a need for meaningful understanding and deliberate investigation. A research problem does not state how to do something, offer a vague or broad proposition, or present a value question. In the social and behavioral sciences, studies are most often framed around examining a problem that needs to be understood and resolved in order to improve society and the human condition.

Bryman, Alan. “The Research Question in Social Research: What is its Role?” International Journal of Social Research Methodology 10 (2007): 5-20; Guba, Egon G., and Yvonna S. Lincoln. “Competing Paradigms in Qualitative Research.” In Handbook of Qualitative Research . Norman K. Denzin and Yvonna S. Lincoln, editors. (Thousand Oaks, CA: Sage, 1994), pp. 105-117; Pardede, Parlindungan. “Identifying and Formulating the Research Problem." Research in ELT: Module 4 (October 2018): 1-13; Li, Yanmei, and Sumei Zhang. "Identifying the Research Problem." In Applied Research Methods in Urban and Regional Planning . (Cham, Switzerland: Springer International Publishing, 2022), pp. 13-21.

Importance of...

The purpose of a problem statement is to:

• Introduce the reader to the importance of the topic being studied . The reader is oriented to the significance of the study.
• Anchors the research questions, hypotheses, or assumptions to follow . It offers a concise statement about the purpose of your paper.
• Place the topic into a particular context that defines the parameters of what is to be investigated.
• Provide the framework for reporting the results and indicates what is probably necessary to conduct the study and explain how the findings will present this information.

In the social sciences, the research problem establishes the means by which you must answer the "So What?" question. This declarative question refers to a research problem surviving the relevancy test [the quality of a measurement procedure that provides repeatability and accuracy]. Note that answering the "So What?" question requires a commitment on your part to not only show that you have reviewed the literature, but that you have thoroughly considered the significance of the research problem and its implications applied to creating new knowledge and understanding or informing practice.

To survive the "So What" question, problem statements should possess the following attributes:

• Clarity and precision [a well-written statement does not make sweeping generalizations and irresponsible pronouncements; it also does include unspecific determinates like "very" or "giant"],
• Demonstrate a researchable topic or issue [i.e., feasibility of conducting the study is based upon access to information that can be effectively acquired, gathered, interpreted, synthesized, and understood],
• Identification of what would be studied, while avoiding the use of value-laden words and terms,
• Identification of an overarching question or small set of questions accompanied by key factors or variables,
• Identification of key concepts and terms,
• Articulation of the study's conceptual boundaries or parameters or limitations,
• Some generalizability in regards to applicability and bringing results into general use,
• Conveyance of the study's importance, benefits, and justification [i.e., regardless of the type of research, it is important to demonstrate that the research is not trivial],
• Does not have unnecessary jargon or overly complex sentence constructions; and,
• Conveyance of more than the mere gathering of descriptive data providing only a snapshot of the issue or phenomenon under investigation.

Bryman, Alan. “The Research Question in Social Research: What is its Role?” International Journal of Social Research Methodology 10 (2007): 5-20; Brown, Perry J., Allen Dyer, and Ross S. Whaley. "Recreation Research—So What?" Journal of Leisure Research 5 (1973): 16-24; Castellanos, Susie. Critical Writing and Thinking. The Writing Center. Dean of the College. Brown University; Ellis, Timothy J. and Yair Levy Nova. "Framework of Problem-Based Research: A Guide for Novice Researchers on the Development of a Research-Worthy Problem." Informing Science: the International Journal of an Emerging Transdiscipline 11 (2008); Thesis and Purpose Statements. The Writer’s Handbook. Writing Center. University of Wisconsin, Madison; Thesis Statements. The Writing Center. University of North Carolina; Tips and Examples for Writing Thesis Statements. The Writing Lab and The OWL. Purdue University; Selwyn, Neil. "‘So What?’…A Question that Every Journal Article Needs to Answer." Learning, Media, and Technology 39 (2014): 1-5; Shoket, Mohd. "Research Problem: Identification and Formulation." International Journal of Research 1 (May 2014): 512-518.

Structure and Writing Style

I.  Types and Content

There are four general conceptualizations of a research problem in the social sciences:

• Casuist Research Problem -- this type of problem relates to the determination of right and wrong in questions of conduct or conscience by analyzing moral dilemmas through the application of general rules and the careful distinction of special cases.
• Difference Research Problem -- typically asks the question, “Is there a difference between two or more groups or treatments?” This type of problem statement is used when the researcher compares or contrasts two or more phenomena. This a common approach to defining a problem in the clinical social sciences or behavioral sciences.
• Descriptive Research Problem -- typically asks the question, "what is...?" with the underlying purpose to describe the significance of a situation, state, or existence of a specific phenomenon. This problem is often associated with revealing hidden or understudied issues.
• Relational Research Problem -- suggests a relationship of some sort between two or more variables to be investigated. The underlying purpose is to investigate specific qualities or characteristics that may be connected in some way.

A problem statement in the social sciences should contain :

• A lead-in that helps ensure the reader will maintain interest over the study,
• A declaration of originality [e.g., mentioning a knowledge void or a lack of clarity about a topic that will be revealed in the literature review of prior research],
• An indication of the central focus of the study [establishing the boundaries of analysis], and
• An explanation of the study's significance or the benefits to be derived from investigating the research problem.

NOTE:   A statement describing the research problem of your paper should not be viewed as a thesis statement that you may be familiar with from high school. Given the content listed above, a description of the research problem is usually a short paragraph in length.

II.  Sources of Problems for Investigation

The identification of a problem to study can be challenging, not because there's a lack of issues that could be investigated, but due to the challenge of formulating an academically relevant and researchable problem which is unique and does not simply duplicate the work of others. To facilitate how you might select a problem from which to build a research study, consider these sources of inspiration:

Deductions from Theory This relates to deductions made from social philosophy or generalizations embodied in life and in society that the researcher is familiar with. These deductions from human behavior are then placed within an empirical frame of reference through research. From a theory, the researcher can formulate a research problem or hypothesis stating the expected findings in certain empirical situations. The research asks the question: “What relationship between variables will be observed if theory aptly summarizes the state of affairs?” One can then design and carry out a systematic investigation to assess whether empirical data confirm or reject the hypothesis, and hence, the theory.

Interdisciplinary Perspectives Identifying a problem that forms the basis for a research study can come from academic movements and scholarship originating in disciplines outside of your primary area of study. This can be an intellectually stimulating exercise. A review of pertinent literature should include examining research from related disciplines that can reveal new avenues of exploration and analysis. An interdisciplinary approach to selecting a research problem offers an opportunity to construct a more comprehensive understanding of a very complex issue that any single discipline may be able to provide.

Interviewing Practitioners The identification of research problems about particular topics can arise from formal interviews or informal discussions with practitioners who provide insight into new directions for future research and how to make research findings more relevant to practice. Discussions with experts in the field, such as, teachers, social workers, health care providers, lawyers, business leaders, etc., offers the chance to identify practical, “real world” problems that may be understudied or ignored within academic circles. This approach also provides some practical knowledge which may help in the process of designing and conducting your study.

Personal Experience Don't undervalue your everyday experiences or encounters as worthwhile problems for investigation. Think critically about your own experiences and/or frustrations with an issue facing society or related to your community, your neighborhood, your family, or your personal life. This can be derived, for example, from deliberate observations of certain relationships for which there is no clear explanation or witnessing an event that appears harmful to a person or group or that is out of the ordinary.

Relevant Literature The selection of a research problem can be derived from a thorough review of pertinent research associated with your overall area of interest. This may reveal where gaps exist in understanding a topic or where an issue has been understudied. Research may be conducted to: 1) fill such gaps in knowledge; 2) evaluate if the methodologies employed in prior studies can be adapted to solve other problems; or, 3) determine if a similar study could be conducted in a different subject area or applied in a different context or to different study sample [i.e., different setting or different group of people]. Also, authors frequently conclude their studies by noting implications for further research; read the conclusion of pertinent studies because statements about further research can be a valuable source for identifying new problems to investigate. The fact that a researcher has identified a topic worthy of further exploration validates the fact it is worth pursuing.

III.  What Makes a Good Research Statement?

A good problem statement begins by introducing the broad area in which your research is centered, gradually leading the reader to the more specific issues you are investigating. The statement need not be lengthy, but a good research problem should incorporate the following features:

1.  Compelling Topic The problem chosen should be one that motivates you to address it but simple curiosity is not a good enough reason to pursue a research study because this does not indicate significance. The problem that you choose to explore must be important to you, but it must also be viewed as important by your readers and to a the larger academic and/or social community that could be impacted by the results of your study. 2.  Supports Multiple Perspectives The problem must be phrased in a way that avoids dichotomies and instead supports the generation and exploration of multiple perspectives. A general rule of thumb in the social sciences is that a good research problem is one that would generate a variety of viewpoints from a composite audience made up of reasonable people. 3.  Researchability This isn't a real word but it represents an important aspect of creating a good research statement. It seems a bit obvious, but you don't want to find yourself in the midst of investigating a complex research project and realize that you don't have enough prior research to draw from for your analysis. There's nothing inherently wrong with original research, but you must choose research problems that can be supported, in some way, by the resources available to you. If you are not sure if something is researchable, don't assume that it isn't if you don't find information right away--seek help from a librarian !

NOTE:   Do not confuse a research problem with a research topic. A topic is something to read and obtain information about, whereas a problem is something to be solved or framed as a question raised for inquiry, consideration, or solution, or explained as a source of perplexity, distress, or vexation. In short, a research topic is something to be understood; a research problem is something that needs to be investigated.

IV.  Asking Analytical Questions about the Research Problem

Research problems in the social and behavioral sciences are often analyzed around critical questions that must be investigated. These questions can be explicitly listed in the introduction [i.e., "This study addresses three research questions about women's psychological recovery from domestic abuse in multi-generational home settings..."], or, the questions are implied in the text as specific areas of study related to the research problem. Explicitly listing your research questions at the end of your introduction can help in designing a clear roadmap of what you plan to address in your study, whereas, implicitly integrating them into the text of the introduction allows you to create a more compelling narrative around the key issues under investigation. Either approach is appropriate.

The number of questions you attempt to address should be based on the complexity of the problem you are investigating and what areas of inquiry you find most critical to study. Practical considerations, such as, the length of the paper you are writing or the availability of resources to analyze the issue can also factor in how many questions to ask. In general, however, there should be no more than four research questions underpinning a single research problem.

Given this, well-developed analytical questions can focus on any of the following:

• Highlights a genuine dilemma, area of ambiguity, or point of confusion about a topic open to interpretation by your readers;
• Yields an answer that is unexpected and not obvious rather than inevitable and self-evident;
• Provokes meaningful thought or discussion;
• Raises the visibility of the key ideas or concepts that may be understudied or hidden;
• Suggests the need for complex analysis or argument rather than a basic description or summary; and,
• Offers a specific path of inquiry that avoids eliciting generalizations about the problem.

NOTE:   Questions of how and why concerning a research problem often require more analysis than questions about who, what, where, and when. You should still ask yourself these latter questions, however. Thinking introspectively about the who, what, where, and when of a research problem can help ensure that you have thoroughly considered all aspects of the problem under investigation and helps define the scope of the study in relation to the problem.

V.  Mistakes to Avoid

Beware of circular reasoning! Do not state the research problem as simply the absence of the thing you are suggesting. For example, if you propose the following, "The problem in this community is that there is no hospital," this only leads to a research problem where:

• The need is for a hospital
• The objective is to create a hospital
• The method is to plan for building a hospital, and
• The evaluation is to measure if there is a hospital or not.

This is an example of a research problem that fails the "So What?" test . In this example, the problem does not reveal the relevance of why you are investigating the fact there is no hospital in the community [e.g., perhaps there's a hospital in the community ten miles away]; it does not elucidate the significance of why one should study the fact there is no hospital in the community [e.g., that hospital in the community ten miles away has no emergency room]; the research problem does not offer an intellectual pathway towards adding new knowledge or clarifying prior knowledge [e.g., the county in which there is no hospital already conducted a study about the need for a hospital, but it was conducted ten years ago]; and, the problem does not offer meaningful outcomes that lead to recommendations that can be generalized for other situations or that could suggest areas for further research [e.g., the challenges of building a new hospital serves as a case study for other communities].

Alvesson, Mats and Jörgen Sandberg. “Generating Research Questions Through Problematization.” Academy of Management Review 36 (April 2011): 247-271 ; Choosing and Refining Topics. Writing@CSU. Colorado State University; D'Souza, Victor S. "Use of Induction and Deduction in Research in Social Sciences: An Illustration." Journal of the Indian Law Institute 24 (1982): 655-661; Ellis, Timothy J. and Yair Levy Nova. "Framework of Problem-Based Research: A Guide for Novice Researchers on the Development of a Research-Worthy Problem." Informing Science: the International Journal of an Emerging Transdiscipline 11 (2008); How to Write a Research Question. The Writing Center. George Mason University; Invention: Developing a Thesis Statement. The Reading/Writing Center. Hunter College; Problem Statements PowerPoint Presentation. The Writing Lab and The OWL. Purdue University; Procter, Margaret. Using Thesis Statements. University College Writing Centre. University of Toronto; Shoket, Mohd. "Research Problem: Identification and Formulation." International Journal of Research 1 (May 2014): 512-518; Trochim, William M.K. Problem Formulation. Research Methods Knowledge Base. 2006; Thesis and Purpose Statements. The Writer’s Handbook. Writing Center. University of Wisconsin, Madison; Thesis Statements. The Writing Center. University of North Carolina; Tips and Examples for Writing Thesis Statements. The Writing Lab and The OWL. Purdue University; Pardede, Parlindungan. “Identifying and Formulating the Research Problem." Research in ELT: Module 4 (October 2018): 1-13; Walk, Kerry. Asking an Analytical Question. [Class handout or worksheet]. Princeton University; White, Patrick. Developing Research Questions: A Guide for Social Scientists . New York: Palgrave McMillan, 2009; Li, Yanmei, and Sumei Zhang. "Identifying the Research Problem." In Applied Research Methods in Urban and Regional Planning . (Cham, Switzerland: Springer International Publishing, 2022), pp. 13-21.

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The Problem-Definition Process

Developing the right solution.

By the Mind Tools Content Team

When we try to solve business problems, we can often pressurize ourselves to find solutions quickly.

The problem with this is that we can end up only partially solving the problem, or we can solve the wrong problem altogether, with all of the delay, expense, and lost business opportunity that goes with this.

The Problem-Definition Process helps you avoid this. In this article, we'll look at this process and we'll see how to apply it.

Dwayne Spradlin published the Problem-Definition Process in September 2012's Harvard Business Review . (We refer to this with permission.)

Spradlin was the President and CEO of Innocentive, an organization that connected organizations with freelance problem solvers. He developed the process over 10 years, while working with a community of more than 25,000 "problem solvers" such as engineers, scientists, and industry experts.

The process gives you four steps that help you better understand complex problems. These steps are:

• Establish the need.
• Justify the need.
• Understand the problem and its wider context.
• Write a problem statement.

The Problem-Definition Process encourages you to define and understand the problem that you're trying to solve, in detail. It also helps you confirm that solving the problem contributes towards your organization's objectives.

This stops you spending time, energy, and resources on unimportant problems, or on initiatives that don't align with your organization's overall strategy.

It also encourages you to fully define the problem and its boundaries. You can then use this information to justify the need for change, brief designers and contractors, and kick-off new projects successfully.

Use the Problem-Definition Process alongside tools such as Simplex and Hurson's Productive Thinking Model . These will guide you through the full problem-solving process .

Using the Problem-Definition Process

The four main steps in the Problem-Definition Process contain several smaller questions that, once answered, help you define and clarify the problem thoroughly.

Let's look at each step in more detail.

The process we present below is an adaptation of Spradlin's original model. We’ve included additional questions and sub-steps where appropriate.

1. Establish the Need

The first step is to identify why you need a solution to the problem. To do this, answer these questions:

a. What is the basic need? First, write your problem down in simple terms. Then, identify the basic need that you'll fulfill once you've solved the problem.

For example:

b. What is the ideal outcome? Next, identify the outcome that you want to see once you've implemented a solution.

Don't think of any particular solutions at this point – your aim is to visualize the result of a successful solution, not the solution itself.

It helps to be specific here: "Increase weekly sign-ups by 20 percent" is more useful than "Increase weekly sign-ups."

c. Who will (and won't) benefit? Finally in this step, identify all of the stakeholders who will benefit, both directly and indirectly, once you've solved the problem and reached your desired outcome. Write down who these people or groups are, and the advantages that they'll see.

Also consider who may be at a disadvantage if you solve the problem.

Tools like Impact Analysis and the Futures Wheel are useful here, as they help identify the possible consequences of a change.

As you work through the next steps of this process and get more of an understanding of your problem, you may find it useful to go back and refine your answers to previous questions.

2. Justify the Need

Once you understand the need for solving the problem, you must then justify why you should solve it. To do this, answer these questions:

a. Is effort aligned with your overall strategy? This problem, and the effort that you'll be putting into solving it, must align with your organization's strategic priorities , as well as its mission and values .

b. What benefits do we want, and how can we measure these? Identify what benefits your organization, as a whole, will see when you solve this problem, and think about how you can measure these in relation to its overall strategy and objectives. Be as specific as possible.

c. Are we likely to be able to implement a solution? Think about factors such as how you'll get support from stakeholders and decision-makers, and how you'll access the required resources and expertise. This may involve speaking with senior managers in your organization to understand what resources may be available.

3. Understand the Problem and Its Wider Context

In steps 1 and 2, you identified why you need a solution, and why it's important to your strategy and mission.

The three questions in this third step encourage you to look at the problem in more depth, and to look back into the past to see what you can learn from past efforts.

a. What's the cause? First in this step, make sure that you've identified all of the causes of your problem, using tools like CATWOE , Root Cause Analysis , Cause and Effect Analysis , Systems Diagrams , and Interrelationship Diagrams .

b. What solutions already exist? Have other people in your organization tried to solve this or a similar problem in the past? If so, what did they do? What worked and what didn't work?

Next you need to find out if people outside of your organization have already tried to do something about this problem. Widen your search to include trade journals, field studies, past research, competitors, industry experts, and your personal network.

Your goal is to look at what's been done already, and what hasn't worked, so that you don't waste time working on a solution that already exists, or working on a solution that's likely to fail.

c. What are the constraints? By now, you're starting to have a deeper understanding of the problem and how it relates to your organization. Now you can brainstorm factors that might prevent you from implementing a solution. (Use your answers from question c in step 2 to help with this.)

First, look at internal constraints. Will you have access to enough people, money, and other resources to solve this problem? Are there any stakeholders who might try to block your efforts? Are there any rules or procedures that you must follow? (For instance, a new website would need to align with your organization's brand guidelines.)

Next, look externally. Are there any government regulations or laws that might stall or block your solutions? Is the technology available?

d. What requirements must a solution meet? Write down the requirements that the solution must meet in order to solve the problem successfully. As part of this, also identify other factors that, while not essential for solving the problem successfully, would add value to the final solution. For example, you might want "quiet machinery," or a "database that you can access from anywhere with an Internet connection."

e. How will we define success? Identify how you'll define success once you've implemented a solution.

4. Write a Problem Statement

The final step is to pull together all of the information that you've gathered into a clear, comprehensive problem statement. This should provide a thorough overview of the problem, and outline a plan for how you will go about solving it.

If someone else (for example, a contractor, outside organization, or other department) will be tasked with solving the problem, also work through the following questions, and include the answers to these in your problem statement:

a. Which problem solvers should we use? Identify who, specifically, is best placed to help solve this problem. This could be a person, a team, or an outside firm.

b. What information and language should the problem statement include? The problem statement needs to be clear, specific, and understood by the people who should solve it. Avoid industry jargon , and make sure that it relates to its intended audience.

c. What do problem solvers need to produce? What will you or your organization need from them? For instance, will you need a comprehensive report, or a presentation on the proposed solution? Do you want a prototype? Is there a deadline? Spell the details out here.

d. What incentives do solvers need? This question addresses motivation. If an internal team will be working on the solution, how will they be rewarded? If an external team or firm will be addressing this problem, what incentives are you offering?

e. How will we evaluate the solutions? Who will be responsible for analyzing proposals, and what evaluation method will you use?

Dwayne Spradlin published the Problem-Definition Process in the September 2012 Harvard Business Review.

The process presents four steps that help you better understand complex problems. These four steps are:

The main advantage of using the process is that it helps you to define and understand the problem in detail, and helps you understand how important a problem is in relation to your organization's mission and strategy. From this, you can determine whether or not it's worth developing a solution.

Spradlin, D. (2012) 'Are You Solving the Right Problem?' Harvard Business Review . Available here . [Accessed November 8, 2018.]

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• Knowledge Base
• Research process
• How to Define a Research Problem | Ideas & Examples

How to Define a Research Problem | Ideas & Examples

Published on 8 November 2022 by Shona McCombes and Tegan George.

A research problem is a specific issue or gap in existing knowledge that you aim to address in your research. You may choose to look for practical problems aimed at contributing to change, or theoretical problems aimed at expanding knowledge.

Some research will do both of these things, but usually the research problem focuses on one or the other. The type of research problem you choose depends on your broad topic of interest and the type of research you think will fit best.

This article helps you identify and refine a research problem. When writing your research proposal or introduction , formulate it as a problem statement and/or research questions .

Table of contents

Why is the research problem important, step 1: identify a broad problem area, step 2: learn more about the problem, frequently asked questions about research problems.

Having an interesting topic isn’t a strong enough basis for academic research. Without a well-defined research problem, you are likely to end up with an unfocused and unmanageable project.

You might end up repeating what other people have already said, trying to say too much, or doing research without a clear purpose and justification. You need a clear problem in order to do research that contributes new and relevant insights.

Whether you’re planning your thesis , starting a research paper , or writing a research proposal , the research problem is the first step towards knowing exactly what you’ll do and why.

Prevent plagiarism, run a free check.

As you read about your topic, look for under-explored aspects or areas of concern, conflict, or controversy. Your goal is to find a gap that your research project can fill.

Practical research problems

If you are doing practical research, you can identify a problem by reading reports, following up on previous research, or talking to people who work in the relevant field or organisation. You might look for:

• Issues with performance or efficiency
• Processes that could be improved
• Areas of concern among practitioners
• Difficulties faced by specific groups of people

Examples of practical research problems

Voter turnout in New England has been decreasing, in contrast to the rest of the country.

The HR department of a local chain of restaurants has a high staff turnover rate.

A non-profit organisation faces a funding gap that means some of its programs will have to be cut.

Theoretical research problems

If you are doing theoretical research, you can identify a research problem by reading existing research, theory, and debates on your topic to find a gap in what is currently known about it. You might look for:

• A phenomenon or context that has not been closely studied
• A contradiction between two or more perspectives
• A situation or relationship that is not well understood
• A troubling question that has yet to be resolved

Examples of theoretical research problems

The effects of long-term Vitamin D deficiency on cardiovascular health are not well understood.

The relationship between gender, race, and income inequality has yet to be closely studied in the context of the millennial gig economy.

Historians of Scottish nationalism disagree about the role of the British Empire in the development of Scotland’s national identity.

Next, you have to find out what is already known about the problem, and pinpoint the exact aspect that your research will address.

Context and background

• Who does the problem affect?
• Is it a newly-discovered problem, or a well-established one?
• What research has already been done?
• What, if any, solutions have been proposed?
• What are the current debates about the problem? What is missing from these debates?

Specificity and relevance

• What particular place, time, and/or group of people will you focus on?
• What aspects will you not be able to tackle?
• What will the consequences be if the problem is not resolved?

Example of a specific research problem

A local non-profit organisation focused on alleviating food insecurity has always fundraised from its existing support base. It lacks understanding of how best to target potential new donors. To be able to continue its work, the organisation requires research into more effective fundraising strategies.

Once you have narrowed down your research problem, the next step is to formulate a problem statement , as well as your research questions or hypotheses .

Once you’ve decided on your research objectives , you need to explain them in your paper, at the end of your problem statement.

Keep your research objectives clear and concise, and use appropriate verbs to accurately convey the work that you will carry out for each one.

I will compare …

The way you present your research problem in your introduction varies depending on the nature of your research paper . A research paper that presents a sustained argument will usually encapsulate this argument in a thesis statement .

A research paper designed to present the results of empirical research tends to present a research question that it seeks to answer. It may also include a hypothesis – a prediction that will be confirmed or disproved by your research.

Research objectives describe what you intend your research project to accomplish.

They summarise the approach and purpose of the project and help to focus your research.

Your objectives should appear in the introduction of your research paper , at the end of your problem statement .

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Pendant 3-tree-connectivity of augmented cubes

• Published: 27 May 2024

Cite this article

• S. A. Mane 1 &
• S. A. Kandekar 1  

The Steiner tree problem in graphs is widely studied because of its usefulness in network design and circuit layout. In this context, given a set of vertices \(S(|S| \ge 2,)\) a tree that connects all vertices in S is called an S -Steiner tree. This helps to measure how well a network G can connect any set of S vertices together. In an S -Steiner tree, if each vertex in S has only one connection, it is called a pendant S -Steiner tree. Two pendant S -Steiner trees, T and \(T',\) are internally disjoint if \(E(T) \cap E(T') = \emptyset\) and \(V(T) \cap V(T') = S.\) The local pendant tree-connectivity, denoted as \(\tau _{G}(S),\) represents the maximum number of internally disjoint pendant S -Steiner trees in graph G . For an integer k with \(2 \le k \le n,\) where n is the number of vertices, the pendant k -tree-connectivity, denoted as \(\tau _{k}(G),\) is defined as \(\tau _{k}(G) = min\{ \tau _{G}(S): S \subseteq V(G), |S| = k\}.\) This paper focuses on studying the pendant 3-tree-connectivity of augmented cubes, which are modified versions of hypercubes designed to enhance connectivity and reduce diameter. This research demonstrates that the pendant 3-tree-connectivity of augmented cubes, denoted as \(\tau _3(AQ_n)\) is \(2n-3\) . This result matches the upper bound of \(\tau _3(G)\) provided by Hager, specifically for the augmented cube graph \(AQ_n\) .

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Acknowledgements

The authors extend their sincere appreciation to the anonymous referees for their valuable suggestions and corrections, which significantly contributed to the enhancement of the original manuscript. The first author gratefully acknowledges the Department of Science and Technology, New Delhi, India for the award of Women Scientist Scheme(DST/WOS-A/PM-14/2021(G)) for research grant in Basic/Applied Sciences.

The first author receives the research grant from the Department of Science and Technology, New Delhi, India, DST/WOS-A/PM-14/2021(G) for the period of three years, 1/4/2023 to 31/3/2026.

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Department of Mathematics, Center for Advanced Studies in Mathematics, Savitribai Phule Pune University, Pune, M.S., 411007, India

S. A. Mane & S. A. Kandekar

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SK wrote the main manuscript text and prepared all figures. Both SM and SK reviewed and revised the manuscript.

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Mane, S.A., Kandekar, S.A. Pendant 3-tree-connectivity of augmented cubes. J Supercomput (2024). https://doi.org/10.1007/s11227-024-06168-9

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Accepted : 27 April 2024

Published : 27 May 2024

DOI : https://doi.org/10.1007/s11227-024-06168-9

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