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Here's What You Need to Understand About Research Methodology

Table of Contents

Research methodology involves a systematic and well-structured approach to conducting scholarly or scientific inquiries. Knowing the significance of research methodology and its different components is crucial as it serves as the basis for any study.

Typically, your research topic will start as a broad idea you want to investigate more thoroughly. Once you’ve identified a research problem and created research questions , you must choose the appropriate methodology and frameworks to address those questions effectively.

What is the definition of a research methodology?

Research methodology is the process or the way you intend to execute your study. The methodology section of a research paper outlines how you plan to conduct your study. It covers various steps such as collecting data, statistical analysis, observing participants, and other procedures involved in the research process

The methods section should give a description of the process that will convert your idea into a study. Additionally, the outcomes of your process must provide valid and reliable results resonant with the aims and objectives of your research. This thumb rule holds complete validity, no matter whether your paper has inclinations for qualitative or quantitative usage.

Studying research methods used in related studies can provide helpful insights and direction for your own research. Now easily discover papers related to your topic on SciSpace and utilize our AI research assistant, Copilot , to quickly review the methodologies applied in different papers.

The need for a good research methodology

While deciding on your approach towards your research, the reason or factors you weighed in choosing a particular problem and formulating a research topic need to be validated and explained. A research methodology helps you do exactly that. Moreover, a good research methodology lets you build your argument to validate your research work performed through various data collection methods, analytical methods, and other essential points.

Just imagine it as a strategy documented to provide an overview of what you intend to do.

While undertaking any research writing or performing the research itself, you may get drifted in not something of much importance. In such a case, a research methodology helps you to get back to your outlined work methodology.

A research methodology helps in keeping you accountable for your work. Additionally, it can help you evaluate whether your work is in sync with your original aims and objectives or not. Besides, a good research methodology enables you to navigate your research process smoothly and swiftly while providing effective planning to achieve your desired results.

What is the basic structure of a research methodology?

Usually, you must ensure to include the following stated aspects while deciding over the basic structure of your research methodology:

1. Your research procedure

Explain what research methods you’re going to use. Whether you intend to proceed with quantitative or qualitative, or a composite of both approaches, you need to state that explicitly. The option among the three depends on your research’s aim, objectives, and scope.

2. Provide the rationality behind your chosen approach

Based on logic and reason, let your readers know why you have chosen said research methodologies. Additionally, you have to build strong arguments supporting why your chosen research method is the best way to achieve the desired outcome.

3. Explain your mechanism

The mechanism encompasses the research methods or instruments you will use to develop your research methodology. It usually refers to your data collection methods. You can use interviews, surveys, physical questionnaires, etc., of the many available mechanisms as research methodology instruments. The data collection method is determined by the type of research and whether the data is quantitative data(includes numerical data) or qualitative data (perception, morale, etc.) Moreover, you need to put logical reasoning behind choosing a particular instrument.

4. Significance of outcomes

The results will be available once you have finished experimenting. However, you should also explain how you plan to use the data to interpret the findings. This section also aids in understanding the problem from within, breaking it down into pieces, and viewing the research problem from various perspectives.

5. Reader’s advice

Anything that you feel must be explained to spread more awareness among readers and focus groups must be included and described in detail. You should not just specify your research methodology on the assumption that a reader is aware of the topic.  

All the relevant information that explains and simplifies your research paper must be included in the methodology section. If you are conducting your research in a non-traditional manner, give a logical justification and list its benefits.

6. Explain your sample space

Include information about the sample and sample space in the methodology section. The term "sample" refers to a smaller set of data that a researcher selects or chooses from a larger group of people or focus groups using a predetermined selection method. Let your readers know how you are going to distinguish between relevant and non-relevant samples. How you figured out those exact numbers to back your research methodology, i.e. the sample spacing of instruments, must be discussed thoroughly.

For example, if you are going to conduct a survey or interview, then by what procedure will you select the interviewees (or sample size in case of surveys), and how exactly will the interview or survey be conducted.

7. Challenges and limitations

This part, which is frequently assumed to be unnecessary, is actually very important. The challenges and limitations that your chosen strategy inherently possesses must be specified while you are conducting different types of research.

The importance of a good research methodology

You must have observed that all research papers, dissertations, or theses carry a chapter entirely dedicated to research methodology. This section helps maintain your credibility as a better interpreter of results rather than a manipulator.

A good research methodology always explains the procedure, data collection methods and techniques, aim, and scope of the research. In a research study, it leads to a well-organized, rationality-based approach, while the paper lacking it is often observed as messy or disorganized.

You should pay special attention to validating your chosen way towards the research methodology. This becomes extremely important in case you select an unconventional or a distinct method of execution.

Curating and developing a strong, effective research methodology can assist you in addressing a variety of situations, such as:

• When someone tries to duplicate or expand upon your research after few years.
• If a contradiction or conflict of facts occurs at a later time. This gives you the security you need to deal with these contradictions while still being able to defend your approach.
• Gaining a tactical approach in getting your research completed in time. Just ensure you are using the right approach while drafting your research methodology, and it can help you achieve your desired outcomes. Additionally, it provides a better explanation and understanding of the research question itself.
• Documenting the results so that the final outcome of the research stays as you intended it to be while starting.

Instruments you could use while writing a good research methodology

As a researcher, you must choose which tools or data collection methods that fit best in terms of the relevance of your research. This decision has to be wise.

There exists many research equipments or tools that you can use to carry out your research process. These are classified as:

a. Interviews (One-on-One or a Group)

An interview aimed to get your desired research outcomes can be undertaken in many different ways. For example, you can design your interview as structured, semi-structured, or unstructured. What sets them apart is the degree of formality in the questions. On the other hand, in a group interview, your aim should be to collect more opinions and group perceptions from the focus groups on a certain topic rather than looking out for some formal answers.

In surveys, you are in better control if you specifically draft the questions you seek the response for. For example, you may choose to include free-style questions that can be answered descriptively, or you may provide a multiple-choice type response for questions. Besides, you can also opt to choose both ways, deciding what suits your research process and purpose better.

c. Sample Groups

Similar to the group interviews, here, you can select a group of individuals and assign them a topic to discuss or freely express their opinions over that. You can simultaneously note down the answers and later draft them appropriately, deciding on the relevance of every response.

d. Observations

If your research domain is humanities or sociology, observations are the best-proven method to draw your research methodology. Of course, you can always include studying the spontaneous response of the participants towards a situation or conducting the same but in a more structured manner. A structured observation means putting the participants in a situation at a previously decided time and then studying their responses.

Of all the tools described above, it is you who should wisely choose the instruments and decide what’s the best fit for your research. You must not restrict yourself from multiple methods or a combination of a few instruments if appropriate in drafting a good research methodology.

Types of research methodology

A research methodology exists in various forms. Depending upon their approach, whether centered around words, numbers, or both, methodologies are distinguished as qualitative, quantitative, or an amalgamation of both.

1. Qualitative research methodology

When a research methodology primarily focuses on words and textual data, then it is generally referred to as qualitative research methodology. This type is usually preferred among researchers when the aim and scope of the research are mainly theoretical and explanatory.

The instruments used are observations, interviews, and sample groups. You can use this methodology if you are trying to study human behavior or response in some situations. Generally, qualitative research methodology is widely used in sociology, psychology, and other related domains.

2. Quantitative research methodology

If your research is majorly centered on data, figures, and stats, then analyzing these numerical data is often referred to as quantitative research methodology. You can use quantitative research methodology if your research requires you to validate or justify the obtained results.

In quantitative methods, surveys, tests, experiments, and evaluations of current databases can be advantageously used as instruments If your research involves testing some hypothesis, then use this methodology.

3. Amalgam methodology

As the name suggests, the amalgam methodology uses both quantitative and qualitative approaches. This methodology is used when a part of the research requires you to verify the facts and figures, whereas the other part demands you to discover the theoretical and explanatory nature of the research question.

The instruments for the amalgam methodology require you to conduct interviews and surveys, including tests and experiments. The outcome of this methodology can be insightful and valuable as it provides precise test results in line with theoretical explanations and reasoning.

The amalgam method, makes your work both factual and rational at the same time.

Final words: How to decide which is the best research methodology?

If you have kept your sincerity and awareness intact with the aims and scope of research well enough, you must have got an idea of which research methodology suits your work best.

Before deciding which research methodology answers your research question, you must invest significant time in reading and doing your homework for that. Taking references that yield relevant results should be your first approach to establishing a research methodology.

Moreover, you should never refrain from exploring other options. Before setting your work in stone, you must try all the available options as it explains why the choice of research methodology that you finally make is more appropriate than the other available options.

You should always go for a quantitative research methodology if your research requires gathering large amounts of data, figures, and statistics. This research methodology will provide you with results if your research paper involves the validation of some hypothesis.

Whereas, if  you are looking for more explanations, reasons, opinions, and public perceptions around a theory, you must use qualitative research methodology.The choice of an appropriate research methodology ultimately depends on what you want to achieve through your research.

Frequently Asked Questions (FAQs) about Research Methodology

1. how to write a research methodology.

You can always provide a separate section for research methodology where you should specify details about the methods and instruments used during the research, discussions on result analysis, including insights into the background information, and conveying the research limitations.

2. What are the types of research methodology?

There generally exists four types of research methodology i.e.

• Observation
• Experimental
• Derivational

3. What is the true meaning of research methodology?

The set of techniques or procedures followed to discover and analyze the information gathered to validate or justify a research outcome is generally called Research Methodology.

4. Where lies the importance of research methodology?

Your research methodology directly reflects the validity of your research outcomes and how well-informed your research work is. Moreover, it can help future researchers cite or refer to your research if they plan to use a similar research methodology.

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Published by Nicolas at March 21st, 2024 , Revised On March 12, 2024

The Ultimate Guide To Research Methodology

Research methodology is a crucial aspect of any investigative process, serving as the blueprint for the entire research journey. If you are stuck in the methodology section of your research paper , then this blog will guide you on what is a research methodology, its types and how to successfully conduct one. 

Table of Contents

What Is Research Methodology?

Research methodology can be defined as the systematic framework that guides researchers in designing, conducting, and analyzing their investigations. It encompasses a structured set of processes, techniques, and tools employed to gather and interpret data, ensuring the reliability and validity of the research findings. 

Research methodology is not confined to a singular approach; rather, it encapsulates a diverse range of methods tailored to the specific requirements of the research objectives.

Here is why Research methodology is important in academic and professional settings.

Facilitating Rigorous Inquiry

Research methodology forms the backbone of rigorous inquiry. It provides a structured approach that aids researchers in formulating precise thesis statements , selecting appropriate methodologies, and executing systematic investigations. This, in turn, enhances the quality and credibility of the research outcomes.

Ensuring Reproducibility And Reliability

In both academic and professional contexts, the ability to reproduce research outcomes is paramount. A well-defined research methodology establishes clear procedures, making it possible for others to replicate the study. This not only validates the findings but also contributes to the cumulative nature of knowledge.

Guiding Decision-Making Processes

In professional settings, decisions often hinge on reliable data and insights. Research methodology equips professionals with the tools to gather pertinent information, analyze it rigorously, and derive meaningful conclusions.

This informed decision-making is instrumental in achieving organizational goals and staying ahead in competitive environments.

Contributing To Academic Excellence

For academic researchers, adherence to robust research methodology is a hallmark of excellence. Institutions value research that adheres to high standards of methodology, fostering a culture of academic rigour and intellectual integrity. Furthermore, it prepares students with critical skills applicable beyond academia.

Enhancing Problem-Solving Abilities

Research methodology instills a problem-solving mindset by encouraging researchers to approach challenges systematically. It equips individuals with the skills to dissect complex issues, formulate hypotheses , and devise effective strategies for investigation.

Understanding Research Methodology

In the pursuit of knowledge and discovery, understanding the fundamentals of research methodology is paramount. 

Basics Of Research

Research, in its essence, is a systematic and organized process of inquiry aimed at expanding our understanding of a particular subject or phenomenon. It involves the exploration of existing knowledge, the formulation of hypotheses, and the collection and analysis of data to draw meaningful conclusions. 

Research is a dynamic and iterative process that contributes to the continuous evolution of knowledge in various disciplines.

Types of Research

Research takes on various forms, each tailored to the nature of the inquiry. Broadly classified, research can be categorized into two main types:

• Quantitative Research: This type involves the collection and analysis of numerical data to identify patterns, relationships, and statistical significance. It is particularly useful for testing hypotheses and making predictions.
• Qualitative Research: Qualitative research focuses on understanding the depth and details of a phenomenon through non-numerical data. It often involves methods such as interviews, focus groups, and content analysis, providing rich insights into complex issues.

Components Of Research Methodology

To conduct effective research, one must go through the different components of research methodology. These components form the scaffolding that supports the entire research process, ensuring its coherence and validity.

Research Design

Research design serves as the blueprint for the entire research project. It outlines the overall structure and strategy for conducting the study. The three primary types of research design are:

• Exploratory Research: Aimed at gaining insights and familiarity with the topic, often used in the early stages of research.
• Descriptive Research: Involves portraying an accurate profile of a situation or phenomenon, answering the ‘what,’ ‘who,’ ‘where,’ and ‘when’ questions.
• Explanatory Research: Seeks to identify the causes and effects of a phenomenon, explaining the ‘why’ and ‘how.’

Data Collection Methods

Choosing the right data collection methods is crucial for obtaining reliable and relevant information. Common methods include:

• Surveys and Questionnaires: Employed to gather information from a large number of respondents through standardized questions.
• Interviews: In-depth conversations with participants, offering qualitative insights.
• Observation: Systematic watching and recording of behaviour, events, or processes in their natural setting.

Data Analysis Techniques

Once data is collected, analysis becomes imperative to derive meaningful conclusions. Different methodologies exist for quantitative and qualitative data:

• Quantitative Data Analysis: Involves statistical techniques such as descriptive statistics, inferential statistics, and regression analysis to interpret numerical data.
• Qualitative Data Analysis: Methods like content analysis, thematic analysis, and grounded theory are employed to extract patterns, themes, and meanings from non-numerical data.

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Choosing a Research Method

Selecting an appropriate research method is a critical decision in the research process. It determines the approach, tools, and techniques that will be used to answer the research questions. 

Quantitative Research Methods

Quantitative research involves the collection and analysis of numerical data, providing a structured and objective approach to understanding and explaining phenomena.

Experimental Research

Experimental research involves manipulating variables to observe the effect on another variable under controlled conditions. It aims to establish cause-and-effect relationships.

Key Characteristics:

• Controlled Environment: Experiments are conducted in a controlled setting to minimize external influences.
• Random Assignment: Participants are randomly assigned to different experimental conditions.
• Quantitative Data: Data collected is numerical, allowing for statistical analysis.

Applications: Commonly used in scientific studies and psychology to test hypotheses and identify causal relationships.

Survey Research

Survey research gathers information from a sample of individuals through standardized questionnaires or interviews. It aims to collect data on opinions, attitudes, and behaviours.

• Structured Instruments: Surveys use structured instruments, such as questionnaires, to collect data.
• Large Sample Size: Surveys often target a large and diverse group of participants.
• Quantitative Data Analysis: Responses are quantified for statistical analysis.

Applications: Widely employed in social sciences, marketing, and public opinion research to understand trends and preferences.

Descriptive Research

Descriptive research seeks to portray an accurate profile of a situation or phenomenon. It focuses on answering the ‘what,’ ‘who,’ ‘where,’ and ‘when’ questions.

• Observation and Data Collection: This involves observing and documenting without manipulating variables.
• Objective Description: Aim to provide an unbiased and factual account of the subject.
• Quantitative or Qualitative Data: T his can include both types of data, depending on the research focus.

Applications: Useful in situations where researchers want to understand and describe a phenomenon without altering it, common in social sciences and education.

Qualitative Research Methods

Qualitative research emphasizes exploring and understanding the depth and complexity of phenomena through non-numerical data.

A case study is an in-depth exploration of a particular person, group, event, or situation. It involves detailed, context-rich analysis.

• Rich Data Collection: Uses various data sources, such as interviews, observations, and documents.
• Contextual Understanding: Aims to understand the context and unique characteristics of the case.
• Holistic Approach: Examines the case in its entirety.

Applications: Common in social sciences, psychology, and business to investigate complex and specific instances.

Ethnography

Ethnography involves immersing the researcher in the culture or community being studied to gain a deep understanding of their behaviours, beliefs, and practices.

• Participant Observation: Researchers actively participate in the community or setting.
• Holistic Perspective: Focuses on the interconnectedness of cultural elements.
• Qualitative Data: In-depth narratives and descriptions are central to ethnographic studies.

Applications: Widely used in anthropology, sociology, and cultural studies to explore and document cultural practices.

Grounded Theory

Grounded theory aims to develop theories grounded in the data itself. It involves systematic data collection and analysis to construct theories from the ground up.

• Constant Comparison: Data is continually compared and analyzed during the research process.
• Inductive Reasoning: Theories emerge from the data rather than being imposed on it.
• Iterative Process: The research design evolves as the study progresses.

Applications: Commonly applied in sociology, nursing, and management studies to generate theories from empirical data.

Research design is the structural framework that outlines the systematic process and plan for conducting a study. It serves as the blueprint, guiding researchers on how to collect, analyze, and interpret data.

Exploratory, Descriptive, And Explanatory Designs

Exploratory design.

Exploratory research design is employed when a researcher aims to explore a relatively unknown subject or gain insights into a complex phenomenon.

• Flexibility: Allows for flexibility in data collection and analysis.
• Open-Ended Questions: Uses open-ended questions to gather a broad range of information.
• Preliminary Nature: Often used in the initial stages of research to formulate hypotheses.

Applications: Valuable in the early stages of investigation, especially when the researcher seeks a deeper understanding of a subject before formalizing research questions.

Descriptive Design

Descriptive research design focuses on portraying an accurate profile of a situation, group, or phenomenon.

• Structured Data Collection: Involves systematic and structured data collection methods.
• Objective Presentation: Aims to provide an unbiased and factual account of the subject.
• Quantitative or Qualitative Data: Can incorporate both types of data, depending on the research objectives.

Applications: Widely used in social sciences, marketing, and educational research to provide detailed and objective descriptions.

Explanatory Design

Explanatory research design aims to identify the causes and effects of a phenomenon, explaining the ‘why’ and ‘how’ behind observed relationships.

• Causal Relationships: Seeks to establish causal relationships between variables.
• Controlled Variables : Often involves controlling certain variables to isolate causal factors.
• Quantitative Analysis: Primarily relies on quantitative data analysis techniques.

Applications: Commonly employed in scientific studies and social sciences to delve into the underlying reasons behind observed patterns.

Cross-Sectional Vs. Longitudinal Designs

Cross-sectional design.

Cross-sectional designs collect data from participants at a single point in time.

• Snapshot View: Provides a snapshot of a population at a specific moment.
• Efficiency: More efficient in terms of time and resources.
• Limited Temporal Insights: Offers limited insights into changes over time.

Applications: Suitable for studying characteristics or behaviours that are stable or not expected to change rapidly.

Longitudinal Design

Longitudinal designs involve the collection of data from the same participants over an extended period.

• Temporal Sequence: Allows for the examination of changes over time.
• Causality Assessment: Facilitates the assessment of cause-and-effect relationships.
• Resource-Intensive: Requires more time and resources compared to cross-sectional designs.

Applications: Ideal for studying developmental processes, trends, or the impact of interventions over time.

Experimental Vs Non-experimental Designs

Experimental design.

Experimental designs involve manipulating variables under controlled conditions to observe the effect on another variable.

• Causality Inference: Enables the inference of cause-and-effect relationships.
• Quantitative Data: Primarily involves the collection and analysis of numerical data.

Applications: Commonly used in scientific studies, psychology, and medical research to establish causal relationships.

Non-Experimental Design

Non-experimental designs observe and describe phenomena without manipulating variables.

• Natural Settings: Data is often collected in natural settings without intervention.
• Descriptive or Correlational: Focuses on describing relationships or correlations between variables.
• Quantitative or Qualitative Data: This can involve either type of data, depending on the research approach.

Applications: Suitable for studying complex phenomena in real-world settings where manipulation may not be ethical or feasible.

Effective data collection is fundamental to the success of any research endeavour. 

Designing Effective Surveys

Objective Design:

• Clearly define the research objectives to guide the survey design.
• Craft questions that align with the study’s goals and avoid ambiguity.

Structured Format:

• Use a structured format with standardized questions for consistency.
• Include a mix of closed-ended and open-ended questions for detailed insights.

Pilot Testing:

• Conduct pilot tests to identify and rectify potential issues with survey design.
• Ensure clarity, relevance, and appropriateness of questions.

Sampling Strategy:

• Develop a robust sampling strategy to ensure a representative participant group.
• Consider random sampling or stratified sampling based on the research goals.

Conducting Interviews

Establishing Rapport:

• Build rapport with participants to create a comfortable and open environment.
• Clearly communicate the purpose of the interview and the value of participants’ input.

Open-Ended Questions:

• Frame open-ended questions to encourage detailed responses.
• Allow participants to express their thoughts and perspectives freely.

Active Listening:

• Practice active listening to understand areas and gather rich data.
• Avoid interrupting and maintain a non-judgmental stance during the interview.

Ethical Considerations:

• Obtain informed consent and assure participants of confidentiality.
• Be transparent about the study’s purpose and potential implications.

Observation

1. participant observation.

Immersive Participation:

• Actively immerse yourself in the setting or group being observed.
• Develop a deep understanding of behaviours, interactions, and context.

Field Notes:

• Maintain detailed and reflective field notes during observations.
• Document observed patterns, unexpected events, and participant reactions.

Ethical Awareness:

• Be conscious of ethical considerations, ensuring respect for participants.
• Balance the role of observer and participant to minimize bias.

2. Non-participant Observation

Objective Observation:

• Maintain a more detached and objective stance during non-participant observation.
• Focus on recording behaviours, events, and patterns without direct involvement.

Data Reliability:

• Enhance the reliability of data by reducing observer bias.
• Develop clear observation protocols and guidelines.

Contextual Understanding:

• Strive for a thorough understanding of the observed context.
• Consider combining non-participant observation with other methods for triangulation.

Archival Research

1. using existing data.

Identifying Relevant Archives:

• Locate and access archives relevant to the research topic.
• Collaborate with institutions or repositories holding valuable data.

Data Verification:

• Verify the accuracy and reliability of archived data.
• Cross-reference with other sources to ensure data integrity.

Ethical Use:

• Adhere to ethical guidelines when using existing data.
• Respect copyright and intellectual property rights.

2. Challenges and Considerations

Incomplete or Inaccurate Archives:

• Address the possibility of incomplete or inaccurate archival records.
• Acknowledge limitations and uncertainties in the data.

Temporal Bias:

• Recognize potential temporal biases in archived data.
• Consider the historical context and changes that may impact interpretation.

Access Limitations:

• Address potential limitations in accessing certain archives.
• Seek alternative sources or collaborate with institutions to overcome barriers.

Common Challenges in Research Methodology

Conducting research is a complex and dynamic process, often accompanied by a myriad of challenges. Addressing these challenges is crucial to ensure the reliability and validity of research findings.

Sampling Issues

Sampling bias:.

• The presence of sampling bias can lead to an unrepresentative sample, affecting the generalizability of findings.
• Employ random sampling methods and ensure the inclusion of diverse participants to reduce bias.

Sample Size Determination:

• Determining an appropriate sample size is a delicate balance. Too small a sample may lack statistical power, while an excessively large sample may strain resources.
• Conduct a power analysis to determine the optimal sample size based on the research objectives and expected effect size.

Data Quality And Validity

Measurement error:.

• Inaccuracies in measurement tools or data collection methods can introduce measurement errors, impacting the validity of results.
• Pilot test instruments, calibrate equipment, and use standardized measures to enhance the reliability of data.

Construct Validity:

• Ensuring that the chosen measures accurately capture the intended constructs is a persistent challenge.
• Use established measurement instruments and employ multiple measures to assess the same construct for triangulation.

Time And Resource Constraints

Timeline pressures:.

• Limited timeframes can compromise the depth and thoroughness of the research process.
• Develop a realistic timeline, prioritize tasks, and communicate expectations with stakeholders to manage time constraints effectively.

Resource Availability:

• Inadequate resources, whether financial or human, can impede the execution of research activities.
• Seek external funding, collaborate with other researchers, and explore alternative methods that require fewer resources.

Managing Bias in Research

Selection bias:.

• Selecting participants in a way that systematically skews the sample can introduce selection bias.
• Employ randomization techniques, use stratified sampling, and transparently report participant recruitment methods.

Confirmation Bias:

• Researchers may unintentionally favour information that confirms their preconceived beliefs or hypotheses.
• Adopt a systematic and open-minded approach, use blinded study designs, and engage in peer review to mitigate confirmation bias.

Tips On How To Write A Research Methodology

Conducting successful research relies not only on the application of sound methodologies but also on strategic planning and effective collaboration. Here are some tips to enhance the success of your research methodology:

Tip 1. Clear Research Objectives

Well-defined research objectives guide the entire research process. Clearly articulate the purpose of your study, outlining specific research questions or hypotheses.

Tip 2. Comprehensive Literature Review

A thorough literature review provides a foundation for understanding existing knowledge and identifying gaps. Invest time in reviewing relevant literature to inform your research design and methodology.

Tip 3. Detailed Research Plan

A detailed plan serves as a roadmap, ensuring all aspects of the research are systematically addressed. Develop a detailed research plan outlining timelines, milestones, and tasks.

Tip 4. Ethical Considerations

Ethical practices are fundamental to maintaining the integrity of research. Address ethical considerations early, obtain necessary approvals, and ensure participant rights are safeguarded.

Tip 5. Stay Updated On Methodologies

Research methodologies evolve, and staying updated is essential for employing the most effective techniques. Engage in continuous learning by attending workshops, conferences, and reading recent publications.

Tip 6. Adaptability In Methods

Unforeseen challenges may arise during research, necessitating adaptability in methods. Be flexible and willing to modify your approach when needed, ensuring the integrity of the study.

Tip 7. Iterative Approach

Research is often an iterative process, and refining methods based on ongoing findings enhance the study’s robustness. Regularly review and refine your research design and methods as the study progresses.

Frequently Asked Questions

What is the research methodology.

Research methodology is the systematic process of planning, executing, and evaluating scientific investigation. It encompasses the techniques, tools, and procedures used to collect, analyze, and interpret data, ensuring the reliability and validity of research findings.

What are the methodologies in research?

Research methodologies include qualitative and quantitative approaches. Qualitative methods involve in-depth exploration of non-numerical data, while quantitative methods use statistical analysis to examine numerical data. Mixed methods combine both approaches for a comprehensive understanding of research questions.

How to write research methodology?

To write a research methodology, clearly outline the study’s design, data collection, and analysis procedures. Specify research tools, participants, and sampling methods. Justify choices and discuss limitations. Ensure clarity, coherence, and alignment with research objectives for a robust methodology section.

How to write the methodology section of a research paper?

In the methodology section of a research paper, describe the study’s design, data collection, and analysis methods. Detail procedures, tools, participants, and sampling. Justify choices, address ethical considerations, and explain how the methodology aligns with research objectives, ensuring clarity and rigour.

What is mixed research methodology?

Mixed research methodology combines both qualitative and quantitative research approaches within a single study. This approach aims to enhance the details and depth of research findings by providing a more comprehensive understanding of the research problem or question.

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What is research methodology?

The basics of research methodology

Why do you need a research methodology, what needs to be included, why do you need to document your research method, what are the different types of research instruments, qualitative / quantitative / mixed research methodologies, how do you choose the best research methodology for you, frequently asked questions about research methodology, related articles.

When you’re working on your first piece of academic research, there are many different things to focus on, and it can be overwhelming to stay on top of everything. This is especially true of budding or inexperienced researchers.

If you’ve never put together a research proposal before or find yourself in a position where you need to explain your research methodology decisions, there are a few things you need to be aware of.

Once you understand the ins and outs, handling academic research in the future will be less intimidating. We break down the basics below:

A research methodology encompasses the way in which you intend to carry out your research. This includes how you plan to tackle things like collection methods, statistical analysis, participant observations, and more.

You can think of your research methodology as being a formula. One part will be how you plan on putting your research into practice, and another will be why you feel this is the best way to approach it. Your research methodology is ultimately a methodological and systematic plan to resolve your research problem.

In short, you are explaining how you will take your idea and turn it into a study, which in turn will produce valid and reliable results that are in accordance with the aims and objectives of your research. This is true whether your paper plans to make use of qualitative methods or quantitative methods.

The purpose of a research methodology is to explain the reasoning behind your approach to your research - you'll need to support your collection methods, methods of analysis, and other key points of your work.

Think of it like writing a plan or an outline for you what you intend to do.

When carrying out research, it can be easy to go off-track or depart from your standard methodology.

Tip: Having a methodology keeps you accountable and on track with your original aims and objectives, and gives you a suitable and sound plan to keep your project manageable, smooth, and effective.

With all that said, how do you write out your standard approach to a research methodology?

As a general plan, your methodology should include the following information:

• Your research method.  You need to state whether you plan to use quantitative analysis, qualitative analysis, or mixed-method research methods. This will often be determined by what you hope to achieve with your research.
• Explain your reasoning. Why are you taking this methodological approach? Why is this particular methodology the best way to answer your research problem and achieve your objectives?
• Explain your instruments.  This will mainly be about your collection methods. There are varying instruments to use such as interviews, physical surveys, questionnaires, for example. Your methodology will need to detail your reasoning in choosing a particular instrument for your research.
• What will you do with your results?  How are you going to analyze the data once you have gathered it?
• Advise your reader.  If there is anything in your research methodology that your reader might be unfamiliar with, you should explain it in more detail. For example, you should give any background information to your methods that might be relevant or provide your reasoning if you are conducting your research in a non-standard way.
• How will your sampling process go?  What will your sampling procedure be and why? For example, if you will collect data by carrying out semi-structured or unstructured interviews, how will you choose your interviewees and how will you conduct the interviews themselves?
• Any practical limitations?  You should discuss any limitations you foresee being an issue when you’re carrying out your research.

In any dissertation, thesis, or academic journal, you will always find a chapter dedicated to explaining the research methodology of the person who carried out the study, also referred to as the methodology section of the work.

A good research methodology will explain what you are going to do and why, while a poor methodology will lead to a messy or disorganized approach.

You should also be able to justify in this section your reasoning for why you intend to carry out your research in a particular way, especially if it might be a particularly unique method.

Having a sound methodology in place can also help you with the following:

• When another researcher at a later date wishes to try and replicate your research, they will need your explanations and guidelines.
• In the event that you receive any criticism or questioning on the research you carried out at a later point, you will be able to refer back to it and succinctly explain the how and why of your approach.
• It provides you with a plan to follow throughout your research. When you are drafting your methodology approach, you need to be sure that the method you are using is the right one for your goal. This will help you with both explaining and understanding your method.
• It affords you the opportunity to document from the outset what you intend to achieve with your research, from start to finish.

A research instrument is a tool you will use to help you collect, measure and analyze the data you use as part of your research.

The choice of research instrument will usually be yours to make as the researcher and will be whichever best suits your methodology.

There are many different research instruments you can use in collecting data for your research.

Generally, they can be grouped as follows:

• Interviews (either as a group or one-on-one). You can carry out interviews in many different ways. For example, your interview can be structured, semi-structured, or unstructured. The difference between them is how formal the set of questions is that is asked of the interviewee. In a group interview, you may choose to ask the interviewees to give you their opinions or perceptions on certain topics.
• Surveys (online or in-person). In survey research, you are posing questions in which you ask for a response from the person taking the survey. You may wish to have either free-answer questions such as essay-style questions, or you may wish to use closed questions such as multiple choice. You may even wish to make the survey a mixture of both.
• Focus Groups.  Similar to the group interview above, you may wish to ask a focus group to discuss a particular topic or opinion while you make a note of the answers given.
• Observations.  This is a good research instrument to use if you are looking into human behaviors. Different ways of researching this include studying the spontaneous behavior of participants in their everyday life, or something more structured. A structured observation is research conducted at a set time and place where researchers observe behavior as planned and agreed upon with participants.

These are the most common ways of carrying out research, but it is really dependent on your needs as a researcher and what approach you think is best to take.

It is also possible to combine a number of research instruments if this is necessary and appropriate in answering your research problem.

There are three different types of methodologies, and they are distinguished by whether they focus on words, numbers, or both.

➡️ Want to learn more about the differences between qualitative and quantitative research, and how to use both methods? Check out our guide for that!

If you've done your due diligence, you'll have an idea of which methodology approach is best suited to your research.

It’s likely that you will have carried out considerable reading and homework before you reach this point and you may have taken inspiration from other similar studies that have yielded good results.

Still, it is important to consider different options before setting your research in stone. Exploring different options available will help you to explain why the choice you ultimately make is preferable to other methods.

If proving your research problem requires you to gather large volumes of numerical data to test hypotheses, a quantitative research method is likely to provide you with the most usable results.

If instead you’re looking to try and learn more about people, and their perception of events, your methodology is more exploratory in nature and would therefore probably be better served using a qualitative research methodology.

It helps to always bring things back to the question: what do I want to achieve with my research?

Once you have conducted your research, you need to analyze it. Here are some helpful guides for qualitative data analysis:

➡️  How to do a content analysis

➡️  How to do a thematic analysis

➡️  How to do a rhetorical analysis

Research methodology refers to the techniques used to find and analyze information for a study, ensuring that the results are valid, reliable and that they address the research objective.

Data can typically be organized into four different categories or methods: observational, experimental, simulation, and derived.

Writing a methodology section is a process of introducing your methods and instruments, discussing your analysis, providing more background information, addressing your research limitations, and more.

Your research methodology section will need a clear research question and proposed research approach. You'll need to add a background, introduce your research question, write your methodology and add the works you cited during your data collecting phase.

The research methodology section of your study will indicate how valid your findings are and how well-informed your paper is. It also assists future researchers planning to use the same methodology, who want to cite your study or replicate it.

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Advanced Research Methods

• Writing a Research Proposal
• What Is Research?
• Library Research

What Is a Research Proposal?

Reference books.

• Writing the Research Paper
• Presenting the Research Paper

When applying for a research grant or scholarship, or, just before you start a major research project, you may be asked to write a preliminary document that includes basic information about your future research. This is the information that is usually needed in your proposal:

• The topic and goal of the research project.
• The kind of result expected from the research.
• The theory or framework in which the research will be done and presented.
• What kind of methods will be used (statistical, empirical, etc.).
• Short reference on the preliminary scholarship and why your research project is needed; how will it continue/justify/disprove the previous scholarship.
• How much will the research project cost; how will it be budgeted (what for the money will be spent).
• Why is it you who can do this research and not somebody else.

Most agencies that offer scholarships or grants provide information about the required format of the proposal. It may include filling out templates, types of information they need, suggested/maximum length of the proposal, etc.

Research proposal formats vary depending on the size of the planned research, the number of participants, the discipline, the characteristics of the research, etc. The following outline assumes an individual researcher. This is just a SAMPLE; several other ways are equally good and can be successful. If possible, discuss your research proposal with an expert in writing, a professor, your colleague, another student who already wrote successful proposals, etc.

Author, author's affiliation

Introduction:

• Explain the topic and why you chose it. If possible explain your goal/outcome of the research . How much time you need to complete the research?

Previous scholarship:

• Give a brief summary of previous scholarship and explain why your topic and goals are important.
• Relate your planned research to previous scholarship. What will your research add to our knowledge of the topic.

Specific issues to be investigated:

• Break down the main topic into smaller research questions. List them one by one and explain why these questions need to be investigated. Relate them to previous scholarship.
• Include your hypothesis into the descriptions of the detailed research issues if you have one. Explain why it is important to justify your hypothesis.

Methodology:

• This part depends of the methods conducted in the research process. List the methods; explain how the results will be presented; how they will be assessed.
• Explain what kind of results will justify or  disprove your hypothesis. 
• Explain how much money you need.
• Explain the details of the budget (how much you want to spend for what).

Conclusion:

• Describe why your research is important.

References:

• List the sources you have used for writing the research proposal, including a few main citations of the preliminary scholarship.

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How To Choose Your Research Methodology

Qualitative vs quantitative vs mixed methods.

By: Derek Jansen (MBA). Expert Reviewed By: Dr Eunice Rautenbach | June 2021

Without a doubt, one of the most common questions we receive at Grad Coach is “ How do I choose the right methodology for my research? ”. It’s easy to see why – with so many options on the research design table, it’s easy to get intimidated, especially with all the complex lingo!

In this post, we’ll explain the three overarching types of research – qualitative, quantitative and mixed methods – and how you can go about choosing the best methodological approach for your research.

Overview: Choosing Your Methodology

Understanding the options – Qualitative research – Quantitative research – Mixed methods-based research

Choosing a research methodology – Nature of the research – Research area norms – Practicalities

1. Understanding the options

Before we jump into the question of how to choose a research methodology, it’s useful to take a step back to understand the three overarching types of research – qualitative , quantitative and mixed methods -based research. Each of these options takes a different methodological approach.

Qualitative research utilises data that is not numbers-based. In other words, qualitative research focuses on words , descriptions , concepts or ideas – while quantitative research makes use of numbers and statistics. Qualitative research investigates the “softer side” of things to explore and describe, while quantitative research focuses on the “hard numbers”, to measure differences between variables and the relationships between them.

Importantly, qualitative research methods are typically used to explore and gain a deeper understanding of the complexity of a situation – to draw a rich picture . In contrast to this, quantitative methods are usually used to confirm or test hypotheses . In other words, they have distinctly different purposes. The table below highlights a few of the key differences between qualitative and quantitative research – you can learn more about the differences here.

• Uses an inductive approach
• Is used to build theories
• Takes a subjective approach
• Adopts an open and flexible approach
• The researcher is close to the respondents
• Interviews and focus groups are oftentimes used to collect word-based data.
• Generally, draws on small sample sizes
• Uses qualitative data analysis techniques (e.g. content analysis , thematic analysis , etc)
• Uses a deductive approach
• Is used to test theories
• Takes an objective approach
• Adopts a closed, highly planned approach
• The research is disconnected from respondents
• Surveys or laboratory equipment are often used to collect number-based data.
• Generally, requires large sample sizes
• Uses statistical analysis techniques to make sense of the data

Mixed methods -based research, as you’d expect, attempts to bring these two types of research together, drawing on both qualitative and quantitative data. Quite often, mixed methods-based studies will use qualitative research to explore a situation and develop a potential model of understanding (this is called a conceptual framework), and then go on to use quantitative methods to test that model empirically.

In other words, while qualitative and quantitative methods (and the philosophies that underpin them) are completely different, they are not at odds with each other. It’s not a competition of qualitative vs quantitative. On the contrary, they can be used together to develop a high-quality piece of research. Of course, this is easier said than done, so we usually recommend that first-time researchers stick to a single approach , unless the nature of their study truly warrants a mixed-methods approach.

The key takeaway here, and the reason we started by looking at the three options, is that it’s important to understand that each methodological approach has a different purpose – for example, to explore and understand situations (qualitative), to test and measure (quantitative) or to do both. They’re not simply alternative tools for the same job. 

Right – now that we’ve got that out of the way, let’s look at how you can go about choosing the right methodology for your research.

2. How to choose a research methodology

To choose the right research methodology for your dissertation or thesis, you need to consider three important factors . Based on these three factors, you can decide on your overarching approach – qualitative, quantitative or mixed methods. Once you’ve made that decision, you can flesh out the finer details of your methodology, such as the sampling , data collection methods and analysis techniques (we discuss these separately in other posts ).

The three factors you need to consider are:

• The nature of your research aims, objectives and research questions
• The methodological approaches taken in the existing literature
• Practicalities and constraints

Let’s take a look at each of these.

Factor #1: The nature of your research

As I mentioned earlier, each type of research (and therefore, research methodology), whether qualitative, quantitative or mixed, has a different purpose and helps solve a different type of question. So, it’s logical that the key deciding factor in terms of which research methodology you adopt is the nature of your research aims, objectives and research questions .

But, what types of research exist?

Broadly speaking, research can fall into one of three categories:

• Exploratory – getting a better understanding of an issue and potentially developing a theory regarding it
• Confirmatory – confirming a potential theory or hypothesis by testing it empirically
• A mix of both – building a potential theory or hypothesis and then testing it

As a rule of thumb, exploratory research tends to adopt a qualitative approach , whereas confirmatory research tends to use quantitative methods . This isn’t set in stone, but it’s a very useful heuristic. Naturally then, research that combines a mix of both, or is seeking to develop a theory from the ground up and then test that theory, would utilize a mixed-methods approach.

Let’s look at an example in action.

If your research aims were to understand the perspectives of war veterans regarding certain political matters, you’d likely adopt a qualitative methodology, making use of interviews to collect data and one or more qualitative data analysis methods to make sense of the data.

If, on the other hand, your research aims involved testing a set of hypotheses regarding the link between political leaning and income levels, you’d likely adopt a quantitative methodology, using numbers-based data from a survey to measure the links between variables and/or constructs .

So, the first (and most important thing) thing you need to consider when deciding which methodological approach to use for your research project is the nature of your research aims , objectives and research questions. Specifically, you need to assess whether your research leans in an exploratory or confirmatory direction or involves a mix of both.

The importance of achieving solid alignment between these three factors and your methodology can’t be overstated. If they’re misaligned, you’re going to be forcing a square peg into a round hole. In other words, you’ll be using the wrong tool for the job, and your research will become a disjointed mess.

If your research is a mix of both exploratory and confirmatory, but you have a tight word count limit, you may need to consider trimming down the scope a little and focusing on one or the other. One methodology executed well has a far better chance of earning marks than a poorly executed mixed methods approach. So, don’t try to be a hero, unless there is a very strong underpinning logic.

Need a helping hand?

Factor #2: The disciplinary norms

Choosing the right methodology for your research also involves looking at the approaches used by other researchers in the field, and studies with similar research aims and objectives to yours. Oftentimes, within a discipline, there is a common methodological approach (or set of approaches) used in studies. While this doesn’t mean you should follow the herd “just because”, you should at least consider these approaches and evaluate their merit within your context.

A major benefit of reviewing the research methodologies used by similar studies in your field is that you can often piggyback on the data collection techniques that other (more experienced) researchers have developed. For example, if you’re undertaking a quantitative study, you can often find tried and tested survey scales with high Cronbach’s alphas. These are usually included in the appendices of journal articles, so you don’t even have to contact the original authors. By using these, you’ll save a lot of time and ensure that your study stands on the proverbial “shoulders of giants” by using high-quality measurement instruments .

Of course, when reviewing existing literature, keep point #1 front of mind. In other words, your methodology needs to align with your research aims, objectives and questions. Don’t fall into the trap of adopting the methodological “norm” of other studies just because it’s popular. Only adopt that which is relevant to your research.

Factor #3: Practicalities

When choosing a research methodology, there will always be a tension between doing what’s theoretically best (i.e., the most scientifically rigorous research design ) and doing what’s practical , given your constraints . This is the nature of doing research and there are always trade-offs, as with anything else.

But what constraints, you ask?

When you’re evaluating your methodological options, you need to consider the following constraints:

• Data access
• Equipment and software
• Your knowledge and skills

Let’s look at each of these.

Constraint #1: Data access

The first practical constraint you need to consider is your access to data . If you’re going to be undertaking primary research , you need to think critically about the sample of respondents you realistically have access to. For example, if you plan to use in-person interviews , you need to ask yourself how many people you’ll need to interview, whether they’ll be agreeable to being interviewed, where they’re located, and so on.

If you’re wanting to undertake a quantitative approach using surveys to collect data, you’ll need to consider how many responses you’ll require to achieve statistically significant results. For many statistical tests, a sample of a few hundred respondents is typically needed to develop convincing conclusions.

So, think carefully about what data you’ll need access to, how much data you’ll need and how you’ll collect it. The last thing you want is to spend a huge amount of time on your research only to find that you can’t get access to the required data.

Constraint #2: Time

The next constraint is time. If you’re undertaking research as part of a PhD, you may have a fairly open-ended time limit, but this is unlikely to be the case for undergrad and Masters-level projects. So, pay attention to your timeline, as the data collection and analysis components of different methodologies have a major impact on time requirements . Also, keep in mind that these stages of the research often take a lot longer than originally anticipated.

Another practical implication of time limits is that it will directly impact which time horizon you can use – i.e. longitudinal vs cross-sectional . For example, if you’ve got a 6-month limit for your entire research project, it’s quite unlikely that you’ll be able to adopt a longitudinal time horizon. 

Constraint #3: Money

As with so many things, money is another important constraint you’ll need to consider when deciding on your research methodology. While some research designs will cost near zero to execute, others may require a substantial budget .

Some of the costs that may arise include:

• Software costs – e.g. survey hosting services, analysis software, etc.
• Promotion costs – e.g. advertising a survey to attract respondents
• Incentive costs – e.g. providing a prize or cash payment incentive to attract respondents
• Equipment rental costs – e.g. recording equipment, lab equipment, etc.
• Travel costs
• Food & beverages

These are just a handful of costs that can creep into your research budget. Like most projects, the actual costs tend to be higher than the estimates, so be sure to err on the conservative side and expect the unexpected. It’s critically important that you’re honest with yourself about these costs, or you could end up getting stuck midway through your project because you’ve run out of money.

Constraint #4: Equipment & software

Another practical consideration is the hardware and/or software you’ll need in order to undertake your research. Of course, this variable will depend on the type of data you’re collecting and analysing. For example, you may need lab equipment to analyse substances, or you may need specific analysis software to analyse statistical data. So, be sure to think about what hardware and/or software you’ll need for each potential methodological approach, and whether you have access to these.

Constraint #5: Your knowledge and skillset

The final practical constraint is a big one. Naturally, the research process involves a lot of learning and development along the way, so you will accrue knowledge and skills as you progress. However, when considering your methodological options, you should still consider your current position on the ladder.

Some of the questions you should ask yourself are:

• Am I more of a “numbers person” or a “words person”?
• How much do I know about the analysis methods I’ll potentially use (e.g. statistical analysis)?
• How much do I know about the software and/or hardware that I’ll potentially use?
• How excited am I to learn new research skills and gain new knowledge?
• How much time do I have to learn the things I need to learn?

Answering these questions honestly will provide you with another set of criteria against which you can evaluate the research methodology options you’ve shortlisted.

So, as you can see, there is a wide range of practicalities and constraints that you need to take into account when you’re deciding on a research methodology. These practicalities create a tension between the “ideal” methodology and the methodology that you can realistically pull off. This is perfectly normal, and it’s your job to find the option that presents the best set of trade-offs.

Recap: Choosing a methodology

In this post, we’ve discussed how to go about choosing a research methodology. The three major deciding factors we looked at were:

• Exploratory
• Confirmatory
• Combination
• Research area norms
• Hardware and software
• Your knowledge and skillset

If you have any questions, feel free to leave a comment below. If you’d like a helping hand with your research methodology, check out our 1-on-1 research coaching service , or book a free consultation with a friendly Grad Coach.

Psst… there’s more (for free)

This post is part of our dissertation mini-course, which covers everything you need to get started with your dissertation, thesis or research project. 

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Very useful and informative especially for beginners

Nice article! I’m a beginner in the field of cybersecurity research. I am a Telecom and Network Engineer and Also aiming for PhD scholarship.

I find the article very informative especially for my decitation it has been helpful and an eye opener.

Hi I am Anna ,

I am a PHD candidate in the area of cyber security, maybe we can link up

The Examples shows by you, for sure they are really direct me and others to knows and practices the Research Design and prepration.

I found the post very informative and practical.

I’m the process of constructing my research design and I want to know if the data analysis I plan to present in my thesis defense proposal possibly change especially after I gathered the data already.

Thank you so much this site is such a life saver. How I wish 1-1 coaching is available in our country but sadly it’s not.

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Defining your research methodology

Find out more about The Open University's Education courses and qualifications .

One of the things your proposal needs to demonstrate is that your project is feasible. Start by specifying the physical or digital context of your research. For example, is it in a classroom, lab, health, social care setting or in the field? Will it be conducted online, offline, or both?

Then, outline your research methodology, keeping in mind that your research questions will influence the methodology you choose. You will want to demonstrate that your methodology is systematic and – for certain studies - can be replicated by other researchers in similar contexts.

Research methodologies

Your methodology is the approach you will take to guide your research process and explain why you use particular methods. There are several approaches to choose from and you'll need to decide based on:

(a) Your study’s aims and objectives.

(b) Your personal perspective (including your assumptions, beliefs, values, and experiences related to the topic).

(c) The theoretical or philosophical theories you hold. For example, a positivist approach holds that knowledge is real and objective, obtainable through measurements and statistics; an interpretivist approach holds that knowledge is dependent on beliefs, values, and lived experiences; and a pragmatist approach holds that knowledge is acquired through action and doing.

Methodological approaches can be quantitative (numerical), qualitative (non-numerical), or mixed methods.

Quantitative methodologies have two main strategies: experimental and non-experimental.

• The experimental strategy is used when you aim to measure the effects of a change, like comparing learning outcomes of students taught through a standard classroom book versus simulations. In this strategy, participants are randomly assigned to a control or experimental group (for example, the classroom book or the simulation group).  
• The non-experimental strategy is used when you don't aim to change a situation, but still measure outcomes in different populations and situations.
• Descriptive or single-variable research : This type answers interesting and important questions involving one variable. For example, how many primary school students own mobile devices.
• Correlational research : This type looks at the relationship between two things, by measuring two continuous variables. Researchers don't control any other factors that might be affecting the relationship. For example, assessing whether there is a relationship between students’ wellbeing and academic performance.
• Q uasi-experimental research : In this type, the researcher changes an independent variable they think can make a difference but does not randomly assign participants to groups. For example, a researcher might compare the academic performance of students in a school that implements a wellbeing program with the academic performance of students in a school that does not.

Qualitative methodologies have several strategies, far too many to list them all here, they may involve:

• Case study , where the focus is on a specific case like the experiences of healthcare professionals in a particular organization;
• Ethnographic studies , where the focus is on describing and interpreting the culture and social structure of a group;
• Grounded theory studies , where the aim is to develop a theory based on the study itself;
• Narrative research , where the focus is on identifying or telling stories;
• Phenomenological research , where the focus is on understanding individuals' perspectives and the world around them;
• Action research , a practitioner-based approach focused on contributing to the development of a profession.  

Methodologies using mixed methods combine resources and approaches to answer different research questions or different aspects of the same question. They aim at producing more in-depth findings. For example, you can explore what the levels of online engagement are of students who scored below 50% in exams using quantitative methods. You can then understand why they had these levels of online engagement using qualitative methods. We will explore the different data collection methods further down.   

These are some of the well-established methodologies, but there are many others that have been developed to address specific research topics, such as visual methodologies, impact evaluations, and secondary data research.  

This OU-produced open access handbook on Research Method s can help you get more insights into the different layers of research design.

Postgraduate researcher talks about research questions and methodology

Data collection techniques

There are many methods available for you to collect your data. Robson (2011, pp. 232-233) outlines the following rule of thumb for selecting which method is more suitable for you when collecting data from participants:

• Use direct observation to find out what people do in public
• Use interview or questionnaires to find out what they do in private
• Use interviews, questionnaire or attitude scales to investigate/ explore what they think, feel and believe
• Use standardised tests to determine their abilities or personality  

These are some well-known data collection techniques. However, you’ve probably heard about other techniques, such as the collection of texts, documents, images and artefacts. Further, there are also some more recent approaches to data collection, such as internet-based methods, social media research, as well as data analytic platforms.

Data analysis

Once you establish which data collection methods you’ll use, you need to specify how your data will be analysed. Make sure you don’t give the impression in your proposal that you’ll gather the data and think about it later!

There are different methods for analysing quantitative and qualitative data.

For quantitative data, methods include frequency distributions and graphical displays, descriptive statistics, exploring relationships between two or more variables, and analysing differences between variables.

For qualitative data, methods include thematic analysis, discourse analysis, document analysis, and multimodal analysis.

• Thematic analysis focuses on identifying and interpreting patterns of meaning in the dataset.
• Discourse analysis focuses on the communication between individuals and their contextual meanings.
• Document analysis evaluates electronic or physical documents to understand their meaning.
• Multimodal analysis analyses data that combines multiple forms, such as a video with moving images, audio, and text.

Mixed methods can combine different data collection and analysis methods in many ways. For example, interviews can explain or triangulate findings from data analytics. Cresswell (2002) explains the different sequences with mixed method approaches. For example, the emphasis can be equal between qualitative and quantitative research, or tip in the direction of either quantitative or qualitative.  

Context, timeline and limitations

As mentioned earlier, you need to have an idea about what you plan to do. You need to clarify the details of your research plan, including participants, location and settings. In your proposal, mention your current ideas about the scale of your research (e.g., sample size), access requirements (e.g., permission or gatekeepers), and the location/space of your study.

A good idea would be to produce a timeline showing what happens when. Your timeline can be textual (bullets with date intervals) or visual (an excel sheet). You can sort tasks in chronological order or in larger categories.

Finally, be transparent about any limitations that may impact the research, such as access to equipment, number of participants, time constraints, and timing issues. Acknowledging the known limitations is a strength in a proposal because it shows that you obtain a critical and overall appraisal of possible impacts on your study.

Creswell, J.W. (2002)  Educational research: Planning, conducting, and evaluating quantitative and qualitative research  (Vol. 7). Prentice Hall Upper Saddle River: NJ.

Robson. C. (2011)  Real world research.  Wiley: Cornwall.

Further reading:

Farrow, R., Iniesto, F., Weller, M. & Pitt., R. (2020)  The GO-GN Research Methods Handbook.  Open Education Research Hub: The Open University, UK. CC-BY 4.0.  http://go-gn.net/gogn_outputs/research-methods-handbook/

The next article in this series will help you consider ethical issues in your research and in your proposal. Before you move to the next article, the following links will give you some more information about research perspectives, which may be helpful as you shape your ideas.  

• Understanding different research perspectives
• Engaging with postgraduate research: education, childhood & youth
• Adolescent Participation in Research: Innovation, rationale and next steps
• Understanding research with children and young people
• Digital humanities: humanities research in the digital age
• Engaging with educational research

More articles from the research proposal collection

Writing your research proposal

A doctoral research degree is the highest academic qualification that a student can achieve. The guidance provided in these articles will help you apply for one of the two main types of research degree offered by The Open University.

Level: 1 Introductory

Addressing ethical issues in your research proposal

This article explores the ethical issues that may arise in your proposed study during your doctoral research degree.

Writing your proposal and preparing for your interview

The final article looks at writing your research proposal - from the introduction through to citations and referencing - as well as preparing for your interview.

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This free course, Succeeding in postgraduate study, will help you to become familiar with the requirements and demands of postgraduate study and to develop the skills and confidence to pursue your learning further.

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What is Research Methodology? Definition, Types, and Examples

Research methodology 1,2 is a structured and scientific approach used to collect, analyze, and interpret quantitative or qualitative data to answer research questions or test hypotheses. A research methodology is like a plan for carrying out research and helps keep researchers on track by limiting the scope of the research. Several aspects must be considered before selecting an appropriate research methodology, such as research limitations and ethical concerns that may affect your research.

The research methodology section in a scientific paper describes the different methodological choices made, such as the data collection and analysis methods, and why these choices were selected. The reasons should explain why the methods chosen are the most appropriate to answer the research question. A good research methodology also helps ensure the reliability and validity of the research findings. There are three types of research methodology—quantitative, qualitative, and mixed-method, which can be chosen based on the research objectives.

What is research methodology ?

A research methodology describes the techniques and procedures used to identify and analyze information regarding a specific research topic. It is a process by which researchers design their study so that they can achieve their objectives using the selected research instruments. It includes all the important aspects of research, including research design, data collection methods, data analysis methods, and the overall framework within which the research is conducted. While these points can help you understand what is research methodology, you also need to know why it is important to pick the right methodology.

Why is research methodology important?

Having a good research methodology in place has the following advantages: 3

• Helps other researchers who may want to replicate your research; the explanations will be of benefit to them.
• You can easily answer any questions about your research if they arise at a later stage.
• A research methodology provides a framework and guidelines for researchers to clearly define research questions, hypotheses, and objectives.
• It helps researchers identify the most appropriate research design, sampling technique, and data collection and analysis methods.
• A sound research methodology helps researchers ensure that their findings are valid and reliable and free from biases and errors.
• It also helps ensure that ethical guidelines are followed while conducting research.
• A good research methodology helps researchers in planning their research efficiently, by ensuring optimum usage of their time and resources.

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Types of research methodology.

There are three types of research methodology based on the type of research and the data required. 1

• Quantitative research methodology focuses on measuring and testing numerical data. This approach is good for reaching a large number of people in a short amount of time. This type of research helps in testing the causal relationships between variables, making predictions, and generalizing results to wider populations.
• Qualitative research methodology examines the opinions, behaviors, and experiences of people. It collects and analyzes words and textual data. This research methodology requires fewer participants but is still more time consuming because the time spent per participant is quite large. This method is used in exploratory research where the research problem being investigated is not clearly defined.
• Mixed-method research methodology uses the characteristics of both quantitative and qualitative research methodologies in the same study. This method allows researchers to validate their findings, verify if the results observed using both methods are complementary, and explain any unexpected results obtained from one method by using the other method.

What are the types of sampling designs in research methodology?

Sampling 4 is an important part of a research methodology and involves selecting a representative sample of the population to conduct the study, making statistical inferences about them, and estimating the characteristics of the whole population based on these inferences. There are two types of sampling designs in research methodology—probability and nonprobability.

• Probability sampling

In this type of sampling design, a sample is chosen from a larger population using some form of random selection, that is, every member of the population has an equal chance of being selected. The different types of probability sampling are:

• Systematic —sample members are chosen at regular intervals. It requires selecting a starting point for the sample and sample size determination that can be repeated at regular intervals. This type of sampling method has a predefined range; hence, it is the least time consuming.
• Stratified —researchers divide the population into smaller groups that don’t overlap but represent the entire population. While sampling, these groups can be organized, and then a sample can be drawn from each group separately.
• Cluster —the population is divided into clusters based on demographic parameters like age, sex, location, etc.
• Convenience —selects participants who are most easily accessible to researchers due to geographical proximity, availability at a particular time, etc.
• Purposive —participants are selected at the researcher’s discretion. Researchers consider the purpose of the study and the understanding of the target audience.
• Snowball —already selected participants use their social networks to refer the researcher to other potential participants.
• Quota —while designing the study, the researchers decide how many people with which characteristics to include as participants. The characteristics help in choosing people most likely to provide insights into the subject.

What are data collection methods?

During research, data are collected using various methods depending on the research methodology being followed and the research methods being undertaken. Both qualitative and quantitative research have different data collection methods, as listed below.

Qualitative research 5

• One-on-one interviews: Helps the interviewers understand a respondent’s subjective opinion and experience pertaining to a specific topic or event
• Document study/literature review/record keeping: Researchers’ review of already existing written materials such as archives, annual reports, research articles, guidelines, policy documents, etc.
• Focus groups: Constructive discussions that usually include a small sample of about 6-10 people and a moderator, to understand the participants’ opinion on a given topic.
• Qualitative observation : Researchers collect data using their five senses (sight, smell, touch, taste, and hearing).

Quantitative research 6

• Sampling: The most common type is probability sampling.
• Interviews: Commonly telephonic or done in-person.
• Observations: Structured observations are most commonly used in quantitative research. In this method, researchers make observations about specific behaviors of individuals in a structured setting.
• Document review: Reviewing existing research or documents to collect evidence for supporting the research.
• Surveys and questionnaires. Surveys can be administered both online and offline depending on the requirement and sample size.

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What are data analysis methods.

The data collected using the various methods for qualitative and quantitative research need to be analyzed to generate meaningful conclusions. These data analysis methods 7 also differ between quantitative and qualitative research.

Quantitative research involves a deductive method for data analysis where hypotheses are developed at the beginning of the research and precise measurement is required. The methods include statistical analysis applications to analyze numerical data and are grouped into two categories—descriptive and inferential.

Descriptive analysis is used to describe the basic features of different types of data to present it in a way that ensures the patterns become meaningful. The different types of descriptive analysis methods are:

• Measures of frequency (count, percent, frequency)
• Measures of central tendency (mean, median, mode)
• Measures of dispersion or variation (range, variance, standard deviation)
• Measure of position (percentile ranks, quartile ranks)

Inferential analysis is used to make predictions about a larger population based on the analysis of the data collected from a smaller population. This analysis is used to study the relationships between different variables. Some commonly used inferential data analysis methods are:

• Correlation: To understand the relationship between two or more variables.
• Cross-tabulation: Analyze the relationship between multiple variables.
• Regression analysis: Study the impact of independent variables on the dependent variable.
• Frequency tables: To understand the frequency of data.
• Analysis of variance: To test the degree to which two or more variables differ in an experiment.

Qualitative research involves an inductive method for data analysis where hypotheses are developed after data collection. The methods include:

• Content analysis: For analyzing documented information from text and images by determining the presence of certain words or concepts in texts.
• Narrative analysis: For analyzing content obtained from sources such as interviews, field observations, and surveys. The stories and opinions shared by people are used to answer research questions.
• Discourse analysis: For analyzing interactions with people considering the social context, that is, the lifestyle and environment, under which the interaction occurs.
• Grounded theory: Involves hypothesis creation by data collection and analysis to explain why a phenomenon occurred.
• Thematic analysis: To identify important themes or patterns in data and use these to address an issue.

How to choose a research methodology?

Here are some important factors to consider when choosing a research methodology: 8

• Research objectives, aims, and questions —these would help structure the research design.
• Review existing literature to identify any gaps in knowledge.
• Check the statistical requirements —if data-driven or statistical results are needed then quantitative research is the best. If the research questions can be answered based on people’s opinions and perceptions, then qualitative research is most suitable.
• Sample size —sample size can often determine the feasibility of a research methodology. For a large sample, less effort- and time-intensive methods are appropriate.
• Constraints —constraints of time, geography, and resources can help define the appropriate methodology.

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How to write a research methodology .

A research methodology should include the following components: 3,9

• Research design —should be selected based on the research question and the data required. Common research designs include experimental, quasi-experimental, correlational, descriptive, and exploratory.
• Research method —this can be quantitative, qualitative, or mixed-method.
• Reason for selecting a specific methodology —explain why this methodology is the most suitable to answer your research problem.
• Research instruments —explain the research instruments you plan to use, mainly referring to the data collection methods such as interviews, surveys, etc. Here as well, a reason should be mentioned for selecting the particular instrument.
• Sampling —this involves selecting a representative subset of the population being studied.
• Data collection —involves gathering data using several data collection methods, such as surveys, interviews, etc.
• Data analysis —describe the data analysis methods you will use once you’ve collected the data.
• Research limitations —mention any limitations you foresee while conducting your research.
• Validity and reliability —validity helps identify the accuracy and truthfulness of the findings; reliability refers to the consistency and stability of the results over time and across different conditions.
• Ethical considerations —research should be conducted ethically. The considerations include obtaining consent from participants, maintaining confidentiality, and addressing conflicts of interest.

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Frequently Asked Questions

Q1. What are the key components of research methodology?

A1. A good research methodology has the following key components:

• Research design
• Data collection procedures
• Data analysis methods
• Ethical considerations

Q2. Why is ethical consideration important in research methodology?

A2. Ethical consideration is important in research methodology to ensure the readers of the reliability and validity of the study. Researchers must clearly mention the ethical norms and standards followed during the conduct of the research and also mention if the research has been cleared by any institutional board. The following 10 points are the important principles related to ethical considerations: 10

• Participants should not be subjected to harm.
• Respect for the dignity of participants should be prioritized.
• Full consent should be obtained from participants before the study.
• Participants’ privacy should be ensured.
• Confidentiality of the research data should be ensured.
• Anonymity of individuals and organizations participating in the research should be maintained.
• The aims and objectives of the research should not be exaggerated.
• Affiliations, sources of funding, and any possible conflicts of interest should be declared.
• Communication in relation to the research should be honest and transparent.
• Misleading information and biased representation of primary data findings should be avoided.

Q3. What is the difference between methodology and method?

A3. Research methodology is different from a research method, although both terms are often confused. Research methods are the tools used to gather data, while the research methodology provides a framework for how research is planned, conducted, and analyzed. The latter guides researchers in making decisions about the most appropriate methods for their research. Research methods refer to the specific techniques, procedures, and tools used by researchers to collect, analyze, and interpret data, for instance surveys, questionnaires, interviews, etc.

Research methodology is, thus, an integral part of a research study. It helps ensure that you stay on track to meet your research objectives and answer your research questions using the most appropriate data collection and analysis tools based on your research design.

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• Research methodologies. Pfeiffer Library website. Accessed August 15, 2023. https://library.tiffin.edu/researchmethodologies/whatareresearchmethodologies
• Types of research methodology. Eduvoice website. Accessed August 16, 2023. https://eduvoice.in/types-research-methodology/
• The basics of research methodology: A key to quality research. Voxco. Accessed August 16, 2023. https://www.voxco.com/blog/what-is-research-methodology/
• Sampling methods: Types with examples. QuestionPro website. Accessed August 16, 2023. https://www.questionpro.com/blog/types-of-sampling-for-social-research/
• What is qualitative research? Methods, types, approaches, examples. Researcher.Life blog. Accessed August 15, 2023. https://researcher.life/blog/article/what-is-qualitative-research-methods-types-examples/
• What is quantitative research? Definition, methods, types, and examples. Researcher.Life blog. Accessed August 15, 2023. https://researcher.life/blog/article/what-is-quantitative-research-types-and-examples/
• Data analysis in research: Types & methods. QuestionPro website. Accessed August 16, 2023. https://www.questionpro.com/blog/data-analysis-in-research/#Data_analysis_in_qualitative_research
• Factors to consider while choosing the right research methodology. PhD Monster website. Accessed August 17, 2023. https://www.phdmonster.com/factors-to-consider-while-choosing-the-right-research-methodology/
• What is research methodology? Research and writing guides. Accessed August 14, 2023. https://paperpile.com/g/what-is-research-methodology/
• Ethical considerations. Business research methodology website. Accessed August 17, 2023. https://research-methodology.net/research-methodology/ethical-considerations/

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How to Write Research Methodology

Last Updated: May 21, 2023 Approved

This article was co-authored by Alexander Ruiz, M.Ed. and by wikiHow staff writer, Jennifer Mueller, JD . Alexander Ruiz is an Educational Consultant and the Educational Director of Link Educational Institute, a tutoring business based in Claremont, California that provides customizable educational plans, subject and test prep tutoring, and college application consulting. With over a decade and a half of experience in the education industry, Alexander coaches students to increase their self-awareness and emotional intelligence while achieving skills and the goal of achieving skills and higher education. He holds a BA in Psychology from Florida International University and an MA in Education from Georgia Southern University. wikiHow marks an article as reader-approved once it receives enough positive feedback. In this case, several readers have written to tell us that this article was helpful to them, earning it our reader-approved status. This article has been viewed 517,565 times.

The research methodology section of any academic research paper gives you the opportunity to convince your readers that your research is useful and will contribute to your field of study. An effective research methodology is grounded in your overall approach – whether qualitative or quantitative – and adequately describes the methods you used. Justify why you chose those methods over others, then explain how those methods will provide answers to your research questions. [1] X Research source

Describing Your Methods

• In your restatement, include any underlying assumptions that you're making or conditions that you're taking for granted. These assumptions will also inform the research methods you've chosen.
• Generally, state the variables you'll test and the other conditions you're controlling or assuming are equal.

• If you want to research and document measurable social trends, or evaluate the impact of a particular policy on various variables, use a quantitative approach focused on data collection and statistical analysis.
• If you want to evaluate people's views or understanding of a particular issue, choose a more qualitative approach.
• You can also combine the two. For example, you might look primarily at a measurable social trend, but also interview people and get their opinions on how that trend is affecting their lives.

• For example, if you conducted a survey, you would describe the questions included in the survey, where and how the survey was conducted (such as in person, online, over the phone), how many surveys were distributed, and how long your respondents had to complete the survey.
• Include enough detail that your study can be replicated by others in your field, even if they may not get the same results you did. [4] X Research source

• Qualitative research methods typically require more detailed explanation than quantitative methods.
• Basic investigative procedures don't need to be explained in detail. Generally, you can assume that your readers have a general understanding of common research methods that social scientists use, such as surveys or focus groups.

• For example, suppose you conducted a survey and used a couple of other research papers to help construct the questions on your survey. You would mention those as contributing sources.

Justifying Your Choice of Methods

• Describe study participants specifically, and list any inclusion or exclusion criteria you used when forming your group of participants.
• Justify the size of your sample, if applicable, and describe how this affects whether your study can be generalized to larger populations. For example, if you conducted a survey of 30 percent of the student population of a university, you could potentially apply those results to the student body as a whole, but maybe not to students at other universities.

• Reading other research papers is a good way to identify potential problems that commonly arise with various methods. State whether you actually encountered any of these common problems during your research.

• If you encountered any problems as you collected data, explain clearly the steps you took to minimize the effect that problem would have on your results.

• In some cases, this may be as simple as stating that while there were numerous studies using one method, there weren't any using your method, which caused a gap in understanding of the issue.
• For example, there may be multiple papers providing quantitative analysis of a particular social trend. However, none of these papers looked closely at how this trend was affecting the lives of people.

Connecting Your Methods to Your Research Goals

• Depending on your research questions, you may be mixing quantitative and qualitative analysis – just as you could potentially use both approaches. For example, you might do a statistical analysis, and then interpret those statistics through a particular theoretical lens.

• For example, suppose you're researching the effect of college education on family farms in rural America. While you could do interviews of college-educated people who grew up on a family farm, that would not give you a picture of the overall effect. A quantitative approach and statistical analysis would give you a bigger picture.

• If in answering your research questions, your findings have raised other questions that may require further research, state these briefly.
• You can also include here any limitations to your methods, or questions that weren't answered through your research.

• Generalization is more typically used in quantitative research. If you have a well-designed sample, you can statistically apply your results to the larger population your sample belongs to.

Template to Write Research Methodology

Community Q&A

• Organize your methodology section chronologically, starting with how you prepared to conduct your research methods, how you gathered data, and how you analyzed that data. [13] X Research source Thanks Helpful 0 Not Helpful 0
• Write your research methodology section in past tense, unless you're submitting the methodology section before the research described has been carried out. [14] X Research source Thanks Helpful 2 Not Helpful 0
• Discuss your plans in detail with your advisor or supervisor before committing to a particular methodology. They can help identify possible flaws in your study. [15] X Research source Thanks Helpful 0 Not Helpful 0

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• ↑ http://expertjournals.com/how-to-write-a-research-methodology-for-your-academic-article/
• ↑ http://libguides.usc.edu/writingguide/methodology
• ↑ https://www.skillsyouneed.com/learn/dissertation-methodology.html
• ↑ https://uir.unisa.ac.za/bitstream/handle/10500/4245/05Chap%204_Research%20methodology%20and%20design.pdf
• ↑ https://elc.polyu.edu.hk/FYP/html/method.htm

About This Article

To write a research methodology, start with a section that outlines the problems or questions you'll be studying, including your hypotheses or whatever it is you're setting out to prove. Then, briefly explain why you chose to use either a qualitative or quantitative approach for your study. Next, go over when and where you conducted your research and what parameters you used to ensure you were objective. Finally, cite any sources you used to decide on the methodology for your research. To learn how to justify your choice of methods in your research methodology, scroll down! Did this summary help you? Yes No

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• Research Process

Choosing the Right Research Methodology: A Guide for Researchers

• 3 minute read
• 35.5K views

Table of Contents

Choosing an optimal research methodology is crucial for the success of any research project. The methodology you select will determine the type of data you collect, how you collect it, and how you analyse it. Understanding the different types of research methods available along with their strengths and weaknesses, is thus imperative to make an informed decision.

Understanding different research methods:

There are several research methods available depending on the type of study you are conducting, i.e., whether it is laboratory-based, clinical, epidemiological, or survey based . Some common methodologies include qualitative research, quantitative research, experimental research, survey-based research, and action research. Each method can be opted for and modified, depending on the type of research hypotheses and objectives.

Qualitative vs quantitative research:

When deciding on a research methodology, one of the key factors to consider is whether your research will be qualitative or quantitative. Qualitative research is used to understand people’s experiences, concepts, thoughts, or behaviours . Quantitative research, on the contrary, deals with numbers, graphs, and charts, and is used to test or confirm hypotheses, assumptions, and theories. 

Qualitative research methodology:

Qualitative research is often used to examine issues that are not well understood, and to gather additional insights on these topics. Qualitative research methods include open-ended survey questions, observations of behaviours described through words, and reviews of literature that has explored similar theories and ideas. These methods are used to understand how language is used in real-world situations, identify common themes or overarching ideas, and describe and interpret various texts. Data analysis for qualitative research typically includes discourse analysis, thematic analysis, and textual analysis. 

Quantitative research methodology:

The goal of quantitative research is to test hypotheses, confirm assumptions and theories, and determine cause-and-effect relationships. Quantitative research methods include experiments, close-ended survey questions, and countable and numbered observations. Data analysis for quantitative research relies heavily on statistical methods.

Analysing qualitative vs quantitative data:

The methods used for data analysis also differ for qualitative and quantitative research. As mentioned earlier, quantitative data is generally analysed using statistical methods and does not leave much room for speculation. It is more structured and follows a predetermined plan. In quantitative research, the researcher starts with a hypothesis and uses statistical methods to test it. Contrarily, methods used for qualitative data analysis can identify patterns and themes within the data, rather than provide statistical measures of the data. It is an iterative process, where the researcher goes back and forth trying to gauge the larger implications of the data through different perspectives and revising the analysis if required.

When to use qualitative vs quantitative research:

The choice between qualitative and quantitative research will depend on the gap that the research project aims to address, and specific objectives of the study. If the goal is to establish facts about a subject or topic, quantitative research is an appropriate choice. However, if the goal is to understand people’s experiences or perspectives, qualitative research may be more suitable. 

Conclusion:

In conclusion, an understanding of the different research methods available, their applicability, advantages, and disadvantages is essential for making an informed decision on the best methodology for your project. If you need any additional guidance on which research methodology to opt for, you can head over to Elsevier Author Services (EAS). EAS experts will guide you throughout the process and help you choose the perfect methodology for your research goals.

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Home » How To Write A Research Proposal – Step-by-Step [Template]

How To Write A Research Proposal – Step-by-Step [Template]

Table of Contents

How To Write a Research Proposal

Writing a Research proposal involves several steps to ensure a well-structured and comprehensive document. Here is an explanation of each step:

1. Title and Abstract

• Choose a concise and descriptive title that reflects the essence of your research.
• Write an abstract summarizing your research question, objectives, methodology, and expected outcomes. It should provide a brief overview of your proposal.

2. Introduction:

• Provide an introduction to your research topic, highlighting its significance and relevance.
• Clearly state the research problem or question you aim to address.
• Discuss the background and context of the study, including previous research in the field.

3. Research Objectives

• Outline the specific objectives or aims of your research. These objectives should be clear, achievable, and aligned with the research problem.

4. Literature Review:

• Conduct a comprehensive review of relevant literature and studies related to your research topic.
• Summarize key findings, identify gaps, and highlight how your research will contribute to the existing knowledge.

5. Methodology:

• Describe the research design and methodology you plan to employ to address your research objectives.
• Explain the data collection methods, instruments, and analysis techniques you will use.
• Justify why the chosen methods are appropriate and suitable for your research.

6. Timeline:

• Create a timeline or schedule that outlines the major milestones and activities of your research project.
• Break down the research process into smaller tasks and estimate the time required for each task.

7. Resources:

• Identify the resources needed for your research, such as access to specific databases, equipment, or funding.
• Explain how you will acquire or utilize these resources to carry out your research effectively.

8. Ethical Considerations:

• Discuss any ethical issues that may arise during your research and explain how you plan to address them.
• If your research involves human subjects, explain how you will ensure their informed consent and privacy.

9. Expected Outcomes and Significance:

• Clearly state the expected outcomes or results of your research.
• Highlight the potential impact and significance of your research in advancing knowledge or addressing practical issues.

10. References:

• Provide a list of all the references cited in your proposal, following a consistent citation style (e.g., APA, MLA).

11. Appendices:

• Include any additional supporting materials, such as survey questionnaires, interview guides, or data analysis plans.

Research Proposal Format

The format of a research proposal may vary depending on the specific requirements of the institution or funding agency. However, the following is a commonly used format for a research proposal:

1. Title Page:

• Include the title of your research proposal, your name, your affiliation or institution, and the date.

2. Abstract:

• Provide a brief summary of your research proposal, highlighting the research problem, objectives, methodology, and expected outcomes.

3. Introduction:

• Introduce the research topic and provide background information.
• State the research problem or question you aim to address.
• Explain the significance and relevance of the research.
• Review relevant literature and studies related to your research topic.
• Summarize key findings and identify gaps in the existing knowledge.
• Explain how your research will contribute to filling those gaps.

5. Research Objectives:

• Clearly state the specific objectives or aims of your research.
• Ensure that the objectives are clear, focused, and aligned with the research problem.

6. Methodology:

• Describe the research design and methodology you plan to use.
• Explain the data collection methods, instruments, and analysis techniques.
• Justify why the chosen methods are appropriate for your research.

7. Timeline:

8. Resources:

• Explain how you will acquire or utilize these resources effectively.

9. Ethical Considerations:

• If applicable, explain how you will ensure informed consent and protect the privacy of research participants.

10. Expected Outcomes and Significance:

11. References:

12. Appendices:

Research Proposal Template

Here’s a template for a research proposal:

1. Introduction:

2. Literature Review:

3. Research Objectives:

4. Methodology:

5. Timeline:

6. Resources:

7. Ethical Considerations:

8. Expected Outcomes and Significance:

9. References:

10. Appendices:

Research Proposal Sample

Title: The Impact of Online Education on Student Learning Outcomes: A Comparative Study

1. Introduction

Online education has gained significant prominence in recent years, especially due to the COVID-19 pandemic. This research proposal aims to investigate the impact of online education on student learning outcomes by comparing them with traditional face-to-face instruction. The study will explore various aspects of online education, such as instructional methods, student engagement, and academic performance, to provide insights into the effectiveness of online learning.

2. Objectives

The main objectives of this research are as follows:

• To compare student learning outcomes between online and traditional face-to-face education.
• To examine the factors influencing student engagement in online learning environments.
• To assess the effectiveness of different instructional methods employed in online education.
• To identify challenges and opportunities associated with online education and suggest recommendations for improvement.

3. Methodology

3.1 Study Design

This research will utilize a mixed-methods approach to gather both quantitative and qualitative data. The study will include the following components:

3.2 Participants

The research will involve undergraduate students from two universities, one offering online education and the other providing face-to-face instruction. A total of 500 students (250 from each university) will be selected randomly to participate in the study.

3.3 Data Collection

The research will employ the following data collection methods:

• Quantitative: Pre- and post-assessments will be conducted to measure students’ learning outcomes. Data on student demographics and academic performance will also be collected from university records.
• Qualitative: Focus group discussions and individual interviews will be conducted with students to gather their perceptions and experiences regarding online education.

3.4 Data Analysis

Quantitative data will be analyzed using statistical software, employing descriptive statistics, t-tests, and regression analysis. Qualitative data will be transcribed, coded, and analyzed thematically to identify recurring patterns and themes.

4. Ethical Considerations

The study will adhere to ethical guidelines, ensuring the privacy and confidentiality of participants. Informed consent will be obtained, and participants will have the right to withdraw from the study at any time.

5. Significance and Expected Outcomes

This research will contribute to the existing literature by providing empirical evidence on the impact of online education on student learning outcomes. The findings will help educational institutions and policymakers make informed decisions about incorporating online learning methods and improving the quality of online education. Moreover, the study will identify potential challenges and opportunities related to online education and offer recommendations for enhancing student engagement and overall learning outcomes.

6. Timeline

The proposed research will be conducted over a period of 12 months, including data collection, analysis, and report writing.

The estimated budget for this research includes expenses related to data collection, software licenses, participant compensation, and research assistance. A detailed budget breakdown will be provided in the final research plan.

8. Conclusion

This research proposal aims to investigate the impact of online education on student learning outcomes through a comparative study with traditional face-to-face instruction. By exploring various dimensions of online education, this research will provide valuable insights into the effectiveness and challenges associated with online learning. The findings will contribute to the ongoing discourse on educational practices and help shape future strategies for maximizing student learning outcomes in online education settings.

About the author

Muhammad Hassan

Researcher, Academic Writer, Web developer

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• What Is a Research Design | Types, Guide & Examples

What Is a Research Design | Types, Guide & Examples

Published on June 7, 2021 by Shona McCombes . Revised on November 20, 2023 by Pritha Bhandari.

A research design is a strategy for answering your   research question  using empirical data. Creating a research design means making decisions about:

• Your overall research objectives and approach
• Whether you’ll rely on primary research or secondary research
• Your sampling methods or criteria for selecting subjects
• Your data collection methods
• The procedures you’ll follow to collect data
• Your data analysis methods

A well-planned research design helps ensure that your methods match your research objectives and that you use the right kind of analysis for your data.

Table of contents

Step 1: consider your aims and approach, step 2: choose a type of research design, step 3: identify your population and sampling method, step 4: choose your data collection methods, step 5: plan your data collection procedures, step 6: decide on your data analysis strategies, other interesting articles, frequently asked questions about research design.

• Introduction

Before you can start designing your research, you should already have a clear idea of the research question you want to investigate.

There are many different ways you could go about answering this question. Your research design choices should be driven by your aims and priorities—start by thinking carefully about what you want to achieve.

The first choice you need to make is whether you’ll take a qualitative or quantitative approach.

Qualitative research designs tend to be more flexible and inductive , allowing you to adjust your approach based on what you find throughout the research process.

Quantitative research designs tend to be more fixed and deductive , with variables and hypotheses clearly defined in advance of data collection.

It’s also possible to use a mixed-methods design that integrates aspects of both approaches. By combining qualitative and quantitative insights, you can gain a more complete picture of the problem you’re studying and strengthen the credibility of your conclusions.

Practical and ethical considerations when designing research

As well as scientific considerations, you need to think practically when designing your research. If your research involves people or animals, you also need to consider research ethics .

• How much time do you have to collect data and write up the research?
• Will you be able to gain access to the data you need (e.g., by travelling to a specific location or contacting specific people)?
• Do you have the necessary research skills (e.g., statistical analysis or interview techniques)?
• Will you need ethical approval ?

At each stage of the research design process, make sure that your choices are practically feasible.

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Within both qualitative and quantitative approaches, there are several types of research design to choose from. Each type provides a framework for the overall shape of your research.

Types of quantitative research designs

Quantitative designs can be split into four main types.

• Experimental and   quasi-experimental designs allow you to test cause-and-effect relationships
• Descriptive and correlational designs allow you to measure variables and describe relationships between them.

With descriptive and correlational designs, you can get a clear picture of characteristics, trends and relationships as they exist in the real world. However, you can’t draw conclusions about cause and effect (because correlation doesn’t imply causation ).

Experiments are the strongest way to test cause-and-effect relationships without the risk of other variables influencing the results. However, their controlled conditions may not always reflect how things work in the real world. They’re often also more difficult and expensive to implement.

Types of qualitative research designs

Qualitative designs are less strictly defined. This approach is about gaining a rich, detailed understanding of a specific context or phenomenon, and you can often be more creative and flexible in designing your research.

The table below shows some common types of qualitative design. They often have similar approaches in terms of data collection, but focus on different aspects when analyzing the data.

Your research design should clearly define who or what your research will focus on, and how you’ll go about choosing your participants or subjects.

In research, a population is the entire group that you want to draw conclusions about, while a sample is the smaller group of individuals you’ll actually collect data from.

Defining the population

A population can be made up of anything you want to study—plants, animals, organizations, texts, countries, etc. In the social sciences, it most often refers to a group of people.

For example, will you focus on people from a specific demographic, region or background? Are you interested in people with a certain job or medical condition, or users of a particular product?

The more precisely you define your population, the easier it will be to gather a representative sample.

• Sampling methods

Even with a narrowly defined population, it’s rarely possible to collect data from every individual. Instead, you’ll collect data from a sample.

To select a sample, there are two main approaches: probability sampling and non-probability sampling . The sampling method you use affects how confidently you can generalize your results to the population as a whole.

Probability sampling is the most statistically valid option, but it’s often difficult to achieve unless you’re dealing with a very small and accessible population.

For practical reasons, many studies use non-probability sampling, but it’s important to be aware of the limitations and carefully consider potential biases. You should always make an effort to gather a sample that’s as representative as possible of the population.

Case selection in qualitative research

In some types of qualitative designs, sampling may not be relevant.

For example, in an ethnography or a case study , your aim is to deeply understand a specific context, not to generalize to a population. Instead of sampling, you may simply aim to collect as much data as possible about the context you are studying.

In these types of design, you still have to carefully consider your choice of case or community. You should have a clear rationale for why this particular case is suitable for answering your research question .

For example, you might choose a case study that reveals an unusual or neglected aspect of your research problem, or you might choose several very similar or very different cases in order to compare them.

Data collection methods are ways of directly measuring variables and gathering information. They allow you to gain first-hand knowledge and original insights into your research problem.

You can choose just one data collection method, or use several methods in the same study.

Survey methods

Surveys allow you to collect data about opinions, behaviors, experiences, and characteristics by asking people directly. There are two main survey methods to choose from: questionnaires and interviews .

Observation methods

Observational studies allow you to collect data unobtrusively, observing characteristics, behaviors or social interactions without relying on self-reporting.

Observations may be conducted in real time, taking notes as you observe, or you might make audiovisual recordings for later analysis. They can be qualitative or quantitative.

Other methods of data collection

There are many other ways you might collect data depending on your field and topic.

If you’re not sure which methods will work best for your research design, try reading some papers in your field to see what kinds of data collection methods they used.

Secondary data

If you don’t have the time or resources to collect data from the population you’re interested in, you can also choose to use secondary data that other researchers already collected—for example, datasets from government surveys or previous studies on your topic.

With this raw data, you can do your own analysis to answer new research questions that weren’t addressed by the original study.

Using secondary data can expand the scope of your research, as you may be able to access much larger and more varied samples than you could collect yourself.

However, it also means you don’t have any control over which variables to measure or how to measure them, so the conclusions you can draw may be limited.

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As well as deciding on your methods, you need to plan exactly how you’ll use these methods to collect data that’s consistent, accurate, and unbiased.

Planning systematic procedures is especially important in quantitative research, where you need to precisely define your variables and ensure your measurements are high in reliability and validity.

Operationalization

Some variables, like height or age, are easily measured. But often you’ll be dealing with more abstract concepts, like satisfaction, anxiety, or competence. Operationalization means turning these fuzzy ideas into measurable indicators.

If you’re using observations , which events or actions will you count?

If you’re using surveys , which questions will you ask and what range of responses will be offered?

You may also choose to use or adapt existing materials designed to measure the concept you’re interested in—for example, questionnaires or inventories whose reliability and validity has already been established.

Reliability and validity

Reliability means your results can be consistently reproduced, while validity means that you’re actually measuring the concept you’re interested in.

For valid and reliable results, your measurement materials should be thoroughly researched and carefully designed. Plan your procedures to make sure you carry out the same steps in the same way for each participant.

If you’re developing a new questionnaire or other instrument to measure a specific concept, running a pilot study allows you to check its validity and reliability in advance.

Sampling procedures

As well as choosing an appropriate sampling method , you need a concrete plan for how you’ll actually contact and recruit your selected sample.

That means making decisions about things like:

• How many participants do you need for an adequate sample size?
• What inclusion and exclusion criteria will you use to identify eligible participants?
• How will you contact your sample—by mail, online, by phone, or in person?

If you’re using a probability sampling method , it’s important that everyone who is randomly selected actually participates in the study. How will you ensure a high response rate?

If you’re using a non-probability method , how will you avoid research bias and ensure a representative sample?

Data management

It’s also important to create a data management plan for organizing and storing your data.

Will you need to transcribe interviews or perform data entry for observations? You should anonymize and safeguard any sensitive data, and make sure it’s backed up regularly.

Keeping your data well-organized will save time when it comes to analyzing it. It can also help other researchers validate and add to your findings (high replicability ).

On its own, raw data can’t answer your research question. The last step of designing your research is planning how you’ll analyze the data.

Quantitative data analysis

In quantitative research, you’ll most likely use some form of statistical analysis . With statistics, you can summarize your sample data, make estimates, and test hypotheses.

Using descriptive statistics , you can summarize your sample data in terms of:

• The distribution of the data (e.g., the frequency of each score on a test)
• The central tendency of the data (e.g., the mean to describe the average score)
• The variability of the data (e.g., the standard deviation to describe how spread out the scores are)

The specific calculations you can do depend on the level of measurement of your variables.

Using inferential statistics , you can:

• Make estimates about the population based on your sample data.
• Test hypotheses about a relationship between variables.

Regression and correlation tests look for associations between two or more variables, while comparison tests (such as t tests and ANOVAs ) look for differences in the outcomes of different groups.

Your choice of statistical test depends on various aspects of your research design, including the types of variables you’re dealing with and the distribution of your data.

Qualitative data analysis

In qualitative research, your data will usually be very dense with information and ideas. Instead of summing it up in numbers, you’ll need to comb through the data in detail, interpret its meanings, identify patterns, and extract the parts that are most relevant to your research question.

Two of the most common approaches to doing this are thematic analysis and discourse analysis .

There are many other ways of analyzing qualitative data depending on the aims of your research. To get a sense of potential approaches, try reading some qualitative research papers in your field.

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

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

 Statistics

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

Research bias

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

A research design is a strategy for answering your   research question . It defines your overall approach and determines how you will collect and analyze data.

A well-planned research design helps ensure that your methods match your research aims, that you collect high-quality data, and that you use the right kind of analysis to answer your questions, utilizing credible sources . This allows you to draw valid , trustworthy conclusions.

Quantitative research designs can be divided into two main categories:

• Correlational and descriptive designs are used to investigate characteristics, averages, trends, and associations between variables.
• Experimental and quasi-experimental designs are used to test causal relationships .

Qualitative research designs tend to be more flexible. Common types of qualitative design include case study , ethnography , and grounded theory designs.

The priorities of a research design can vary depending on the field, but you usually have to specify:

• Your research questions and/or hypotheses
• Your overall approach (e.g., qualitative or quantitative )
• The type of design you’re using (e.g., a survey , experiment , or case study )
• Your data collection methods (e.g., questionnaires , observations)
• Your data collection procedures (e.g., operationalization , timing and data management)
• Your data analysis methods (e.g., statistical tests  or thematic analysis )

A sample is a subset of individuals from a larger population . Sampling means selecting the group that you will actually collect data from in your research. For example, if you are researching the opinions of students in your university, you could survey a sample of 100 students.

In statistics, sampling allows you to test a hypothesis about the characteristics of a population.

Operationalization means turning abstract conceptual ideas into measurable observations.

For example, the concept of social anxiety isn’t directly observable, but it can be operationally defined in terms of self-rating scores, behavioral avoidance of crowded places, or physical anxiety symptoms in social situations.

Before collecting data , it’s important to consider how you will operationalize the variables that you want to measure.

A research project is an academic, scientific, or professional undertaking to answer a research question . Research projects can take many forms, such as qualitative or quantitative , descriptive , longitudinal , experimental , or correlational . What kind of research approach you choose will depend on your topic.

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How to prepare a Research Proposal

Health research, medical education and clinical practice form the three pillars of modern day medical practice. As one authority rightly put it: ‘Health research is not a luxury, but an essential need that no nation can afford to ignore’. Health research can and should be pursued by a broad range of people. Even if they do not conduct research themselves, they need to grasp the principles of the scientific method to understand the value and limitations of science and to be able to assess and evaluate results of research before applying them. This review paper aims to highlight the essential concepts to the students and beginning researchers and sensitize and motivate the readers to access the vast literature available on research methodologies.

Most students and beginning researchers do not fully understand what a research proposal means, nor do they understand its importance. 1 A research proposal is a detailed description of a proposed study designed to investigate a given problem. 2

A research proposal is intended to convince others that you have a worthwhile research project and that you have the competence and the work-plan to complete it. Broadly the research proposal must address the following questions regardless of your research area and the methodology you choose: What you plan to accomplish, why do you want to do it and how are you going to do it. 1 The aim of this article is to highlight the essential concepts and not to provide extensive details about this topic.

The elements of a research proposal are highlighted below:

1. Title: It should be concise and descriptive. It must be informative and catchy. An effective title not only prick’s the readers interest, but also predisposes him/her favorably towards the proposal. Often titles are stated in terms of a functional relationship, because such titles clearly indicate the independent and dependent variables. 1 The title may need to be revised after completion of writing of the protocol to reflect more closely the sense of the study. 3

2. Abstract: It is a brief summary of approximately 300 words. It should include the main research question, the rationale for the study, the hypothesis (if any) and the method. Descriptions of the method may include the design, procedures, the sample and any instruments that will be used. 1 It should stand on its own, and not refer the reader to points in the project description. 3

3. Introduction: The introduction provides the readers with the background information. Its purpose is to establish a framework for the research, so that readers can understand how it relates to other research. 4 It should answer the question of why the research needs to be done and what will be its relevance. It puts the proposal in context. 3

The introduction typically begins with a statement of the research problem in precise and clear terms. 1

The importance of the statement of the research problem 5 : The statement of the problem is the essential basis for the construction of a research proposal (research objectives, hypotheses, methodology, work plan and budget etc). It is an integral part of selecting a research topic. It will guide and put into sharper focus the research design being considered for solving the problem. It allows the investigator to describe the problem systematically, to reflect on its importance, its priority in the country and region and to point out why the proposed research on the problem should be undertaken. It also facilitates peer review of the research proposal by the funding agencies.

Then it is necessary to provide the context and set the stage for the research question in such a way as to show its necessity and importance. 1 This step is necessary for the investigators to familiarize themselves with existing knowledge about the research problem and to find out whether or not others have investigated the same or similar problems. This step is accomplished by a thorough and critical review of the literature and by personal communication with experts. 5 It helps further understanding of the problem proposed for research and may lead to refining the statement of the problem, to identify the study variables and conceptualize their relationships, and in formulation and selection of a research hypothesis. 5 It ensures that you are not "re-inventing the wheel" and demonstrates your understanding of the research problem. It gives due credit to those who have laid the groundwork for your proposed research. 1 In a proposal, the literature review is generally brief and to the point. The literature selected should be pertinent and relevant. 6

Against this background, you then present the rationale of the proposed study and clearly indicate why it is worth doing.

4. Objectives: Research objectives are the goals to be achieved by conducting the research. 5 They may be stated as ‘general’ and ‘specific’.

The general objective of the research is what is to be accomplished by the research project, for example, to determine whether or not a new vaccine should be incorporated in a public health program.

The specific objectives relate to the specific research questions the investigator wants to answer through the proposed study and may be presented as primary and secondary objectives, for example, primary: To determine the degree of protection that is attributable to the new vaccine in a study population by comparing the vaccinated and unvaccinated groups. 5 Secondary: To study the cost-effectiveness of this programme.

Young investigators are advised to resist the temptation to put too many objectives or over-ambitious objectives that cannot be adequately achieved by the implementation of the protocol. 3

5. Variables: During the planning stage, it is necessary to identify the key variables of the study and their method of measurement and unit of measurement must be clearly indicated. Four types of variables are important in research 5 :

a. Independent variables: variables that are manipulated or treated in a study in order to see what effect differences in them will have on those variables proposed as being dependent on them. The different synonyms for the term ‘independent variable’ which are used in literature are: cause, input, predisposing factor, risk factor, determinant, antecedent, characteristic and attribute.

b. Dependent variables: variables in which changes are results of the level or amount of the independent variable or variables.

Synonyms: effect, outcome, consequence, result, condition, disease.

c. Confounding or intervening variables: variables that should be studied because they may influence or ‘mix’ the effect of the independent variables. For instance, in a study of the effect of measles (independent variable) on child mortality (dependent variable), the nutritional status of the child may play an intervening (confounding) role.

d. Background variables: variables that are so often of relevance in investigations of groups or populations that they should be considered for possible inclusion in the study. For example sex, age, ethnic origin, education, marital status, social status etc.

The objective of research is usually to determine the effect of changes in one or more independent variables on one or more dependent variables. For example, a study may ask "Will alcohol intake (independent variable) have an effect on development of gastric ulcer (dependent variable)?"

Certain variables may not be easy to identify. The characteristics that define these variables must be clearly identified for the purpose of the study.

6. Questions and/ or hypotheses: If you as a researcher know enough to make prediction concerning what you are studying, then the hypothesis may be formulated. A hypothesis can be defined as a tentative prediction or explanation of the relationship between two or more variables. In other words, the hypothesis translates the problem statement into a precise, unambiguous prediction of expected outcomes. Hypotheses are not meant to be haphazard guesses, but should reflect the depth of knowledge, imagination and experience of the investigator. 5 In the process of formulating the hypotheses, all variables relevant to the study must be identified. For example: "Health education involving active participation by mothers will produce more positive changes in child feeding than health education based on lectures". Here the independent variable is types of health education and the dependent variable is changes in child feeding.

A research question poses a relationship between two or more variables but phrases the relationship as a question; a hypothesis represents a declarative statement of the relations between two or more variables. 7

For exploratory or phenomenological research, you may not have any hypothesis (please do not confuse the hypothesis with the statistical null hypothesis). 1 Questions are relevant to normative or census type research (How many of them are there? Is there a relationship between them?). Deciding whether to use questions or hypotheses depends on factors such as the purpose of the study, the nature of the design and methodology, and the audience of the research (at times even the outlook and preference of the committee members, particularly the Chair). 6

7. Methodology: The method section is very important because it tells your research Committee how you plan to tackle your research problem. The guiding principle for writing the Methods section is that it should contain sufficient information for the reader to determine whether the methodology is sound. Some even argue that a good proposal should contain sufficient details for another qualified researcher to implement the study. 1 Indicate the methodological steps you will take to answer every question or to test every hypothesis illustrated in the Questions/hypotheses section. 6 It is vital that you consult a biostatistician during the planning stage of your study, 8 to resolve the methodological issues before submitting the proposal.

This section should include:

Research design: The selection of the research strategy is the core of research design and is probably the single most important decision the investigator has to make. The choice of the strategy, whether descriptive, analytical, experimental, operational or a combination of these depend on a number of considerations, 5 but this choice must be explained in relation to the study objectives. 3

Research subjects or participants: Depending on the type of your study, the following questions should be answered 3 , 5

• - What are the criteria for inclusion or selection?
• - What are the criteria for exclusion?
• - What is the sampling procedure you will use so as to ensure representativeness and reliability of the sample and to minimize sampling errors? The key reason for being concerned with sampling is the issue of validity-both internal and external of the study results. 9
• - Will there be use of controls in your study? Controls or comparison groups are used in scientific research in order to increase the validity of the conclusions. Control groups are necessary in all analytical epidemiological studies, in experimental studies of drug trials, in research on effects of intervention programmes and disease control measures and in many other investigations. Some descriptive studies (studies of existing data, surveys) may not require control groups.
• - What are the criteria for discontinuation?

Sample size: The proposal should provide information and justification (basis on which the sample size is calculated) about sample size in the methodology section. 3 A larger sample size than needed to test the research hypothesis increases the cost and duration of the study and will be unethical if it exposes human subjects to any potential unnecessary risk without additional benefit. A smaller sample size than needed can also be unethical as it exposes human subjects to risk with no benefit to scientific knowledge. Calculation of sample size has been made easy by computer software programmes, but the principles underlying the estimation should be well understood.

Interventions: If an intervention is introduced, a description must be given of the drugs or devices (proprietary names, manufacturer, chemical composition, dose, frequency of administration) if they are already commercially available. If they are in phases of experimentation or are already commercially available but used for other indications, information must be provided on available pre-clinical investigations in animals and/or results of studies already conducted in humans (in such cases, approval of the drug regulatory agency in the country is needed before the study). 3

Ethical issues 3 : Ethical considerations apply to all types of health research. Before the proposal is submitted to the Ethics Committee for approval, two important documents mentioned below (where appropriate) must be appended to the proposal. In additions, there is another vital issue of Conflict of Interest, wherein the researchers should furnish a statement regarding the same.

The Informed consent form (informed decision-making): A consent form, where appropriate, must be developed and attached to the proposal. It should be written in the prospective subjects’ mother tongue and in simple language which can be easily understood by the subject. The use of medical terminology should be avoided as far as possible. Special care is needed when subjects are illiterate. It should explain why the study is being done and why the subject has been asked to participate. It should describe, in sequence, what will happen in the course of the study, giving enough detail for the subject to gain a clear idea of what to expect. It should clarify whether or not the study procedures offer any benefits to the subject or to others, and explain the nature, likelihood and treatment of anticipated discomfort or adverse effects, including psychological and social risks, if any. Where relevant, a comparison with risks posed by standard drugs or treatment must be included. If the risks are unknown or a comparative risk cannot be given it should be so stated. It should indicate that the subject has the right to withdraw from the study at any time without, in any way, affecting his/her further medical care. It should assure the participant of confidentiality of the findings.

Ethics checklist: The proposal must describe the measures that will be undertaken to ensure that the proposed research is carried out in accordance with the World Medical Association Declaration of Helsinki on Ethical Principles for Medical research involving Human Subjects. 10 It must answer the following questions:

• • Is the research design adequate to provide answers to the research question? It is unethical to expose subjects to research that will have no value.
• • Is the method of selection of research subjects justified? The use of vulnerable subjects as research participants needs special justification. Vulnerable subjects include those in prison, minors and persons with mental disability. In international research it is important to mention that the population in which the study is conducted will benefit from any potential outcome of the research and the research is not being conducted solely for the benefit of some other population. Justification is needed for any inducement, financial or otherwise, for the participants to be enrolled in the study.
• • Are the interventions justified, in terms of risk/benefit ratio? Risks are not limited to physical harm. Psychological and social risks must also be considered.
• • For observations made, have measures been taken to ensure confidentiality?

Research setting 5 : The research setting includes all the pertinent facets of the study, such as the population to be studied (sampling frame), the place and time of study.

Study instruments 3 , 5 : Instruments are the tools by which the data are collected. For validated questionnaires/interview schedules, reference to published work should be given and the instrument appended to the proposal. For new a questionnaire which is being designed specifically for your study the details about preparing, precoding and pretesting of questionnaire should be furnished and the document appended to the proposal. Descriptions of other methods of observations like medical examination, laboratory tests and screening procedures is necessary- for established procedures, reference of published work cited but for new or modified procedure, an adequate description is necessary with justification for the same.

Collection of data: A short description of the protocol of data collection. For example, in a study on blood pressure measurement: time of participant arrival, rest for 5p. 10 minutes, which apparatus (standard calibrated) to be used, in which room to take measurement, measurement in sitting or lying down position, how many measurements, measurement in which arm first (whether this is going to be randomized), details of cuff and its placement, who will take the measurement. This minimizes the possibility of confusion, delays and errors.

Data analysis: The description should include the design of the analysis form, plans for processing and coding the data and the choice of the statistical method to be applied to each data. What will be the procedures for accounting for missing, unused or spurious data?

Monitoring, supervision and quality control: Detailed statement about the all logistical issues to satisfy the requirements of Good Clinical Practices (GCP), protocol procedures, responsibilities of each member of the research team, training of study investigators, steps taken to assure quality control (laboratory procedures, equipment calibration etc)

Gantt chart: A Gantt chart is an overview of tasks/proposed activities and a time frame for the same. You put weeks, days or months at one side, and the tasks at the other. You draw fat lines to indicate the period the task will be performed to give a timeline for your research study (take help of tutorial on youtube). 11

Significance of the study: Indicate how your research will refine, revise or extend existing knowledge in the area under investigation. How will it benefit the concerned stakeholders? What could be the larger implications of your research study?

Dissemination of the study results: How do you propose to share the findings of your study with professional peers, practitioners, participants and the funding agency?

Budget: A proposal budget with item wise/activity wise breakdown and justification for the same. Indicate how will the study be financed.

References: The proposal should end with relevant references on the subject. For web based search include the date of access for the cited website, for example: add the sentence "accessed on June 10, 2008".

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• Published: 16 April 2024

Research on depth measurement calibration of light field camera based on Gaussian fitting

• Miao Yang 1 , 2  

Scientific Reports volume  14 , Article number:  8774 ( 2024 ) Cite this article

Metrics details

• Engineering
• Optics and photonics

Optical field imaging technology does not require a complicated optical path layout and thus reduces hardware costs. Given that only one single exposure of a single camera can obtain three-dimensional information, this paper proposes an improved calibration method for depth measurement based on the theoretical model of optical field imaging. Specifically, the calibration time can be reduced since the Gaussian fitting can reduce the number of refocused images used to obtain the optimal refocusing coefficient calibration. Moreover, the proposed method achieves the same effect as the multiple refocusing calibration strategy but requires less image processing time during calibration. At the same time, this method's depth resolution is analyzed in detail.

Introduction

In recent years, light field imaging technology has attracted significant interest from various fields due to its advantage in obtaining three-dimensional spatial information of objects in a single shot 1 . Light field imaging uses a light field camera to capture the four-dimensional light field information of the measurement space, namely the spatial and angle information 2 . The difference from the traditional two-dimensional camera is that a microlens array is added between the main lens and the sensor 3 . Given that during the measurement process, the accuracy of the camera depth calibration directly affects the accuracy of the entire measurement system, this paper further studies the depth calibration of the light field camera. The existing methods for calibrating the depth values of light fields can be divided into traditional and deep learning-based. Traditional methods are generally based on digital refocusing parameters or the optimal slope of linear structures in epipolar-plane images (EPI). The depth estimation algorithm based on digital refocusing parameters is a method of calculating a series of images focused at different positions (i.e., refocused images), and then obtaining the position information of the region based on a series of refocused image information at different positions. Lin et al. 4 designed a matching term for depth estimation based on the symmetry of the focusing sequence, based on the principle that the offset on both sides of the true depth direction has consistent color. Tao et al. 5 proposed combining consistency, focusing, and defocusing clues in a four-dimensional polar plane image to optimize the depth map by utilizing complementary information provided by each other, in response to the blurring of the corresponding area caused by the occlusion of the focusing sequence and the corresponding changes in the focusing degree. Park et al. 6 proposed an adaptive constrained defocus matching method, which divides the original focusing sequence into different image blocks and selects the unobstructed parts for defocus degree calculation to eliminate the influence of occlusion. Strecke et al. 7 proposed to calculate the symmetry of refocused sequences by using views from four directions: up, down, left, and right, in order to address occlusion in depth extraction based on focused sequences.Suzuki et al. 8 solved the problem of the limited range of optical field disparity. The principle of calculating depth based on the optimal slope of linear structures in Epipolar Plane Image (EPI) is that when fixing one dimension of the image plane coordinates and camera plane coordinates in a light field camera, the corresponding pixels are stacked in the perspective direction. Pixels located in different perspectives form a straight line, and the slope of the line reflects the depth information at the corresponding point. Depth can be estimated directly by calculating the slope of the line. Wanner et al. 9 first proposed using structural tensors to estimate the slope of the oblique line in polar plane images, and then integrated local depth using fast denoising and global optimization methods. Li et al. 10 proposed a new approach to reconstruct continuous depth maps using light fields, obtaining dense and relatively reliable local estimates from the structural information of densely sampled light field views, and then proposing an optimization method based on conjugate gradient method for iteratively solving sparse linear systems. Chen et al. 11 focused on regularizing the initial label confidence map and edge strength weights, detecting partially occluded boundary regions through superpixel based regularization, and then applying a series of shrinkage and reinforcement operations on the label confidence map and edge strength weights of these regions to improve the accuracy of depth estimation in the presence of occlusion. Zhang et al. 12 proposed a Spinning Parallelogram Operator (SPO) based on the assumption of maximizing the two regions of the epipolar line. By comparing the weighted histogram distance differences between the two regions of the epipolar line, the direction of the straight line is fitted. This method has good robustness for some weak occlusion situations. Sheng et al. 13 further proposed a strategy for extracting polar plane images in all available directions based on SPO, and designed a depth information estimation framework that combines local depth and edge direction. Williem et al. 14 used corner blocks and refocused images to measure the constrained angular entropy cost and the constrained adaptive defocus cost, and then combined these two new data costs to reduce the impact of occlusion. The depth estimation algorithm based on polar plane images is prone to interference from occlusion, noise, and other environments, and it requires a large amount of computation, usually requiring subsequent complex optimization to obtain a smoother depth map. Compared to traditional methods, deep learning-based methods have strong feature extraction and representation processing capabilities and use multi-layer neural networks to extract deep clues from light field data and generate depth values. These networks utilize the linear structural features of EPI or the correlation features of sub-aperture images to obtain the depth of the corresponding scene. For instance, Guo et al. 15 designed an occlusion perception network to estimate the depth of light field images and optimize occlusion edges. Shi et al. 16 used an optical flow network to obtain the initial depth map of the light field and optimized the depth using the hourglass network structure. Yoon et al. 17 introduced the light field Convolutional neural network (LFCNN) to improve the angle and spatial resolution of the light field. However, most of the existing neural network-based light field depth estimation methods use branch weight sharing and end-to-end training for the entire network, thus failing to fully utilize the consistency and complementarity of depth information in different directions of the light field data. At the same time, the robustness of neural network logarithmic data is insufficient.

For the focus stack based digital refocusing method of light field, the more times a light field image is refocused, the more accurate the result will be obtained, but the more time it takes to refocus, this article mainly develops a depth calibration method based on the principle of light field imaging and theoretically analyzes the depth resolution. A method for identifying the optimal refocusing coefficient based on the Gaussian fitting is also proposed to reduce calibration and measurement time. Specifically, we built a microlight field imaging system, conducted calibration experiments, and analyzed the impact of different numbers of calibration points on identifying the optimal refocusing coefficient and calibration curve fitting. This is important, as using dot calibration plates and luminescent micropores for depth calibration provides a depth recognition method for particle images that saves calibration time and improves calibration efficiency. At the same time, from the perspective of fitting principles, reducing the number of refocuses will not decrease the robustness to noises. The method is an optimization and improvement of the refocusing method based on the light field focus stack. This method is equally effective in scenarios with occlusion.

Measurement principles

Principles and sampling of light field imaging.

Figure  1 illustrates the light transmission of two kinds of focused light field cameras: Keplerian and Galilean, where \(a\) and l are the distance from the microlens plane to the virtual imaging plane of the main lens and the sensor plane, respectively. \({f}_{L}\) is the focal length of the main lens, and \({B}_{L}\left(=a+{b}_{L}\right)\) is the distance from the main plane of the main lens to the microlens. \({a}_{L}\left(={a}_{0}+d\right)\) is the distance between the distance between the position of interest in the object to the plane of the main lens, where \({a}_{0}\) is the distance from the front end of the main lens (lens group) to the main plane of the main lens, and d is the object's depth mentioned in this article .

Schematic diagram of light transmission sampling for focusing light field camera.

The imaging detector of the unfocussed light field camera 18 is located at one time the focal length \({f}_{m}\) of the microlens, and the main lens and imaging sensor are conjugated with respect to the microlens. The virtual image plane of the main lens and the imaging sensor plane in Fig.  1 are conjugated concerning the microlens. When the distance l from the microlens to the imaging detector is 1 ~ 1.5 times the microlens focal length, it is a Keplerian light field camera. Accordingly, it is a Galilean light field camera when the distance l from the microlens to the imaging detector is 0.5 ~ 1 times the focal length 19 . Assuming that along the optical axis of the main lens, the direction from the object point to the imaging detector is the positive direction. In the Kepler-type light field camera, the distance a from the virtual image plane to the microlens is positive, and the image on the detector is inverted. In the Galileo light field camera, the distance a from the virtual image plane to the microlens is negative, and the image on the detector is positive 20 . As depicted in Fig.  1 , in the focused light field camera, the object point o is imaged on the virtual image plane via the main lens to the virtual image point \({o}_{L}\) . The microlenses image the virtual image plane on the imaging sensor plane. The imaging detector of traditional two-dimensional cameras is located at the virtual image plane, where the virtual image point \({o}_{L}\) occupies N T pixels (nine pixels in the figure), all with spatial information of the object points. The virtual image point \({o}_{L}\) via the N M microlenses (presented in Fig.  1 ) are imaged on the imaging detector, making its spatial resolution \(\frac{{N}_{T}}{{N}_{M}}\) times that of traditional 2D cameras. This increases the angle information by N M , thus sacrificing spatial information in exchange for angle information. In a light field camera, each microlens images the main lens to form a macro pixel, and several pixels at the same position relative to the center of the microlens are spliced to form a single view image according to the position sequence of the microlens in the sensor 21 . As depicted in Fig.  1 , the pixels of each color are spliced to form a single view image, and the number of single view sampling pixels in each macro pixel of the focused light field camera exceeds 1. Figure  1 aims to enhance the reader's understanding; thus, only one pixel is drawn from a single perspective under each microscope.

Refocus of light field

The light field can be parameterized by light rays and two parallel planes intersecting in space 22 . Let \(L\left(u,v,x,y\right)\) represent the Radiant intensity of the beam passing through the point ( u , v ) on the plane where the microlens is located and the point ( x , y ) on the plane where the detector is located. Then the total energy \(I\left(x,y\right)\) from the beam \(L\left(u,v,x,y\right)\) received by the point ( x , y ) is:

According to 23 , refocusing involves extracting a four-dimensional light field from the original two-dimensional light field image and reprojecting it onto a new imaging surface to obtain two-dimensional images at different plane positions. The refocusing principle diagram of a simplified two-dimensional light field is presented in Fig.  2 .

Schematic diagram of light field refocusing.

A virtual image point \({o}_{L}\) is imaged as \({o}_{m}\) on the sensor through a microlens. \({o}_{r}\) is \({o}_{m}\) , which is the point after refocusing transformation. u , x , and \({x}{\prime}\) are the coordinates of the intersection point between the beam L and the microlens plane U , the imaging detector plane X , and the refocusing plane \({X}{\prime}\) , respectively. \({l}{\prime}\) is the distance between the microlens plane and the refocusing plane \({X}{\prime}\) and \({l}{\prime}=\alpha l\) , where \(\mathrm{\alpha }\) is the refocusing coefficient. From the similarity principle and coordinate relationship, it can be obtained that:

Similarly, in the other two dimensions of the four-dimensional light field, the relationship between the coordinates of the intersection point \({y}{\prime}\) of the beam and the refocusing plane \({Y}{\prime}\) and the coordinates \(y\) of the intersection point of the beam and the detector plane are:

Combining Eqs. ( 2 ), ( 3 ), and ( 1 ) provides the refocusing formula:

Depth measurement and depth resolution based on refocusing

Principle of depth measurement.

According to the Gaussian imaging formula, it can be concluded that:

Parameter \({\alpha }_{opt}\) is the optimal refocusing coefficient corresponding to the refocusing plane at the clearest position of the object point imaging. The relationship between depth d and the optimal refocusing coefficient is obtained by combining Fig.  1 and 2 with the Gaussian optics formula:

Formula ( 7 ) is organized as follows:

Among them:

where the coefficients \({c}_{0}\) , \({c}_{1}\) , and \({c}_{2}\) depend only on the fixed parameters of the imaging system. Next, a detailed theoretical analysis will be conducted on the depth resolution of this method, and further research will be conducted on the optimal refocusing coefficient for each depth position.

• Depth resolution

In order to analyze the depth resolution, based on formula ( 8 ), taking the derivative of d over \({\alpha }_{opt}\) yields:

By organizing formula ( 8 ) and bringing it into formula ( 12 ), it can be concluded that:

We set the depth resolution of a certain depth position d to \(\Delta d\) . The increment of the optimal refocusing coefficient at the corresponding depth position is \(\Delta {\alpha }_{opt}\) . Thus:

From the previous analysis, \({c}_{0}\) , \({c}_{1}\) , and \({c}_{2}\) are the coefficients comprising the fixed parameters of the imaging system. So, formula ( 14 ) infers that the depth resolution \(\Delta d\) and depth position d are related to the increment of the optimal refocusing coefficient, which can be resolved at this depth position \(\Delta {\alpha }_{opt}\) . Note that \(\Delta {\alpha }_{opt}\) is related to adjacent refocused images during image processing. Hence, in the same batch of image processing, \(\Delta {\alpha }_{opt}\) can be considered a fixed value, and thus, the depth resolution varies with the depth position. The minimum depth resolution is particularly important for depth resolution. From formula ( 14 ), it is known that \(\frac{\Delta {\alpha }_{opt}}{{c}_{2}+{c}_{1}{c}_{0}}>0\) . Therefore, formula ( 14 ) is a parabolic curve with an upward opening, and the depth is \({d}_{ms}\) when the depth resolution reaches the minimum value. Then:

By incorporating formulas ( 10 ) and ( 11 ) into formula ( 15 ), it can be concluded that:

Experiment and processing

Qualitative verification of the rendering effect of refocused light field images.

To qualitatively verify the relationship between the refocusing coefficient α and depth d and demonstrate the effect of refocusing light field rendering, we experimented using the qualitative verification experimental device for the refocusing effect shown in Fig.  3 . This setup uses a LED backlight, the depth of field target is photographed with a Raytrix R12 Micro light field camera, and the VSZ-0745CO lens is configured. The aperture and magnification of this lens can be adjusted. For the experimental conditions, the camera's exposure time is 20 ms, the magnification is 2.74, and the F-number is 26, which is equal to the F-number of the Raytrix R12 Micro light field camera.

Photo of the experimental setup for qualitative verification of the refocusing effect.

Figure  4 a and b illustrate the refocusing results obtained from the refocusing formula for α = 1.39231 and α = 3.27949.

Refocus image of depth plate focusing on different depth planes.

The refocused images in Fig.  4 a and b were divided into 38 sub-images along the vertical direction. The sharpness of the pixels was characterized based on the point sharpness function Edge Acutance Value (EAV) gradient 24 , and the sum of the sharpness of each sub-image was calculated. The obtained sharpness curve of the target refocused image along the vertical direction is presented in Fig.  5 a and b, with the abscissa being the number of sub-images.

Sharpness map of different regions of the refocused image along the vertical direction.

When the imaging is the clearest, then \(\mathrm{\alpha }={\alpha }_{opt}\) . In the experiment, the upper edge of the depth of the field target is relatively far from the lens. That is, d is larger, and the lower edge is the reverse. When \(\mathrm{\alpha }=1.39231\) , the clear position of the refocused image is near the upper edge, which is marked by the red line in Fig.  4 a. When \(\mathrm{\alpha }=3.27949\) , the clear position of the refocused image is near the lower edge, which is marked by the red line in Fig.  4 b and is consistent with Eq. ( 8 ).

Figure  6 b shows the stripe lines (i.e., red vertical lines) at the edge of the depth plate in Fig.  6 a, with a width of 5 and 7 pixels, respectively, divided into 40 parts vertically. The clarity of each image region is calculated using the EAV gradient to represent the sharpness of each pixel. Since the side of the depth of field plate is a right-angled triangle, the lower edge surface is closer to the lens, i.e., d is smaller, and the upper edge surface is further away from the lens, i.e., d is larger. Referring to the inverse relationship between the optimal refocusing coefficient α opt and d in the formula in Section 2.3, the experimental results are as follows: The sum of the sharpness for each segment is plotted on the graph, which reveals that the clarity gradually decreases as we move from the upper edge toward the center region of the image. This finding is consistent with the theoretical expectations. From the center region to the lower edge of the depth of the field plate, the sharpness slowly increases, which can be attributed to the image extending beyond the measurement range of the system.

Sharpness map of different areas along the vertical direction in the stripe area of the depth plate refocused image.

Deepth calibration experiment

Figure  7 depicts the experimental system setup for depth calibration using a point light source. The experimental system comprises a Raytrix R12 light field camera, a VSZ-0745CO main lens, a one-dimensional displacement platform, and an electric guide rail. The imaging object is an LED point light source with an aperture diaphragm diameter of 5 microns.

Schematic diagram of the point light source depth calibration experimental device.

Using an electric displacement platform, we gradually move the point light source from a distance of 99.0 mm from the front end face of the lens to 104.5 mm from the front end face in steps of 0.1 mm. Then, we extract the four-dimensional light field information in the five original light field images captured at each position and then take the average to obtain the average light field image at that position for subsequent processing to reduce noise impact. This process provides 56 groups of images. Figure  8 illustrates a partially enlarged image of the original light field of a point light source at different depths.

Partial enlarged image of the original light field of a point light source (0.344 mm × 0.344 mm).

The image standard deviation δ is used to represent image clarity, and 500 refocusing images are formed at equal intervals within \(\alpha \in \left(\mathrm{0.1,5}\right)\) . Comparing the clarity among the 500 refocusing images, the value of α that provides the image with the highest clarity is \({\alpha }_{opt}\) , corresponding to depth d . In response to the time-consuming problem of creating many refocused images during depth calibration, this paper conducts fewer refocusing operations on the light field images at each depth position. Each refocused image corresponds to a refocusing coefficient \(\mathrm{\alpha }\) , and then the clarity of each refocused image is calculated. A Gaussian function, which describes the imaging property and quality of the optical imaging system, is used to calculate the refocusing coefficient α that fits with the sharpness of the refocused image 25 , 26 . The value of \(\mathrm{\alpha }\) that corresponds to the sharpness peak of the Gaussian function obtained after fitting is the \({\alpha }_{opt}\) , which corresponds to depth d.

where \(\upsigma\) is the standard deviation, and \(\upmu\) is the mathematical expectation.

Analysis of calibration results

Results of calibrating the optimal refocusing coefficient with fewer points.

Figure  9 shows the α–δ curve after Gaussian fitting with 5, 8, 10, 15, and 500 refocusing images when d  = 103.6 mm. It can be seen from Fig.  9 that the peak value of δ at this depth position is around 3.2, and the corresponding optimal refocusing coefficients \({\alpha }_{opt}\) are all around 1.5. When five refocusing images are used, the peak value of δ differs more compared to using more or fewer images, but it is still around 3.2 and \({\alpha }_{opt}\) is also around 1.5. The optimal refocusing coefficient without Gaussian fitting is also around 1.5, proving our method’s feasibility.

d = 103.6 mm α–δ chart.

Figure  10 illustrates the results of calibrating each depth position with a 5-micron point light source. The graph represents the relationship between each depth value d , and its corresponding optimized alpha \({\alpha }_{opt}\) . The numbers 5, 8, 10, 15, and 500 denote the number of refocusing performed at each depth position. The resulting curve is obtained by Gaussian fitting \(\mathrm{\alpha }\) and \(\delta\) , where the \(\mathrm{\alpha }\) value that corresponds to the maximum value of \(\delta\) is \({\alpha }_{opt}\) . Figure  9 highlights that when performing five refocusing at each depth position and using Gaussian fitting to determine \({\alpha }_{opt}\) , a deviation occurs around the depth range of 99–100 mm. The results are better aligned using 8, 10, 15, and 500 refocusing.

5 micron point light source d ~ \({\alpha }_{opt}\) diagram.

Therefore, when using the Gaussian fitting method to determine \({\alpha }_{opt}\) it is important to consider the influence of the number of refocusing images on the depth calibration range. This study suggests selecting around 10 refocusing images per depth position to determine \({\alpha }_{opt}\) , which reduces the time required for depth calibration significantly. Indeed, only 1/50 of the time is required when using 500 refocusing iterations.

Analysis of depth results and depth resolution for less point calibration

Figure  11 illustrates the depth calibration results obtained by selecting the optimal refocusing coefficient using 10 refocusing images. The rectangular and pentagonal markers represent the 5 and 9 data points used during calibration. The solid line, dashed line, and dotted line correspond to the results obtained from calibration using 5, 9, and 56 points, respectively. Table 1 reports the values of \({c}_{0}\) , \({c}_{1}\) , and \({c}_{2}\) associated with the indicated points.

Depth calibration curve.

In Eq. ( 14 ), the values of the denominator \({c}_{2}+{c}_{1}{c}_{0}\) are − 1.18955, − 1.17691, and − 1.25267, respectively. Additionally, it is worth noting that all values of \({c}_{1}\) are greater than 0, while all values of \({c}_{2}\) are less than 0. This indicates that the depth resolution of the system used in this study decreases as depth increases.

This paper describes the image rendering method for refocusing by combining ray tracing and integral imaging principles. We apply this method to capture and process images of a depth-of-field chart, with the results demonstrating that the refocused images agree well with the theoretical analysis. Furthermore, the experimental methodology for depth calibration based on the light field imaging theory model is improved. We showcase the α–δ curve obtained by Gaussian fitting and quantitatively select the optimal refocusing coefficient using different numbers of refocusing images at specific depths and the corresponding d  ~  α opt curve within the measurement range. The results indicate that when using Gaussian fitting to determine \({\alpha }_{opt}\) The applicable range is limited with a few refocusing images, e.g., five images examined in this paper. It is found that selecting around 10 refocusing images is preferable, significantly reducing the processing time required for image handling during the depth calibration process. Moreover, from the perspective of imaging principles combined with image processing, a detailed theoretical analysis of the depth resolution of this depth measurement method is conducted. For the specific light field system used in this study, the numerical value of the depth resolution decreases with increasing depth and increasing optimal refocusing coefficient.

Data availability

Data sets generated during the current study are available from the corresponding author on reasonable request.

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Yang, M. Research on depth measurement calibration of light field camera based on Gaussian fitting. Sci Rep 14 , 8774 (2024). https://doi.org/10.1038/s41598-024-59479-5

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BMC Medical Research Methodology volume  24 , Article number:  89 ( 2024 ) Cite this article

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Outliers, data points that significantly deviate from the norm, can have a substantial impact on statistical inference and provide valuable insights in data analysis. Multiple methods have been developed for outlier detection, however, almost all available approaches fail to consider the spatial dependence and heterogeneity in spatial data. Spatial data has diverse formats and semantics, requiring specialized outlier detection methodology to handle these unique properties. For now, there is limited research exists on robust spatial outlier detection methods designed specifically under the spatial error model (SEM) structure.

We propose the Spatial-Θ-Iterative Procedure for Outlier Detection (Spatial-Θ-IPOD), which utilizes a mean-shift vector to identify outliers within the SEM. Our method enables an effective detection of spatial outliers while also providing robust coefficient estimates. To assess the performance of our approach, we conducted extensive simulations and applied it to a real-world empirical study using life expectancy data from multiple countries.

Simulation results showed that the masking and JD (Joint Detection) indicators of our Spatial-Θ-IPOD method outperformed several commonly used methods, even in high-dimensional scenarios, demonstrating stable performance. Conversely, the Θ-IPOD method proved to be ineffective in detecting outliers when spatial correlation was present. Moreover, our model successfully provided reliable coefficient estimation alongside outlier detection. The proposed method consistently outperformed other models (both robust and non-robust) in most cases. In the empirical study, our proposed model successfully detected outliers and provided valuable insights in the modeling process.

Conclusions

Our proposed Spatial-Θ-IPOD offers an effective solution for detecting spatial outliers for SEM while providing robust coefficient estimates. Notably, our approach showcases its relative superiority even in the presence of high leverage points. By successfully identifying outliers, our method enhances the overall understanding of the data and provides valuable insights for further analysis.

Peer Review reports

In general, an outlier refers to a data point that significantly deviates from the norm for a specific variable or population [ 1 ]. It is also characterized as an observation that is inconsistent with the remaining data [ 2 ]. Swersky et al. (2016) further defined an outlier as an observation that diverges to the extent of arousing suspicions [ 3 ]. Outliers are inevitable [ 4 ] and sometimes carry special information. While in practice, some outliers may simply be considered as “noise” or “dirty data”, more often than not, they have the potential to influence statistical inference and provide valuable insights within the dataset [ 5 ]. For instance, in a published breast cancer detection system, inliers may represent healthy patients, while outliers may indicate a higher probability of breast cancer [ 6 ]. As a result, incorrect or crude treatment of outliers often results in loss of information, inaccurate statistical inferences and biased estimates. Accurately identifying outliers, especially in the field of public health, is of significant importance for further analysis of outliers to provide additional insights in certain aspects. Therefore, the methodology for detecting outliers is an essential and urgent need in data analysis [ 5 ].

A dataset may contain multiple outliers, posing challenges in detecting and addressing the masking and swamping effects [ 7 ]. Various methods have been employed for multiple outlier detection, including the fully efficient one-step procedure (GY) proposed by Gervini and Yohai (2002) [ 8 ], the least trimmed squares (LTS) [ 9 ], and the MM-estimators [ 10 ]. Moreover, other methods have also been developed to tackle different aspects of outlier detection. For instance, Kong et al. (2018) proposed a method based on the squared loss of the mean-shift model with two penalty functions on the mean-shift vector and the parameter vector, achieving both high breakdown points and high efficiency [ 11 ]. Jiang et al. (2020) introduced the penalized weighted LAD-LASSO (PWLAD-LASSO) estimator, which combines robust estimation and outlier detection properties [ 12 ]. Among these methods, we noticed that the Θ-IPOD method proposed by She & Owen (2011) used a regression model with a mean shift parameter. They incorporated a soft-thresholding penalty and a hard-thresholding penalty, which effectively counter the masking effects [ 13 ].

However, in recent years, the presence of spatial heterogeneity in data has become increasingly common in various fields such as survey studies, surveillance efforts, and longitudinal studies, particularly in cancer-related research [ 14 ]. For instance, the Surveillance, Epidemiology, and End Results (SEER) Program, the China Health and Retirement Longitudinal Study (CHARLS), and the China Northwest Cohort (CNC) often involve the collection of data at small geographical levels (such as communities or counties), which are subsequently aggregated at larger levels. This introduces additional complexity to outlier detection tasks. The primary reason for this is that geographic data often exhibit spatial dependence [ 15 ]. Traditional methods for outlier detection fail to consider the spatial relationships among input variables, while spatial patterns often demonstrate spatial continuity and autocorrelation with neighboring samples. For instance, the Θ-IPOD method relies on a linear structure with a mean-shift vector. However, the existence of spatial dependence violates the assumptions of traditional ordinary least squares (OLS) estimation and can result in a decrease in the efficiency and increase in the bias of the OLS estimator for the regression model parameters [ 16 ]. There have been some approaches to spatial outlier exploration, however, due to the diverse formats and semantics of spatial data, there is still a urgent need for outlier detection methodology that can accommodate these unique properties especially spatial dependence and heterogeneity [ 17 ].

In the area of spatial analysis, one commonly used method is the spatial error model (SEM), which considers the covariance structure between error terms [ 18 ]. The SEM model is adept at effectively addressing challenges related to spatial correlation and heterogeneity. SEM has been successfully applied in various applications, providing valuable insights when the spatially autocorrelated error structure is well-defined [ 19 ]. Some robust spatial regression approaches have been proposed in recent years. José- Montero et al. (2012) introduced a model incorporating a global spatial trend within a Spatial Autoregressive (SAR) framework to address both large-scale spatial dependencies and local spatial autocorrelation. The utilization of penalized splines for model estimation was emphasized, leveraging their representation as mixed models [ 20 ]. Boente et al. (2012) presented a robust estimation framework encompassing parametric and nonparametric components within the context of a generalized partly linear single-index model [ 21 ]. Additionally, Yildirim et al. (2020) proposed a robust estimation approach utilizing robustified likelihood equations specifically tailored for SEM [ 22 ]. However, it is important to highlight that there is limited research available on robust spatial outlier detection specifically tailored to the SEM structure. These spatial robust estimation methods do not yield explicit results identifying which observations are outliers, which is not conducive to our further analysis of outliers.

Therefore, in this study, we propose a novel outlier detection method Spatial-Θ-IPOD for SEM-structure data. Considering the outstanding performance of the Θ-IPOD method in detecting outliers under normal circumstances, we have decided to extend its application to the structure of the SEM model to address the task of spatial outlier detection.

The contributions of this paper are as follows:

(1) We proposed an extension of the IPOD method to incorporate the structure of the SEM model, calling Spatial-Θ-IPOD, enabling the detection of spatial outliers while effectively addressing the challenges posed by masking and swamping effects.

(2) In addition to outlier detection, our approach also provided robust estimates for the coefficients.

(3) We evaluated the effectiveness of the proposed algorithms for spatial outlier detection by applying them to the analysis of Life Expectancy (LE) data from multiple countries. We conduct a comprehensive analysis of the detected outliers, providing valuable insights and robust estimated results.

The Θ-IPOD method

The Θ-IPOD is based on the mean-shift model [ 13 ]:

where  \({\mathbf{X}} = [{\mathbf{x}}_{{\mathbf{1}}} ,...,{\mathbf{x}}_{{\mathbf{n}}} ]^{T} \in {\mathbb{R}}^{n \times p}\) , \({\mathbf{y}} = [y_{1} ,...,y_{n} ]^{T} \in {\mathbb{R}}^{n}\) , \({{\varvec{\upbeta}}} = [\beta_{1} ,...,\beta_{p} ]^{T} \in {\mathbb{R}}^{p}\) , \(\epsilon\in {\mathbb{R}}^{n}\) is a random error vector. \({{\varvec{\upgamma}}} = (\gamma_{1} ,...,\gamma_{n} )^{T} \in {\mathbb{R}}^{n}\) acts as a vector indicating the locations of outliers. If one γ i does not equal 0, it means the corresponding observation is an outlier.

To deal with masking and swamping in the presence of multiple outliers mentioned before, λ is the regularization parameters, a general threshold function Θ was been used. \(\Theta (t;\lambda )\) is an odd monotone unbounded shrinkage rule for t , at any λ , which satisfies:

\(\Theta ( - t;\lambda ) = - \Theta (t;\lambda )\)

\(\Theta (t;\lambda ) \le \Theta \left( {t^{\prime } ;\lambda } \right) \, for \, 0 \le t \le t^{\prime }\)

\(\mathop {\lim }\limits_{t \to \infty } \Theta (t;\lambda ) = \infty\)

\(0 \le \Theta (t;\lambda ) \le t \, for \, 0 \le t < \infty\)

In their study, they considered two version of threshold function Θ, which are:

For any threshold function Θ(·; λ), a penalty function \(P_{\Theta } ( \cdot ;\lambda )\) with the smallest curvature corresponding can be found by following three-step construction,

\(\Theta^{ - 1} (u;\lambda ) = \sup \{ t:\Theta (t;\lambda ) \le u\}\)

\(s(u;\lambda ) = \Theta^{ - 1} (u;\lambda ) - u\)

\(P(\theta ;\lambda ) = P_{\Theta } (\theta ;\lambda ) = \int_{0}^{|\theta |} s (u;\lambda ){\text{d}}u\)

The ultimate goal is to optimize the following formula to obtain the robust estimate of \(({\hat{\mathbf{\beta }}},{\hat{\mathbf{\gamma }}})\) by iterative procedure.

The update of \({{\varvec{\upgamma}}}\) via \({{\varvec{\upgamma}}}^{(j + 1)} = \Theta \left( {{\mathbf{H\gamma }}^{(j)} + ({\mathbf{I}} - {\mathbf{H}}){\mathbf{y}};{{\varvec{\uplambda}}}} \right)\) at each iteration, where \(\lambda_{i} = \lambda \sqrt {1 - h_{i} }\) , the HatMatrix \({\mathbf{H}}\) can be defined as \({\mathbf{H}} = {\mathbf{H(X)}} = {\mathbf{X(X}}^{{\mathbf{T}}} {\mathbf{X)}}^{{{\mathbf{ - 1}}}} {\mathbf{X}}^{{\mathbf{T}}}\) , \(h_{i}\) donates the i th diagonal entry of \({\mathbf{H}}\) .

About the choice of the regularization parameter, the λ can be chosen via BIC (Bayesian information criterion) [ 23 , 24 ]. To be more specific, it can be chosen by a slight modification BIC. Given \(\lambda\) and the corresponding estimate \(\widehat{\gamma }(\lambda )\) , let \(nz(\lambda ) = \{ i:\widehat{\gamma }_{i} (\lambda ) \ne 0\}\) , \(\widehat{\gamma }_{nz}\) is an OLS estimate with one parameter per detected outlier, and the degrees of freedom are given by \(DF(\lambda ) = \left| {nz(\lambda )} \right|\) . The slight modification of BIC is as \({\text{BIC}}^{*} (\lambda ) = m\log ({\text{RSS}} /m) + k(\log (m) + 1)\) ,where \(\mathbf{\overset{\frown}{y}}= {\mathbf{A\gamma }} + \epsilon^{\prime } ,\quad \epsilon^{\prime } \sim {\mathcal{N}}\left( {{\mathbf{0}},\sigma^{2} {\mathbf{I}}_{(n - p) \times (n - p)} } \right)\) , \(\mathbf{\overset{\frown}{y}}= {\mathbf{U}}{}_{{\mathbf{c}}}^{{\mathbf{T}}} {\mathbf{y}}\) , \({\mathbf{A}}\) can be obtained by the spectral decomposition of HatMatrix \({\mathbf{H}}\) , \({\mathbf{H = ADA}}^{{\mathbf{T}}}\) , \(m = n - p\) , \({\text{RSS}} = ||\mathbf{\overset{\frown}{y}}- {\mathbf{A}}\widehat{{{\varvec{\upgamma}}}}||_{2}^{2} = ({\mathbf{I}} - {\mathbf{H}})({\mathbf{y}} - \widehat{{{\varvec{\upgamma}}}})||_{2}^{2}\) , and k  = degrees of freedom + 1.

The selection range of \(\lambda\) is decreasing from \(||({\mathbf{I}} - {\mathbf{H}}){\mathbf{y}}/\sqrt {{\text{diag}} ({\mathbf{I}} - {\mathbf{H}})}||_{\infty }\) to 0, and select the \(\lambda\) with the minimum \({\text{BIC}}^{*} (\lambda )\) .

The detail algorithm is as follows:

Algorithm 1 Θ-IPOD

• Spatial error model

SEM has been extensively utilized in various fields such as econometrics, regional science, forest science, social science, and marketing research. More recently, it has also found applications in the field of public health [ 25 ]. SEM regression model involving the coefficient of spatial dependence or autocorrelation ( μ ) that captures the spatial dependence in the error terms, is presented as follows:

Normal SEM model can be described as

where \({\mathbf{y}}\) contains an n  × 1 vector of dependent variables and \({\mathbf{X}}\) represents an n  ×  p matrix of independent variables. \({{\varvec{\upbeta}}}\) is a vector of p  × 1 vector of regression parameter to be estimated of the model. μ is the spatial autoregressive parameter needed to be estimated. \({\mathbf{W}}\) is the row-standardized weight matrix, which is calculated based on the distance matrix indicating how locations are spatially interconnected. The lag-error term \({{\varvec{\upxi}}} = \mu {\mathbf{W\xi }} +\epsilon ,\quad \epsilon\sim {\mathcal{N}}\left( {0,\sigma^{2} {\mathbf{I}}} \right)\) effectively addresses spatial dependence within the error terms, thereby augmenting the conventional linear model. The Eq. ( 4 ) shows that the observations have a Gaussian distribution with \({\mathbf{y}}\sim {\mathcal{N}}({\mathbf{X\beta }},\sigma^{2} ({\mathbf{I}}_{n} - \mu {\mathbf{W}})^{ - 1} )\) .

Spatial-Θ-IPOD

As mentioned earlier, while Θ-IPOD demonstrates excellent performance under normal regression assumptions, it is observed that the error term deviates from the ordinary linear model. Consequently, Θ-IPOD may no longer be applicable in such cases.

To address this limitation, we propose a modified approach called Spatial-Θ-IPOD, which incorporates a mean shift vector γ into the SEM to identify outliers and obtain robust coefficient estimations. This modification enables the method to be suitable for the SEM data structure. The model is described as follows:

Motivated by Yildirim (2020) [ 22 ], one possible approach for estimating the regression coefficients of the SEM is the generalized least squares (GLS) method. This method is applicable when the spatial autoregressive parameter μ is known or has been previously estimated. Therefore, we generalize Eq. ( 5 ) as follows:

where \({\tilde{\mathbf{y}}} = ({\mathbf{I}}_{n} - \hat{\mu }{\mathbf{W}}){\mathbf{y}},{\tilde{\mathbf{X}}} = ({\mathbf{I}}_{n} - \hat{\mu }{\mathbf{W}}){\mathbf{X}},{\tilde{\mathbf{\gamma }}} = ({\mathbf{I}}_{n} - \hat{\mu }{\mathbf{W}}){{\varvec{\upgamma}}}\) .

Under this model setting, the optimization problem turns to

We utilize the iterative procedure to solve the optimization problem. Before that, if μ is known, it can directly be used for the optimization. If μ is unknown, it can be estimated previously by following method [ 22 ]:

(i) Choose \(\psi\) function

(ii) Choose initial values \(\beta\) , \(\mu\) via OLS (Ordinary least square) or GMM (Generalized Moment Model)

(iii) Compute \({{\varvec{\upbeta}}}^{(i + 1)}\) from equation \({{\varvec{\upbeta}}}^{(i + 1)} = {{\varvec{\upbeta}}}^{(i)} + \left[ {I\left( {{{\varvec{\upbeta}}}^{(i)} } \right)} \right]^{ - 1} s_{\beta }^{(i)}\) .

(iv) Compute residuals with the estimated \({{\varvec{\upbeta}}}^{(i + 1)}\) .

(v) Compute \(\mu^{(i + 1)}\) from equation \(\mu^{(i + 1)} = \mu^{(i)} + [I(\mu^{(i)} )]^{ - 1} s_{\mu }^{(i)}\) .

(vi) Repeat steps iii-v until convergence for \({{\varvec{\upbeta}}}\) and \(\mu\) .

where \({\mathbf{r}} = \hat{\Omega }_{\lambda }^{ - 1/2} \frac{{({\mathbf{y}} - {\mathbf{X\beta }})}}{{\hat{\sigma }}}\) , \(\Omega_{\lambda } = \left( {{\mathbf{I}}_{n} - \lambda {\mathbf{W}}} \right)^{ - 1} \left( {{\mathbf{I}}_{n} - \lambda {\mathbf{W}}^{\prime } } \right)^{ - 1}\) , \(K = \int_{ - \infty }^{\infty } {\psi^{2} } (r)f(r)dr\) , \(\psi ( \cdot )\) is the influence function can be chosen, containing Cauchy function, Insha function, etc. The observed information matrix \(I( \cdot )\) can be obtained as minus the expected value of the second derivatives of the robust log-likelihood functions. The score functions are \(s_{\beta } = \, \frac{{\hat{\sigma }}}{{\sigma^{2} }}{\mathbf{X}}^{\prime } \left( {{\mathbf{I}}_{n} - \mu {\mathbf{W}}} \right)^{2} \left( {{\mathbf{I}}_{n} - \hat{\mu }{\mathbf{W}}} \right)^{ - 1} \psi (r) = 0\) and \(s_{\mu } = - K{\text{tr}} \left( {\left( {{\mathbf{I}}_{n} - \mu {\mathbf{W}}} \right)^{ - 1} {\mathbf{W}}} \right) + \frac{{\hat{\sigma }^{2} }}{{\sigma^{2} }}\psi (r)^{\prime } \left( {{\mathbf{I}}_{n} - \hat{\mu }{\mathbf{W}}} \right)^{ - 1} \left( {{\mathbf{I}}_{n} - \mu {\mathbf{W}}} \right) \times {\mathbf{W}}\left( {{\mathbf{I}}_{n} - \hat{\mu }{\mathbf{W}}} \right)^{ - 1} \psi (r) = 0\) .

The Spatial-Θ-IPOD algorithm is listed as follows:

Algorithm 2 Spatial-Θ-IPOD

Similar with IPOD, the regularization parameter of our proposed Spatial-Θ-IPOD is tuned in a data-dependent way by a slight modification of BIC, with decreasing \(\lambda\) from \(||({\mathbf{I}} - {\tilde{\mathbf{H}}}){\tilde{\mathbf{y}}}/\sqrt {{\text{diag}} ({\mathbf{I}} - {\tilde{\mathbf{H}}})}||_{\infty }\) to 0.

Simulation study

Simulation design.

We carried out simulation experiments to test the performance of the Spatial-Θ-IPOD. It is well known that the presence of leverage points can cause failure in outlier detection methods. To be more specific, a data point whose x-value (independent) is unusual, y-value follows the predicted regression line though. Thus, we considered different combinations of dimensions, outlier quantities, and leverage values.

The observations were generated according to

The predictor matrix \({\mathbf{X}}\) is constructed as follows. Firstly, let \({\mathbf{X}} = {\mathbf{U\Sigma }}^{1/2}\) , where \(U_{ij} \mathop \sim \limits^{iid} U( - 5,5)\) and \(\Sigma_{ij} = \rho^{{1_{i \ne j} }}\) with ρ  = 0.5. The dimension of \({\mathbf{X}}\) is set \(p \in \{ 15,50\}\) , n  = 500. Next, we modify the first O rows to represent leverage points, which are given by \(L \cdot [1,...,1]\) . We consider six cases, involving variations of \(L \in \{ 15,20\}\) and \(O \in \{ 10,20,50\}\) . Additionally, three more cases involve additive outliers at O points that are not leverage points, meaning that no rows of \({\mathbf{X}}\) are changed. The β vector is set as [1,…,1] p . The shift vector is generated by \({{\varvec{\upgamma}}} = (\{ 8\}^{O} ,\{ 0\}^{n - O} )\) . In order to add spatial heterogeneity, we incorporate a spatial error term \({{\varvec{\upxi}}}\) into the model. The generation of the spatial error term \({{\varvec{\upxi}}}\) is constructed as follows, with λ set to 0.7.

The spatial contiguity matrix \({\mathbf{W}} = ({\mathbf{W}}_{ij} )\) can be generated based on \(w_{ij} = \left\{ \begin{gathered} r^{|i - j|} ,i \ne j \hfill \\ 0,i = j \hfill \\ \end{gathered} \right.\) , where r  = 0.5. Here, we assume that these observations are arranged in a linear sequence. Generally, it can be considered as a graph structure. The \(\left| {i - j} \right|\) donates the graph distance between observation i and j . The σ 2 is set 0.2.

Our simulation experiments mainly contain two aspects:

The first part of our simulation experiments focuses on comparing the outlier detection performance of seven different methods: Spatial-hard-IPOD, Spatial-soft-IPOD, hard-IPOD, soft-IPOD, MM-estimator, fully efficient one-step procedure proposed by Gervini and Yohai (donoted by GY), and the least trimmed squares (LTS). These methods are implemented in the robust package (R version 4.1.2) and available in the S–PLUS Robust library. To ensure a fair comparison with Θ-IPOD, we evaluate their performance based on three benchmark measures: the mean masking probability (M), the mean swamping probability (S), and the joint outlier detection rate (JD).

The mean masking probability (M) represents the fraction of true outliers that go undetected. The mean swamping probability (S) indicates the fraction of non-outliers that are incorrectly labeled as outliers. The JD is the joint outlier detection rate, which measures the fraction of simulations with no masking (false negatives). In outlier detection, masking is considered more serious than swamping as it can lead to significant distortions. Swamping, on the other hand, typically results in a loss of efficiency. Ideally, we aim for M to be close to 0, S to be close to 0, and JD to be close to 100%. The joint outlier detection rate (JD) is particularly important for easier problems, while the mean masking probability (M) is more relevant for harder problems.

In the second part of our experiments, we compare the Mean Squared Error (MSE) of the estimated parameter β among 13 methods. These include the seven outlier detection methods mentioned earlier, as well as several robust methods for spatial estimation regression such as RoMLE (Robust estimation approach for spatial error model), including (RoMLE_Cauchy, RoMLE_Welsch, RoMLE_Insha, and RoMLE_Logistic). Because the RoMLE for SEM has smaller mean squared errors and exhibits more robust empirical influence function than the classical methods, when there are outliers in the dataset, we also conclude in our comparison. The difference between the four RoMLE method is that they choose different ψ function. The ψ function is introduced in Method section. Additionally, we consider non-robust methods, such as MLE (Maximum Likelihood Estimation) and GMM (Generalized Moments Method).

All calculations were performed in R. The code and scripts reproducing the examples in this simulation study are publicly available online at GitHub ( https://github.com/Justin0607/spatialoutlierdetection ).

Simulation results

Tables 1 and 2 present the outlier identification performances of seven models in various simulation scenarios. Figs.  1 and 2 illustrate the results of Masking and JD for p  = 15 and 50 respectively. While our main objective is to identify outliers, our proposed Spatial-Θ-IPOD model also provides a robust coefficient estimate \(\hat{\beta }\) .

Masking (M) and joint detection (JD) when p  = 15

Masking (M) and joint detection (JD) when p  = 50

The MSE in β for p equals 15 and 50 can be found in Tables  3 and 4 respectively, with corresponding trends shown in Figs.  3 and 4 . Because our model significantly outperforms other models, even by several orders of magnitude, we have applied a logarithmic transformation to the MSE for ease of visualization and to better illustrate the trend.

Coefficient estimation errors when p  = 15

Coefficient estimation errors when p  = 50

In terms of masking, our proposed model consistently outperforms the other models across all simulation scenarios when p equals 15. We also notice that both our Spatial-hard-IPOD and Spatial-soft-IPOD models exhibit similar performance (Tables  1 and   2 , Figs.  1 and   2 ).

Additionally, we compare our models with three standard methods (MM, GY, and LTS) from the SPLUS Robust library. Among these, the GY-estimator ranks second in terms of performance. However, the MM-estimator, despite its popularity in robust analysis, and Spatial-soft-IPOD show relatively weaker performance. When p equals 50, the overall results remain largely consistent, with a slight improvement in MM's performance, although it still falls in the middle when compared to other models (Tables  1 and   2 , Figs.  1  and   2 ).

In terms of the JD indicator, when p equals 15, our proposed model consistently outperforms the other models in most scenarios, except for one scenario with a small number of outliers and no leverage. In this particular scenario, the Spatial-soft-IPOD model falls slightly behind the soft-IPOD, but the Spatial-hard-IPOD still remains the top-performing model among all. In contrast, the performance of the hard-IPOD, soft-IPOD, MM, and LTS models is not as satisfactory. Notably, the GY-estimator performs poorly across all cases, indicating limited effectiveness in outlier detection even with a large number of simulations. When p  = 50, we find that the performance of our proposed method is not significantly affected, as the JD indicators continue to remain at a high level (Tables  1 and   2 , Figs.  1  and   2 ).

Regarding swamping, it is worth mentioning that although our proposed Spatial-Θ-IPOD model excels in masking, it shows slightly weaker performance in terms of swamping. However, this trade-off is acceptable, as masking poses a greater risk and harm.

Overall, the soft-IPOD, hard-IPOD, MM, LTS, and GY models demonstrate high masking probabilities and low joint detection rates, particularly when the dimensionality ( p ) is high. However, our proposed Spatial-Θ-IPOD method surpasses all of these models in terms of both masking probability and joint detection rate.

We also present the MSE of \(\widehat{\beta }\) . As depicted in Table  3 , when p equals 15, it is evident that our method significantly outperforms other methods in most cases. The hard-IPOD, soft-IPOD, MM, LTS, and GY models exhibit considerably poorer performance, with a magnitude difference that is much larger compared to other models. The MLE and GMM models demonstrate better performance than the aforementioned five methods but still have room for improvement. Among all the models, the four RoMLE models are the closest to our MSE, but generally, our method still yields lower MSE, except in two scenarios (Outliers = 10, no leverage and Outliers = 50, leverage = 20) where we slightly lag behind. In terms of our proposed Spatial-hard-IPOD and Spatial-soft-IPOD models, the Spatial-soft-IPOD consistently outperforms the Spatial-hard-IPOD in all situations, while the MSEs of both methods increase as the number of outliers increases (Tables  3 and   4 , Figs.  3  and   4 ).

When p equals 50, the overall performance situation remains largely unchanged, with our proposed Spatial-Θ-IPOD model still exhibiting the best MSE performance among all the models. The only difference is that the MSE of Spatial-Θ-IPOD is slightly larger compared to that of p equals 15 (Tables  3 and   4 , Figs.  3 and   4 ).

Empirical study

In this section, we conducted a multi-country cross-sectional study using public data from the World Bank ( https://data.worldbank.org/ ) among 267 countries and regions to detect outliers in life expectancy (LE) measurement for the year 2020. In order to ensure that missing values will not affect the results of our empirical study, we excluded data with missing values from some countries, resulting in a selection of 82 countries and regions. The adjacency matrix for these countries was obtained using GeoDa (Luc Anselin 1.22.0.2).

Following the variables chosen by Ranabhat (2018) [ 26 ], the dependent variable in our study is the life expectancy of each country, while the independent variables include economic growth rate, child immunization rate, out-of-pocket expenditure percentage, domestic private health expenditure percentage, and access to improved sanitation percentage.

The fitting model is

\({\mathbf{W}}^{{\mathbf{*}}}\) is spatial contiguity matrix which contains the distance between each country. Because the performance of Spatial-soft-IPOD is slightly better than Spatial-hard-IPOD in our simulation, we apply our proposed Spatial-soft-IPOD to conduct this empirical study.

The results shows that the \(\gamma_{10} = 11.82855\) , while other \(\gamma_{i} = 0\) , it indicates that the 10th observation is an outlier in this situation, which is Suriname, a country in South America. The corresponding map of these countries with one outlier observation (red dot) is shown as Supplementary Fig.  1 .

Accurately detecting outliers has many implications, including detecting outliers often provides valuable insights about the dataset. We furthermore conducted a thorough check of all variables for this country. Suriname's life expectancy ranks 42nd among the 82 countries, while its rankings for the remaining five indicators all fall behind 43rd. Specifically, the rankings for the other indicators are as follows: economic growth rate (81st), child immunization rate (82nd), out-of-pocket expenditure percentage (55th), domestic private health expenditure percentage (47th), and access to improved sanitation percentage (65th).

Generally, these factors all have a positive correlation with life expectancy. Under this assumption, the Suriname’s life expectancy should not rank as high as 42nd. However, the life expectancy of Suriname does not seem to align with the general trend. Therefore, it has been identified as an outlier based on these five variables.

Subsequently, we endeavored to determine the reasons behind the occurrence of this outlier. We examined other predictors related with life expectancy but not included in the study. For instance, Suriname's rankings in current health expenditure, enrollment, external health expenditure, and population growth are 39th, 22nd, 41st, and 42nd, respectively, which are higher than life expectancy ranks 42nd. Therefore, in the study, Suriname has been identified as an outlier, which may be associated with our choice of variables.

In this study, we proposed Spatial-Θ-IPOD for detecting spatial data outliers in SEM structures, while providing robust coefficient estimation results. We extended the IPOD method to incorporate spatial data structures, allowing for consideration of spatial error lag effects and inheriting the desirable properties of IPOD in combating masking.

In addition, due to the potential inadequacy of relying solely on raw residuals for effectively detecting outliers occurring at leverage points. Therefore, we not only examined the impact of outliers but also investigated the influence of leverage points on outlier detection, an aspect that has been rarely addressed in previous spatial outlier detection studies. Our simulation results demonstrated that the original IPOD method was not effective in detecting outliers in the presence of spatial correlation. Our masking and JD indicators outperformed several commonly used methods, both robust and non-robust, even in high-dimensional settings, with stable algorithm performance. While outlier detection was our primary objective, our model also provided stable coefficient estimation. Simulation study showed that our algorithm performed better than other models in the majority of cases, with only slight inferiority to the RoMLE model in a few instances. Furthermore, the MSE of our method slightly increased with increasing data contamination, which is consistent with general knowledge.

Accurately detecting outliers is important because it provides valuable insights about the dataset. The empirical study given is of Suriname being identified as an outlier observation in a study. The rankings of Suriname in various indicators, such as life expectancy and other variables, do not align with the general trend. This exemplifies one aspect of the significance of outlier detection, as analyzing outlier points can provide additional information. As demonstrated in this example, it indicates that the selected variables cannot fully explain all observations. When other four relevant variables are included in the model, Suriname is no longer classified as an outlier. Outliers offer valuable insights for uncovering hidden knowledge and enhancing healthcare services. Medical professionals can utilize these results to make informed predictions from extensive medical databases.

A limitation of this study is that in our simulation study, we have not considered the case of p  >  n . Currently, there are some issues with inadequate sample sizes in existing research, which will be the focus of our future studies. Another limitation of this study is that we tailored for cross-sectional data analysis rather than longitudinal data. The longitudinal data offers benefits such as capturing temporal trends and changes over time. We intend to extend our model to longitudinal data in future research.

In conclusion, we proposed a Spatial-Θ-IPOD method that effectively detects spatial outliers in the context of SEM structure and provides robust estimates of coefficients. Our method demonstrates relative superiority even in the presence of high leverage points. The detection of outliers offers valuable insights and enhances our understanding of the data.

Availability of data and materials

All data involved in the current empirical study were obtained from World Bank program ( https://data.worldbank.org/ ).

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Acknowledgements

We sincerely thank Professor Guoyou Qin for his significant help and guidance in statistical modelling, statistical simulations, and interpretation of results in this study.

This research was supported by the National Social Science Fund of China (21CTJ009, F.C.), the National Natural Science Foundation of China (81703325, F.C.), the Natural Science Basic Research Program of Shaanxi Province (2022JQ-769, F.C.) and the National Key Research and Development Program of China (2017YFC0907200 and 2017YFC0907201, H.Y.).

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Jiaxin Cai, Weiwei Hu, Yuhui Yang, Hong Yan & Fangyao Chen

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J.C., H.Y., and F.C. proposed the study concept and design; J.C., W.H. and Y.Y. drafted the manuscript; J.C. performed statistical analysis; H.Y., and F.C. conducted study supervision; and all authors critically revised the manuscript for important intellectual content.

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Cai, J., Hu, W., Yang, Y. et al. Outlier detection in spatial error models using modified thresholding-based iterative procedure for outlier detection approach. BMC Med Res Methodol 24 , 89 (2024). https://doi.org/10.1186/s12874-024-02208-3

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Title: leave no context behind: efficient infinite context transformers with infini-attention.

Abstract: This work introduces an efficient method to scale Transformer-based Large Language Models (LLMs) to infinitely long inputs with bounded memory and computation. A key component in our proposed approach is a new attention technique dubbed Infini-attention. The Infini-attention incorporates a compressive memory into the vanilla attention mechanism and builds in both masked local attention and long-term linear attention mechanisms in a single Transformer block. We demonstrate the effectiveness of our approach on long-context language modeling benchmarks, 1M sequence length passkey context block retrieval and 500K length book summarization tasks with 1B and 8B LLMs. Our approach introduces minimal bounded memory parameters and enables fast streaming inference for LLMs.

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With proposed standardisation under review, new WFE research provides a robust and useful method of measuring margin model responsiveness to changes in market conditions.

PRESS RELEASE

London, 16 April 2024 – With standard setters considering further guidance on initial margin in centrally cleared markets, the World Federation of Exchanges (“WFE”) has today published  research, co-authored by our Head of Research, Pedro Gurrola-Perez, introducing a novel measure of initial margin model reactiveness (or “procyclicality”) that, unlike other measures, does not rely on particular risk factor paths and quantifies the uncertainty in the measurements. 

The WFE Research Working Paper, “The Impulsive Approach to Procyclicality”, arrives soon after the recent BCBS-CPMI-IOSCO Review of Transparency and Responsiveness of Initial Margin in Centrally Cleared Markets, which seeks to establish a standardised measure of margin responsiveness across the international clearing community.

The responsiveness of initial margin models, both for centrally and non-centrally cleared trades, has been part of the discussions about how to best manage liquidity pressures in the financial system. However, the debate about how reactive margin should be to changes in market conditions has been hampered by the lack of a generally accepted and statistically sound way of measuring such reactiveness. 

Common measures of model procyclicality, including the method being proposed by the Joint Working Group on Margin (“JWGM”) set up by the Basel Committee on Banking Supervision, are strongly dependent on the individual scenarios and, as a consequence, cannot be used to compare margin models across different market conditions and are unlikely to provide a sufficient understanding of how models (and anti-procyclicality tools) could behave when there is an unanticipated change in market conditions. They also ignore the uncertainty surrounding the measurements.

The methodology proposed in this research overcomes these limitations, measuring margin responsiveness to shifts in volatility and market dynamics by:

•    Utilising an impulse response function (IRF) in a Monte Carlo simulation setting,

•    Capturing the variability (uncertainty) surrounding margin model reactiveness,

•    Providing a tool to assess and compare models that does not depend on a particular scenario.

The results presented demonstrate that a model’s impulse response is a robust and useful measure of its reactiveness. Using this measure, the analysis also sheds light on different aspects of procyclicality management:

•    There is a trade-off between model reactiveness and the uncertainty of future model behaviour, 

•    The use of a stress period and the addition of a buffer, two commonly used anti-procyclicality (APC) tools, do not significantly reduce the likelihood of a model over- or under-reacting. In particular, the buffer performs poorly.

•    The impact of the choice of core margin model far exceeds the impact of the APC tools analysed,

•    While the filtered Value at Risk (VaR) models analyzed offer the benefit of higher speeds of reaction, they tend to over-react to sharp, stepwise increases in volatility.

These results support the adoption of an outcome-based approach to procyclicality, recognising that there is no single correct level of procyclicality, but only acceptable choices given a specific situation (including risk factor dynamics, portfolio characteristics, participants’ funding liquidity arrangements), and the desired trade-off between reactiveness, potential extent of over-reaction, and margin accuracy.

This research also highlights the need for an adaptation of the current methodology proposed by BCBS-CPMI-IOSCO before it is put into effect: either by capturing the degree of uncertainty in the measurement, or by including an appropriate warning of the standard setter’s proposed method’s limitations. 

Please find the full study here .

Pedro Gurrola-Perez, Head of Research at the World Federation of Exchanges, commented “As the policy landscape looks set for change in this area, the research we have published today contributes to the sum of knowledge on this topic, sheds light on the shortcomings of the current approaches and proposals to measure model reactiveness (shortcomings which have often obscured the debate around procyclicality), and provides an alternative method for consideration which brings clarity to the discussion and provides the concepts of a model being over- or under-reactive with a statistically robust footing. 

Dr. David Murphy, Visiting Professor at the Department of Law at the London School of Economics, and co-author of the research, commented “As someone who has been studying the procyclicality of initial margin for some years, I am very happy to have been involved with this work. The importance of the measurement of procyclicality is increasingly recognised. For the first time, this paper presents a measure that allows different initial margin models to be robustly compared.”

About the World Federation of Exchanges (WFE)

Established in 1961, the WFE is the global industry association for exchanges and clearing houses. Headquartered in London, it represents over 250 market infrastructure providers, including standalone CCPs that are not part of exchange groups. Of our members, 36% are in Asia-Pacific, 43% in EMEA and 21% in the Americas. WFE’s 87 member CCPs and clearing services collectively ensure that risk takers post some $1.3 trillion (equivalent) of resources to back their positions, in the form of initial margin and default fund requirements. The exchanges covered by WFE data are home to 55,000 listed companies, and the market capitalization of these entities is over $111 trillion; around $124 trillion (EOB) in trading annually passes through WFE members (at end 2023).

The WFE is the definitive source for exchange-traded statistics and publishes over 350 market data indicators. Its free statistics database stretches back more than 40 years and provides information and insight into developments on global exchanges. The WFE works with standard-setters, policy makers, regulators, and government organisations around the world to support and promote the development of fair, transparent, stable and efficient markets. The WFE shares regulatory authorities’ goals of ensuring the safety and soundness of the global financial system.

With extensive experience of developing and enforcing high standards of conduct, the WFE and its members support an orderly, secure, fair and transparent environment for investors; for companies that raise capital; and for all who deal with financial risk. We seek outcomes that maximise the common good, consumer confidence and economic growth. And we engage with policy makers and regulators in an open, collaborative way, reflecting the central, public role that exchanges and CCPs play in a globally integrated financial system.

Click here to view the WFE’s website, sign up for the industry’s Focus magazine or to visit the WFE on LinkedIn . For Twitter see: @TheWFE

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Green-to-red transformation of Euglena gracilis using bonito stock and intense red light

Scientists explore a simple and sustainable method to increase the growth and carotenoid content ratio of an edible microalga.

Euglena gracilis , often regarded as a “superfood,” is a promising microalga with many health and nutritional benefits. In a recent study, researchers from Japan found an efficient and low-resource approach to trigger a reddening reaction in E. gracilis using red light and a bonito fish-based culture medium. This reaction is a sign of higher and diverse carotenoid content ratio, meaning the proposed method could help turn E. gracilis into an even more nutritious food source.

Over the past few years, people have generally become more conscious about the food they consume. Thanks to easier access to information as well as public health campaigns and media coverage, people are more aware of how nutrition ties in with both health benefits and chronic diseases. As a result, there is an ongoing cultural shift in most countries, with people prioritizing eating healthily. In turn, the demand for healthier food options and nutritional supplements is steadily growing.

In line with these changes, Assistant Professor Kyohei Yamashita from Tokyo University of Science (TUS), Japan, has been studying a promising "superfood" called Euglena gracilis for over half a decade. A species of edible microalgae, E. gracilis has a rich nutritional profile, with a unique combination of vitamins, fibers, lipids, and proteins. Like most other photosynthetic plants, E. gracilis also contains carotenoids -- natural substances with a wide variety of health benefits.

In a study published in 2023, a research team from TUS found a simple method to efficiently grow E. gracilis in an inexpensive medium (solid or liquid that contains nutrients and is used to grow bacteria) based on tomato juice. Now, in a new study, the researchers have explored a promising technique to make cultured E. gracilis produce carotenoids at a higher rate, rendering it even more nutritious. This study, which was co-authored by Dr. Kengo Suzuki from Euglena Co., Ltd., as well as Professor Tatsuya Tomo and Professor Eiji Tokunaga from TUS, was published in Volume 13, Issue 4 of the journal Plants in February 12, 2024.

The proposed approach is quite straightforward, and so is its rationale. When a plant is exposed to high-intensity light for extended periods of time, it undergoes a light-stress response. This, in turn, can cause the organism to produce molecules that protect it from further light exposure, including carotenoids. Based on these facts, the researchers investigated whether they could induce such a reaction in E. gracilis to enhance its carotenoid content ratio.

To this end, the team ran a series of experiments on multiple batches of cultured E. gracilis . They exposed cultures to light of different wavelengths (or colors) and at different intensities looking for a "reddening reaction," which is a tell-tale sign of higher carotenoid production in many plant species. Moreover, they also tested a new culture medium based on bonito stock, a soup stock extracted from Katsuobushi, a traditional Japanese dish made from smoked bonito fish.

Interestingly, the researchers found that strong red-light irradiation at 605-660 nm triggered a reddening reaction in E. gracilis when cultured in bonito stock. They also looked at the chemical profiles of the cultures using high-performance liquid chromatography, both at the culture and single-cell level. These analyses revealed that reddened cells not only had a high concentration of diadinoxanthin, the most abundant carotenoid in E. gracilis , but also produced an unidentified xanthophyll-type carotenoid. On top of these, the team also noted that bonito stock cultures grew quicker and reached higher densities than cultures grown on conventional media, and likely produced more types or amounts of carotenoids.

Together, the results of this study could pave the way for an innovative and easily scalable technique for growing nutritious E. gracilis . The method's simplicity is certainly one of its strengths, as Dr. Yamashita remarks, " Our approach does not involve genetic modifications and could thus be readily adopted by the food industry to expand the use of E. gracilis, both in food and as a nutritional supplement. " Notably, bonito stock is a nutritious food and using it in the culture medium would, therefore, provide additional health benefits.

Aside from its benefits to us humans, growing E. gracilis can also help the environment. " E. gracilis cultivation, which requires relatively few resources, can be a sustainable food resource ," explains Dr. Yamashita. " Our research marks an important step toward the development of new food technologies that contribute to people's lives from both health and environmental perspectives. "

With the carotenoid market poised to become a multi-billion-dollar industry by 2030, this study will help deepen our understanding of carotenoid biosynthetic pathways, hopefully leading to the development of sustainable practices in the production of nutritional supplements and emerging foods.

• Food and Agriculture
• Agriculture and Food
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Materials provided by Tokyo University of Science . Note: Content may be edited for style and length.

Journal Reference :

• Kyohei Yamashita, Ryusei Hanaki, Ayaka Mori, Kengo Suzuki, Tatsuya Tomo, Eiji Tokunaga. Reddening of the Unicellular Green Alga Euglena gracilis by Dried Bonito Stock and Intense Red Light Irradiation . Plants , 2024; 13 (4): 510 DOI: 10.3390/plants13040510

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