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How to write the methods section of a research paper

How to Write the Methods Section of a Research Paper

How to write the methods section of a research paper

Writing a research paper is both an art and a skill, and knowing how to write the methods section of a research paper is the first crucial step in mastering scientific writing. If, like the majority of early career researchers, you believe that the methods section is the simplest to write and needs little in the way of careful consideration or thought, this article will help you understand it is not 1 .

We have all probably asked our supervisors, coworkers, or search engines “ how to write a methods section of a research paper ” at some point in our scientific careers, so you are not alone if that’s how you ended up here.  Even for seasoned researchers, selecting what to include in the methods section from a wealth of experimental information can occasionally be a source of distress and perplexity.   

Additionally, journal specifications, in some cases, may make it more of a requirement rather than a choice to provide a selective yet descriptive account of the experimental procedure. Hence, knowing these nuances of how to write the methods section of a research paper is critical to its success. The methods section of the research paper is not supposed to be a detailed heavy, dull section that some researchers tend to write; rather, it should be the central component of the study that justifies the validity and reliability of the research.

Are you still unsure of how the methods section of a research paper forms the basis of every investigation? Consider the last article you read but ignore the methods section and concentrate on the other parts of the paper . Now think whether you could repeat the study and be sure of the credibility of the findings despite knowing the literature review and even having the data in front of you. You have the answer!   

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Having established the importance of the methods section , the next question is how to write the methods section of a research paper that unifies the overall study. The purpose of the methods section , which was earlier called as Materials and Methods , is to describe how the authors went about answering the “research question” at hand. Here, the objective is to tell a coherent story that gives a detailed account of how the study was conducted, the rationale behind specific experimental procedures, the experimental setup, objects (variables) involved, the research protocol employed, tools utilized to measure, calculations and measurements, and the analysis of the collected data 2 .

In this article, we will take a deep dive into this topic and provide a detailed overview of how to write the methods section of a research paper . For the sake of clarity, we have separated the subject into various sections with corresponding subheadings.  

Table of Contents

What is the methods section of a research paper ?  

The methods section is a fundamental section of any paper since it typically discusses the ‘ what ’, ‘ how ’, ‘ which ’, and ‘ why ’ of the study, which is necessary to arrive at the final conclusions. In a research article, the introduction, which serves to set the foundation for comprehending the background and results is usually followed by the methods section, which precedes the result and discussion sections. The methods section must explicitly state what was done, how it was done, which equipment, tools and techniques were utilized, how were the measurements/calculations taken, and why specific research protocols, software, and analytical methods were employed.  

Why is the methods section important?  

The primary goal of the methods section is to provide pertinent details about the experimental approach so that the reader may put the results in perspective and, if necessary, replicate the findings 3 .  This section offers readers the chance to evaluate the reliability and validity of any study. In short, it also serves as the study’s blueprint, assisting researchers who might be unsure about any other portion in establishing the study’s context and validity. The methods plays a rather crucial role in determining the fate of the article; an incomplete and unreliable methods section can frequently result in early rejections and may lead to numerous rounds of modifications during the publication process. This means that the reviewers also often use methods section to assess the reliability and validity of the research protocol and the data analysis employed to address the research topic. In other words, the purpose of the methods section is to demonstrate the research acumen and subject-matter expertise of the author(s) in their field.  

Structure of methods section of a research paper  

Similar to the research paper, the methods section also follows a defined structure; this may be dictated by the guidelines of a specific journal or can be presented in a chronological or thematic manner based on the study type. When writing the methods section , authors should keep in mind that they are telling a story about how the research was conducted. They should only report relevant information to avoid confusing the reader and include details that would aid in connecting various aspects of the entire research activity together. It is generally advisable to present experiments in the order in which they were conducted. This facilitates the logical flow of the research and allows readers to follow the progression of the study design.   

research methods sample paper

It is also essential to clearly state the rationale behind each experiment and how the findings of earlier experiments informed the design or interpretation of later experiments. This allows the readers to understand the overall purpose of the study design and the significance of each experiment within that context. However, depending on the particular research question and method, it may make sense to present information in a different order; therefore, authors must select the best structure and strategy for their individual studies.   

In cases where there is a lot of information, divide the sections into subheadings to cover the pertinent details. If the journal guidelines pose restrictions on the word limit , additional important information can be supplied in the supplementary files. A simple rule of thumb for sectioning the method section is to begin by explaining the methodological approach ( what was done ), describing the data collection methods ( how it was done ), providing the analysis method ( how the data was analyzed ), and explaining the rationale for choosing the methodological strategy. This is described in detail in the upcoming sections.    

How to write the methods section of a research paper  

Contrary to widespread assumption, the methods section of a research paper should be prepared once the study is complete to prevent missing any key parameter. Hence, please make sure that all relevant experiments are done before you start writing a methods section . The next step for authors is to look up any applicable academic style manuals or journal-specific standards to ensure that the methods section is formatted correctly. The methods section of a research paper typically constitutes materials and methods; while writing this section, authors usually arrange the information under each category.

The materials category describes the samples, materials, treatments, and instruments, while experimental design, sample preparation, data collection, and data analysis are a part of the method category. According to the nature of the study, authors should include additional subsections within the methods section, such as ethical considerations like the declaration of Helsinki (for studies involving human subjects), demographic information of the participants, and any other crucial information that can affect the output of the study. Simply put, the methods section has two major components: content and format. Here is an easy checklist for you to consider if you are struggling with how to write the methods section of a research paper .   

  • Explain the research design, subjects, and sample details  
  • Include information on inclusion and exclusion criteria  
  • Mention ethical or any other permission required for the study  
  • Include information about materials, experimental setup, tools, and software  
  • Add details of data collection and analysis methods  
  • Incorporate how research biases were avoided or confounding variables were controlled  
  • Evaluate and justify the experimental procedure selected to address the research question  
  • Provide precise and clear details of each experiment  
  • Flowcharts, infographics, or tables can be used to present complex information     
  • Use past tense to show that the experiments have been done   
  • Follow academic style guides (such as APA or MLA ) to structure the content  
  • Citations should be included as per standard protocols in the field  

Now that you know how to write the methods section of a research paper , let’s address another challenge researchers face while writing the methods section —what to include in the methods section .  How much information is too much is not always obvious when it comes to trying to include data in the methods section of a paper. In the next section, we examine this issue and explore potential solutions.   

research methods sample paper

What to include in the methods section of a research paper  

The technical nature of the methods section occasionally makes it harder to present the information clearly and concisely while staying within the study context. Many young researchers tend to veer off subject significantly, and they frequently commit the sin of becoming bogged down in itty bitty details, making the text harder to read and impairing its overall flow. However, the best way to write the methods section is to start with crucial components of the experiments. If you have trouble deciding which elements are essential, think about leaving out those that would make it more challenging to comprehend the context or replicate the results. The top-down approach helps to ensure all relevant information is incorporated and vital information is not lost in technicalities. Next, remember to add details that are significant to assess the validity and reliability of the study. Here is a simple checklist for you to follow ( bonus tip: you can also make a checklist for your own study to avoid missing any critical information while writing the methods section ).  

  • Structuring the methods section : Authors should diligently follow journal guidelines and adhere to the specific author instructions provided when writing the methods section . Journals typically have specific guidelines for formatting the methods section ; for example, Frontiers in Plant Sciences advises arranging the materials and methods section by subheading and citing relevant literature. There are several standardized checklists available for different study types in the biomedical field, including CONSORT (Consolidated Standards of Reporting Trials) for randomized clinical trials, PRISMA (Preferred Reporting Items for Systematic reviews and Meta-Analysis) for systematic reviews and meta-analysis, and STROBE (STrengthening the Reporting of OBservational studies in Epidemiology) for cohort, case-control, cross-sectional studies. Before starting the methods section , check the checklist available in your field that can function as a guide.     
  • Organizing different sections to tell a story : Once you are sure of the format required for structuring the methods section , the next is to present the sections in a logical manner; as mentioned earlier, the sections can be organized according to the chronology or themes. In the chronological arrangement, you should discuss the methods in accordance with how the experiments were carried out. An example of the method section of a research paper of an animal study should first ideally include information about the species, weight, sex, strain, and age. Next, the number of animals, their initial conditions, and their living and housing conditions should also be mentioned. Second, how the groups are assigned and the intervention (drug treatment, stress, or other) given to each group, and finally, the details of tools and techniques used to measure, collect, and analyze the data. Experiments involving animal or human subjects should additionally state an ethics approval statement. It is best to arrange the section using the thematic approach when discussing distinct experiments not following a sequential order.  
  • Define and explain the objects and procedure: Experimental procedure should clearly be stated in the methods section . Samples, necessary preparations (samples, treatment, and drug), and methods for manipulation need to be included. All variables (control, dependent, independent, and confounding) must be clearly defined, particularly if the confounding variables can affect the outcome of the study.  
  • Match the order of the methods section with the order of results: Though not mandatory, organizing the manuscript in a logical and coherent manner can improve the readability and clarity of the paper. This can be done by following a consistent structure throughout the manuscript; readers can easily navigate through the different sections and understand the methods and results in relation to each other. Using experiment names as headings for both the methods and results sections can also make it simpler for readers to locate specific information and corroborate it if needed.   
  • Relevant information must always be included: The methods section should have information on all experiments conducted and their details clearly mentioned. Ask the journal whether there is a way to offer more information in the supplemental files or external repositories if your target journal has strict word limitations. For example, Nature communications encourages authors to deposit their step-by-step protocols in an open-resource depository, Protocol Exchange which allows the protocols to be linked with the manuscript upon publication. Providing access to detailed protocols also helps to increase the transparency and reproducibility of the research.  
  • It’s all in the details: The methods section should meticulously list all the materials, tools, instruments, and software used for different experiments. Specify the testing equipment on which data was obtained, together with its manufacturer’s information, location, city, and state or any other stimuli used to manipulate the variables. Provide specifics on the research process you employed; if it was a standard protocol, cite previous studies that also used the protocol.  Include any protocol modifications that were made, as well as any other factors that were taken into account when planning the study or gathering data. Any new or modified techniques should be explained by the authors. Typically, readers evaluate the reliability and validity of the procedures using the cited literature, and a widely accepted checklist helps to support the credibility of the methodology. Note: Authors should include a statement on sample size estimation (if applicable), which is often missed. It enables the reader to determine how many subjects will be required to detect the expected change in the outcome variables within a given confidence interval.  
  • Write for the audience: While explaining the details in the methods section , authors should be mindful of their target audience, as some of the rationale or assumptions on which specific procedures are based might not always be obvious to the audience, particularly for a general audience. Therefore, when in doubt, the objective of a procedure should be specified either in relation to the research question or to the entire protocol.  
  • Data interpretation and analysis : Information on data processing, statistical testing, levels of significance, and analysis tools and software should be added. Mention if the recommendations and expertise of an experienced statistician were followed. Also, evaluate and justify the preferred statistical method used in the study and its significance.  

What NOT to include in the methods section of a research paper  

To address “ how to write the methods section of a research paper ”, authors should not only pay careful attention to what to include but also what not to include in the methods section of a research paper . Here is a list of do not’s when writing the methods section :  

  • Do not elaborate on specifics of standard methods/procedures: You should refrain from adding unnecessary details of experiments and practices that are well established and cited previously.  Instead, simply cite relevant literature or mention if the manufacturer’s protocol was followed.  
  • Do not add unnecessary details : Do not include minute details of the experimental procedure and materials/instruments used that are not significant for the outcome of the experiment. For example, there is no need to mention the brand name of the water bath used for incubation.    
  • Do not discuss the results: The methods section is not to discuss the results or refer to the tables and figures; save it for the results and discussion section. Also, focus on the methods selected to conduct the study and avoid diverting to other methods or commenting on their pros or cons.  
  • Do not make the section bulky : For extensive methods and protocols, provide the essential details and share the rest of the information in the supplemental files. The writing should be clear yet concise to maintain the flow of the section.  

We hope that by this point, you understand how crucial it is to write a thoughtful and precise methods section and the ins and outs of how to write the methods section of a research paper . To restate, the entire purpose of the methods section is to enable others to reproduce the results or verify the research. We sincerely hope that this post has cleared up any confusion and given you a fresh perspective on the methods section .

As a parting gift, we’re leaving you with a handy checklist that will help you understand how to write the methods section of a research paper . Feel free to download this checklist and use or share this with those who you think may benefit from it.  

research methods sample paper


  • Bhattacharya, D. How to write the Methods section of a research paper. Editage Insights, 2018. (2018).
  • Kallet, R. H. How to Write the Methods Section of a Research Paper. Respiratory Care 49, 1229–1232 (2004).
  • Grindstaff, T. L. & Saliba, S. A. AVOIDING MANUSCRIPT MISTAKES. Int J Sports Phys Ther 7, 518–524 (2012).

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Research Methodology Example

Detailed Walkthrough + Free Methodology Chapter Template

If you’re working on a dissertation or thesis and are looking for an example of a research methodology chapter , you’ve come to the right place.

In this video, we walk you through a research methodology from a dissertation that earned full distinction , step by step. We start off by discussing the core components of a research methodology by unpacking our free methodology chapter template . We then progress to the sample research methodology to show how these concepts are applied in an actual dissertation, thesis or research project.

If you’re currently working on your research methodology chapter, you may also find the following resources useful:

  • Research methodology 101 : an introductory video discussing what a methodology is and the role it plays within a dissertation
  • Research design 101 : an overview of the most common research designs for both qualitative and quantitative studies
  • Variables 101 : an introductory video covering the different types of variables that exist within research.
  • Sampling 101 : an overview of the main sampling methods
  • Methodology tips : a video discussion covering various tips to help you write a high-quality methodology chapter
  • Private coaching : Get hands-on help with your research methodology

Free Webinar: Research Methodology 101

PS – If you’re working on a dissertation, be sure to also check out our collection of dissertation and thesis examples here .

FAQ: Research Methodology Example

Research methodology example: frequently asked questions, is the sample research methodology real.

Yes. The chapter example is an extract from a Master’s-level dissertation for an MBA program. A few minor edits have been made to protect the privacy of the sponsoring organisation, but these have no material impact on the research methodology.

Can I replicate this methodology for my dissertation?

As we discuss in the video, every research methodology will be different, depending on the research aims, objectives and research questions. Therefore, you’ll need to tailor your literature review to suit your specific context.

You can learn more about the basics of writing a research methodology chapter here .

Where can I find more examples of research methodologies?

The best place to find more examples of methodology chapters would be within dissertation/thesis databases. These databases include dissertations, theses and research projects that have successfully passed the assessment criteria for the respective university, meaning that you have at least some sort of quality assurance.

The Open Access Thesis Database (OATD) is a good starting point.

How do I get the research methodology chapter template?

You can access our free methodology chapter template here .

Is the methodology template really free?

Yes. There is no cost for the template and you are free to use it as you wish.

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Example of two research proposals (Masters and PhD-level)

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Here's What You Need to Understand About Research Methodology

Deeptanshu D

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.

Analyze and understand research methodologies faster with SciSpace Copilot

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.

research methods sample paper

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Research Methods | Definition, Types, Examples

Research methods are specific procedures for collecting and analysing data. Developing your research methods is an integral part of your research design . When planning your methods, there are two key decisions you will make.

First, decide how you will collect data . Your methods depend on what type of data you need to answer your research question :

  • Qualitative vs quantitative : Will your data take the form of words or numbers?
  • Primary vs secondary : Will you collect original data yourself, or will you use data that have already been collected by someone else?
  • Descriptive vs experimental : Will you take measurements of something as it is, or will you perform an experiment?

Second, decide how you will analyse the data .

  • For quantitative data, you can use statistical analysis methods to test relationships between variables.
  • For qualitative data, you can use methods such as thematic analysis to interpret patterns and meanings in the data.

Table of contents

Methods for collecting data, examples of data collection methods, methods for analysing data, examples of data analysis methods, frequently asked questions about methodology.

Data are the information that you collect for the purposes of answering your research question . The type of data you need depends on the aims of your research.

Qualitative vs quantitative data

Your choice of qualitative or quantitative data collection depends on the type of knowledge you want to develop.

For questions about ideas, experiences and meanings, or to study something that can’t be described numerically, collect qualitative data .

If you want to develop a more mechanistic understanding of a topic, or your research involves hypothesis testing , collect quantitative data .

Quantitative .

You can also take a mixed methods approach, where you use both qualitative and quantitative research methods.

Primary vs secondary data

Primary data are any original information that you collect for the purposes of answering your research question (e.g. through surveys , observations and experiments ). Secondary data are information that has already been collected by other researchers (e.g. in a government census or previous scientific studies).

If you are exploring a novel research question, you’ll probably need to collect primary data. But if you want to synthesise existing knowledge, analyse historical trends, or identify patterns on a large scale, secondary data might be a better choice.


Descriptive vs experimental data

In descriptive research , you collect data about your study subject without intervening. The validity of your research will depend on your sampling method .

In experimental research , you systematically intervene in a process and measure the outcome. The validity of your research will depend on your experimental design .

To conduct an experiment, you need to be able to vary your independent variable , precisely measure your dependent variable, and control for confounding variables . If it’s practically and ethically possible, this method is the best choice for answering questions about cause and effect.


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Research methods for collecting data
Research method Primary or secondary? Qualitative or quantitative? When to use
Primary Quantitative To test cause-and-effect relationships.
Primary Quantitative To understand general characteristics of a population.
Interview/focus group Primary Qualitative To gain more in-depth understanding of a topic.
Observation Primary Either To understand how something occurs in its natural setting.
Secondary Either To situate your research in an existing body of work, or to evaluate trends within a research topic.
Either Either To gain an in-depth understanding of a specific group or context, or when you don’t have the resources for a large study.

Your data analysis methods will depend on the type of data you collect and how you prepare them for analysis.

Data can often be analysed both quantitatively and qualitatively. For example, survey responses could be analysed qualitatively by studying the meanings of responses or quantitatively by studying the frequencies of responses.

Qualitative analysis methods

Qualitative analysis is used to understand words, ideas, and experiences. You can use it to interpret data that were collected:

  • From open-ended survey and interview questions, literature reviews, case studies, and other sources that use text rather than numbers.
  • Using non-probability sampling methods .

Qualitative analysis tends to be quite flexible and relies on the researcher’s judgement, so you have to reflect carefully on your choices and assumptions.

Quantitative analysis methods

Quantitative analysis uses numbers and statistics to understand frequencies, averages and correlations (in descriptive studies) or cause-and-effect relationships (in experiments).

You can use quantitative analysis to interpret data that were collected either:

  • During an experiment.
  • Using probability sampling methods .

Because the data are collected and analysed in a statistically valid way, the results of quantitative analysis can be easily standardised and shared among researchers.

Research methods for analysing data
Research method Qualitative or quantitative? When to use
Quantitative To analyse data collected in a statistically valid manner (e.g. from experiments, surveys, and observations).
Meta-analysis Quantitative To statistically analyse the results of a large collection of studies.

Can only be applied to studies that collected data in a statistically valid manner.

Qualitative To analyse data collected from interviews, focus groups or textual sources.

To understand general themes in the data and how they are communicated.

Either To analyse large volumes of textual or visual data collected from surveys, literature reviews, or other sources.

Can be quantitative (i.e. frequencies of words) or qualitative (i.e. meanings of words).

Quantitative research deals with numbers and statistics, while qualitative research deals with words and meanings.

Quantitative methods allow you to test a hypothesis by systematically collecting and analysing data, while qualitative methods allow you to explore ideas and experiences in depth.

In mixed methods research , you use both qualitative and quantitative data collection and analysis methods to answer your research question .

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.

Statistical sampling allows you to test a hypothesis about the characteristics of a population. There are various sampling methods you can use to ensure that your sample is representative of the population as a whole.

The research methods you use depend on the type of data you need to answer your research question .

  • If you want to measure something or test a hypothesis , use quantitative methods . If you want to explore ideas, thoughts, and meanings, use qualitative methods .
  • If you want to analyse a large amount of readily available data, use secondary data. If you want data specific to your purposes with control over how they are generated, collect primary data.
  • If you want to establish cause-and-effect relationships between variables , use experimental methods. If you want to understand the characteristics of a research subject, use descriptive methods.

Methodology refers to the overarching strategy and rationale of your research project . It involves studying the methods used in your field and the theories or principles behind them, in order to develop an approach that matches your objectives.

Methods are the specific tools and procedures you use to collect and analyse data (e.g. experiments, surveys , and statistical tests ).

In shorter scientific papers, where the aim is to report the findings of a specific study, you might simply describe what you did in a methods section .

In a longer or more complex research project, such as a thesis or dissertation , you will probably include a methodology section , where you explain your approach to answering the research questions and cite relevant sources to support your choice of methods.

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These sample papers demonstrate APA Style formatting standards for different student paper types. Students may write the same types of papers as professional authors (e.g., quantitative studies, literature reviews) or other types of papers for course assignments (e.g., reaction or response papers, discussion posts), dissertations, and theses.

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Credits for sample professional paper templates

Quantitative professional paper template: Adapted from “Fake News, Fast and Slow: Deliberation Reduces Belief in False (but Not True) News Headlines,” by B. Bago, D. G. Rand, and G. Pennycook, 2020, Journal of Experimental Psychology: General , 149 (8), pp. 1608–1613 ( ). Copyright 2020 by the American Psychological Association.

Qualitative professional paper template: Adapted from “‘My Smartphone Is an Extension of Myself’: A Holistic Qualitative Exploration of the Impact of Using a Smartphone,” by L. J. Harkin and D. Kuss, 2020, Psychology of Popular Media , 10 (1), pp. 28–38 ( ). Copyright 2020 by the American Psychological Association.

Mixed methods professional paper template: Adapted from “‘I Am a Change Agent’: A Mixed Methods Analysis of Students’ Social Justice Value Orientation in an Undergraduate Community Psychology Course,” by D. X. Henderson, A. T. Majors, and M. Wright, 2019,  Scholarship of Teaching and Learning in Psychology , 7 (1), 68–80. ( ). Copyright 2019 by the American Psychological Association.

Literature review professional paper template: Adapted from “Rethinking Emotions in the Context of Infants’ Prosocial Behavior: The Role of Interest and Positive Emotions,” by S. I. Hammond and J. K. Drummond, 2019, Developmental Psychology , 55 (9), pp. 1882–1888 ( ). Copyright 2019 by the American Psychological Association.

Review professional paper template: Adapted from “Joining the Conversation: Teaching Students to Think and Communicate Like Scholars,” by E. L. Parks, 2022, Scholarship of Teaching and Learning in Psychology , 8 (1), pp. 70–78 ( ). Copyright 2020 by the American Psychological Association.

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This paper should be used only as an example of a research paper write-up. Horizontal rules signify the top and bottom edges of pages. For sample references which are not included with this paper, you should consult the Publication Manual of the American Psychological Association, 4th Edition .

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The Effects of a Supported Employment Program on Psychosocial Indicators for Persons with Severe Mental Illness William M.K. Trochim Cornell University


This paper describes the psychosocial effects of a program of supported employment (SE) for persons with severe mental illness. The SE program involves extended individualized supported employment for clients through a Mobile Job Support Worker (MJSW) who maintains contact with the client after job placement and supports the client in a variety of ways. A 50% simple random sample was taken of all persons who entered the Thresholds Agency between 3/1/93 and 2/28/95 and who met study criteria. The resulting 484 cases were randomly assigned to either the SE condition (treatment group) or the usual protocol (control group) which consisted of life skills training and employment in an in-house sheltered workshop setting. All participants were measured at intake and at 3 months after beginning employment, on two measures of psychological functioning (the BPRS and GAS) and two measures of self esteem (RSE and ESE). Significant treatment effects were found on all four measures, but they were in the opposite direction from what was hypothesized. Instead of functioning better and having more self esteem, persons in SE had lower functioning levels and lower self esteem. The most likely explanation is that people who work in low-paying service jobs in real world settings generally do not like them and experience significant job stress, whether they have severe mental illness or not. The implications for theory in psychosocial rehabilitation are considered.

The Effects of a Supported Employment Program on Psychosocial Indicators for Persons with Severe Mental Illness

Over the past quarter century a shift has occurred from traditional institution-based models of care for persons with severe mental illness (SMI) to more individualized community-based treatments. Along with this, there has been a significant shift in thought about the potential for persons with SMI to be “rehabilitated” toward lifestyles that more closely approximate those of persons without such illness. A central issue is the ability of a person to hold a regular full-time job for a sustained period of time. There have been several attempts to develop novel and radical models for program interventions designed to assist persons with SMI to sustain full-time employment while living in the community. The most promising of these have emerged from the tradition of psychiatric rehabilitation with its emphases on individual consumer goal setting, skills training, job preparation and employment support (Cook, Jonikas and Solomon, 1992). These are relatively new and field evaluations are rare or have only recently been initiated (Cook and Razzano, 1992; Cook, 1992). Most of the early attempts to evaluate such programs have naturally focused almost exclusively on employment outcomes. However, theory suggests that sustained employment and living in the community may have important therapeutic benefits in addition to the obvious economic ones. To date, there have been no formal studies of the effects of psychiatric rehabilitation programs on key illness-related outcomes. To address this issue, this study seeks to examine the effects of a new program of supported employment on psychosocial outcomes for persons with SMI.

Over the past several decades, the theory of vocational rehabilitation has experienced two major stages of evolution. Original models of vocational rehabilitation were based on the idea of sheltered workshop employment. Clients were paid a piece rate and worked only with other individuals who were disabled. Sheltered workshops tended to be “end points” for persons with severe and profound mental retardation since few ever moved from sheltered to competitive employment (Woest, Klein & Atkins, 1986). Controlled studies of sheltered workshop performance of persons with mental illness suggested only minimal success (Griffiths, 1974) and other research indicated that persons with mental illness earned lower wages, presented more behavior problems, and showed poorer workshop attendance than workers with other disabilities (Whitehead, 1977; Ciardiello, 1981).

In the 1980s, a new model of services called Supported Employment (SE) was proposed as less expensive and more normalizing for persons undergoing rehabilitation (Wehman, 1985). The SE model emphasizes first locating a job in an integrated setting for minimum wage or above, and then placing the person on the job and providing the training and support services needed to remain employed (Wehman, 1985). Services such as individualized job development, one-on-one job coaching, advocacy with co-workers and employers, and “fading” support were found to be effective in maintaining employment for individuals with severe and profound mental retardation (Revell, Wehman & Arnold, 1984). The idea that this model could be generalized to persons with all types of severe disabilities, including severe mental illness, became commonly accepted (Chadsey-Rusch & Rusch, 1986).

One of the more notable SE programs was developed at Thresholds, the site for the present study, which created a new staff position called the mobile job support worker (MJSW) and removed the common six month time limit for many placements. MJSWs provide ongoing, mobile support and intervention at or near the work site, even for jobs with high degrees of independence (Cook & Hoffschmidt, 1993). Time limits for many placements were removed so that clients could stay on as permanent employees if they and their employers wished. The suspension of time limits on job placements, along with MJSW support, became the basis of SE services delivered at Thresholds.

There are two key psychosocial outcome constructs of interest in this study. The first is the overall psychological functioning of the person with SMI. This would include the specification of severity of cognitive and affective symptomotology as well as the overall level of psychological functioning. The second is the level of self-reported self esteem of the person. This was measured both generally and with specific reference to employment.

The key hypothesis of this study is:

  • HO: A program of supported employment will result in either no change or negative effects on psychological functioning and self esteem.

which will be tested against the alternative:

  • HA: A program of supported employment will lead to positive effects on psychological functioning and self esteem.

The population of interest for this study is all adults with SMI residing in the U.S. in the early 1990s. The population that is accessible to this study consists of all persons who were clients of the Thresholds Agency in Chicago, Illinois between the dates of March 1, 1993 and February 28, 1995 who met the following criteria: 1) a history of severe mental illness (e.g. either schizophrenia, severe depression or manic-depression); 2) a willingness to achieve paid employment; 3) their primary diagnosis must not include chronic alcoholism or hard drug use; and 4) they must be 18 years of age or older. The sampling frame was obtained from records of the agency. Because of the large number of clients who pass through the agency each year (e.g. approximately 500 who meet the criteria) a simple random sample of 50% was chosen for inclusion in the study. This resulted in a sample size of 484 persons over the two-year course of the study.

On average, study participants were 30 years old and high school graduates (average education level = 13 years). The majority of participants (70%) were male. Most had never married (85%), few (2%) were currently married, and the remainder had been formerly married (13%). Just over half (51%) are African American, with the remainder Caucasian (43%) or other minority groups (6%). In terms of illness history, the members in the sample averaged 4 prior psychiatric hospitalizations and spent a lifetime average of 9 months as patients in psychiatric hospitals. The primary diagnoses were schizophrenia (42%) and severe chronic depression (37%). Participants had spent an average of almost two and one-half years (29 months) at the longest job they ever held.

While the study sample cannot be considered representative of the original population of interest, generalizability was not a primary goal – the major purpose of this study was to determine whether a specific SE program could work in an accessible context. Any effects of SE evident in this study can be generalized to urban psychiatric agencies that are similar to Thresholds, have a similar clientele, and implement a similar program.

All but one of the measures used in this study are well-known instruments in the research literature on psychosocial functioning. All of the instruments were administered as part of a structured interview that an evaluation social worker had with study participants at regular intervals.

Two measures of psychological functioning were used. The Brief Psychiatric Rating Scale (BPRS)(Overall and Gorham, 1962) is an 18-item scale that measures perceived severity of symptoms ranging from “somatic concern” and “anxiety” to “depressive mood” and “disorientation.” Ratings are given on a 0-to-6 Likert-type response scale where 0=“not present” and 6=“extremely severe” and the scale score is simply the sum of the 18 items. The Global Assessment Scale (GAS)(Endicott et al, 1976) is a single 1-to-100 rating on a scale where each ten-point increment has a detailed description of functioning (higher scores indicate better functioning). For instance, one would give a rating between 91-100 if the person showed “no symptoms, superior functioning…” and a value between 1-10 if the person “needs constant supervision…”

Two measures of self esteem were used. The first is the Rosenberg Self Esteem (RSE) Scale (Rosenberg, 1965), a 10-item scale rated on a 6-point response format where 1=“strongly disagree” and 6=“strongly agree” and there is no neutral point. The total score is simply the sum across the ten items, with five of the items being reversals. The second measure was developed explicitly for this study and was designed to measure the Employment Self Esteem (ESE) of a person with SMI. This is a 10-item scale that uses a 4-point response format where 1=“strongly disagree” and 4=“strongly agree” and there is no neutral point. The final ten items were selected from a pool of 97 original candidate items, based upon high item-total score correlations and a judgment of face validity by a panel of three psychologists. This instrument was deliberately kept simple – a shorter response scale and no reversal items – because of the difficulties associated with measuring a population with SMI. The entire instrument is provided in Appendix A.

All four of the measures evidenced strong reliability and validity. Internal consistency reliability estimates using Cronbach’s alpha ranged from .76 for ESE to .88 for SE. Test-retest reliabilities were nearly as high, ranging from .72 for ESE to .83 for the BPRS. Convergent validity was evidenced by the correlations within construct. For the two psychological functioning scales the correlation was .68 while for the self esteem measures it was somewhat lower at .57. Discriminant validity was examined by looking at the cross-construct correlations which ranged from .18 (BPRS-ESE) to .41 (GAS-SE).

A pretest-posttest two-group randomized experimental design was used in this study. In notational form, the design can be depicted as:

  • R = the groups were randomly assigned
  • O = the four measures (i.e. BPRS, GAS, RSE, and ESE)
  • X = supported employment

The comparison group received the standard Thresholds protocol which emphasized in-house training in life skills and employment in an in-house sheltered workshop. All participants were measured at intake (pretest) and at three months after intake (posttest).

This type of randomized experimental design is generally strong in internal validity. It rules out threats of history, maturation, testing, instrumentation, mortality and selection interactions. Its primary weaknesses are in the potential for treatment-related mortality (i.e. a type of selection-mortality) and for problems that result from the reactions of participants and administrators to knowledge of the varying experimental conditions. In this study, the drop-out rate was 4% (N=9) for the control group and 5% (N=13) in the treatment group. Because these rates are low and are approximately equal in each group, it is not plausible that there is differential mortality. There is a possibility that there were some deleterious effects due to participant knowledge of the other group’s existence (e.g. compensatory rivalry, resentful demoralization). Staff were debriefed at several points throughout the study and were explicitly asked about such issues. There were no reports of any apparent negative feelings from the participants in this regard. Nor is it plausible that staff might have equalized conditions between the two groups. Staff were given extensive training and were monitored throughout the course of the study. Overall, this study can be considered strong with respect to internal validity.

Between 3/1/93 and 2/28/95 each person admitted to Thresholds who met the study inclusion criteria was immediately assigned a random number that gave them a 50/50 chance of being selected into the study sample. For those selected, the purpose of the study was explained, including the nature of the two treatments, and the need for and use of random assignment. Participants were assured confidentiality and were given an opportunity to decline to participate in the study. Only 7 people (out of 491) refused to participate. At intake, each selected sample member was assigned a random number giving them a 50/50 chance of being assigned to either the Supported Employment condition or the standard in-agency sheltered workshop. In addition, all study participants were given the four measures at intake.

All participants spent the initial two weeks in the program in training and orientation. This consisted of life skill training (e.g. handling money, getting around, cooking and nutrition) and job preparation (employee roles, coping strategies). At the end of that period, each participant was assigned to a job site – at the agency sheltered workshop for those in the control condition, and to an outside employer if in the Supported Employment group. Control participants were expected to work full-time at the sheltered workshop for a three-month period, at which point they were posttested and given an opportunity to obtain outside employment (either Supported Employment or not). The Supported Employment participants were each assigned a case worker – called a Mobile Job Support Worker (MJSW) – who met with the person at the job site two times per week for an hour each time. The MJSW could provide any support or assistance deemed necessary to help the person cope with job stress, including counseling or working beside the person for short periods of time. In addition, the MJSW was always accessible by cellular telephone, and could be called by the participant or the employer at any time. At the end of three months, each participant was post-tested and given the option of staying with their current job (with or without Supported Employment) or moving to the sheltered workshop.

There were 484 participants in the final sample for this study, 242 in each treatment. There were 9 drop-outs from the control group and 13 from the treatment group, leaving a total of 233 and 229 in each group respectively from whom both pretest and posttest were obtained. Due to unexpected difficulties in coping with job stress, 19 Supported Employment participants had to be transferred into the sheltered workshop prior to the posttest. In all 19 cases, no one was transferred prior to week 6 of employment, and 15 were transferred after week 8. In all analyses, these cases were included with the Supported Employment group (intent-to-treat analysis) yielding treatment effect estimates that are likely to be conservative.

The major results for the four outcome measures are shown in Figure 1.

Insert Figure 1 about here

It is immediately apparent that in all four cases the null hypothesis has to be accepted – contrary to expectations, Supported Employment cases did significantly worse on all four outcomes than did control participants.

The mean gains, standard deviations, sample sizes and t-values (t-test for differences in average gain) are shown for the four outcome measures in Table 1.

Insert Table 1 about here

The results in the table confirm the impressions in the figures. Note that all t-values are negative except for the BPRS where high scores indicate greater severity of illness. For all four outcomes, the t-values were statistically significant (p<.05).


The results of this study were clearly contrary to initial expectations. The alternative hypothesis suggested that SE participants would show improved psychological functioning and self esteem after three months of employment. Exactly the reverse happened – SE participants showed significantly worse psychological functioning and self esteem.

There are two major possible explanations for this outcome pattern. First, it seems reasonable that there might be a delayed positive or “boomerang” effect of employment outside of a sheltered setting. SE cases may have to go through an initial difficult period of adjustment (longer than three months) before positive effects become apparent. This “you have to get worse before you get better” theory is commonly held in other treatment-contexts like drug addiction and alcoholism. But a second explanation seems more plausible – that people working full-time jobs in real-world settings are almost certainly going to be under greater stress and experience more negative outcomes than those who work in the relatively safe confines of an in-agency sheltered workshop. Put more succinctly, the lesson here might very well be that work is hard. Sheltered workshops are generally very nurturing work environments where virtually all employees share similar illness histories and where expectations about productivity are relatively low. In contrast, getting a job at a local hamburger shop or as a shipping clerk puts the person in contact with co-workers who may not be sympathetic to their histories or forgiving with respect to low productivity. This second explanation seems even more plausible in the wake of informal debriefing sessions held as focus groups with the staff and selected research participants. It was clear in the discussion that SE persons experienced significantly higher job stress levels and more negative consequences. However, most of them also felt that the experience was a good one overall and that even their “normal” co-workers “hated their jobs” most of the time.

One lesson we might take from this study is that much of our contemporary theory in psychiatric rehabilitation is naive at best and, in some cases, may be seriously misleading. Theory led us to believe that outside work was a “good” thing that would naturally lead to “good” outcomes like increased psychological functioning and self esteem. But for most people (SMI or not) work is at best tolerable, especially for the types of low-paying service jobs available to study participants. While people with SMI may not function as well or have high self esteem, we should balance this with the desire they may have to “be like other people” including struggling with the vagaries of life and work that others struggle with.

Future research in this are needs to address the theoretical assumptions about employment outcomes for persons with SMI. It is especially important that attempts to replicate this study also try to measure how SE participants feel about the decision to work, even if traditional outcome indicators suffer. It may very well be that negative outcomes on traditional indicators can be associated with a “positive” impact for the participants and for the society as a whole.

Chadsey-Rusch, J. and Rusch, F.R. (1986). The ecology of the workplace. In J. Chadsey-Rusch, C. Haney-Maxwell, L. A. Phelps and F. R. Rusch (Eds.), School-to-Work Transition Issues and Models. (pp. 59-94), Champaign IL: Transition Institute at Illinois.

Ciardiello, J.A. (1981). Job placement success of schizophrenic clients in sheltered workshop programs. Vocational Evaluation and Work Adjustment Bulletin, 14, 125-128, 140.

Cook, J.A. (1992). Job ending among youth and adults with severe mental illness. Journal of Mental Health Administration, 19(2), 158-169.

Cook, J.A. & Hoffschmidt, S. (1993). Psychosocial rehabilitation programming: A comprehensive model for the 1990’s. In R.W. Flexer and P. Solomon (Eds.), Social and Community Support for People with Severe Mental Disabilities: Service Integration in Rehabilitation and Mental Health. Andover, MA: Andover Publishing.

Cook, J.A., Jonikas, J., & Solomon, M. (1992). Models of vocational rehabilitation for youth and adults with severe mental illness. American Rehabilitation, 18, 3, 6-32.

Cook, J.A. & Razzano, L. (1992). Natural vocational supports for persons with severe mental illness: Thresholds Supported Competitive Employment Program, in L. Stein (ed.), New Directions for Mental Health Services, San Francisco: Jossey-Bass, 56, 23-41.

Endicott, J.R., Spitzer, J.L. Fleiss, J.L. and Cohen, J. (1976). The Global Assessment Scale: A procedure for measuring overall severity of psychiatric disturbance. Archives of General Psychiatry, 33, 766-771.

Griffiths, R.D. (1974). Rehabilitation of chronic psychotic patients. Psychological Medicine, 4, 316-325.

Overall, J. E. and Gorham, D. R. (1962). The Brief Psychiatric Rating Scale. Psychological Reports, 10, 799-812.

Rosenberg, M. (1965). Society and Adolescent Self Image. Princeton, NJ, Princeton University Press.

Wehman, P. (1985). Supported competitive employment for persons with severe disabilities. In P. McCarthy, J. Everson, S. Monn & M. Barcus (Eds.), School-to-Work Transition for Youth with Severe Disabilities, (pp. 167-182), Richmond VA: Virginia Commonwealth University.

Whitehead, C.W. (1977). Sheltered Workshop Study: A Nationwide Report on Sheltered Workshops and their Employment of Handicapped Individuals. (Workshop Survey, Volume 1), U.S. Department of Labor Service Publication. Washington, DC: U.S. Government Printing Office.

Woest, J., Klein, M. and Atkins, B.J. (1986). An overview of supported employment strategies. Journal of Rehabilitation Administration, 10(4), 130-135.

Figure 1. Pretest and posttest means for treatment (SE) and control groups for the four outcome measures.

The Employment Self Esteem Scale

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How to Write a Methods Section for a Research Paper

research methods sample paper

A common piece of advice for authors preparing their first journal article for publication is to start with the methods section: just list everything that was done and go from there. While that might seem like a very practical approach to a first draft, if you do this without a clear outline and a story in mind, you can easily end up with journal manuscript sections that are not logically related to each other. 

Since the methods section constitutes the core of your paper, no matter when you write it, you need to use it to guide the reader carefully through your story from beginning to end without leaving questions unanswered. Missing or confusing details in this section will likely lead to early rejection of your manuscript or unnecessary back-and-forth with the reviewers until eventual publication. Here, you will find some useful tips on how to make your methods section the logical foundation of your research paper.

Not just a list of experiments and methods

While your introduction section provides the reader with the necessary background to understand your rationale and research question (and, depending on journal format and your personal preference, might already summarize the results), the methods section explains what exactly you did and how you did it. The point of this section is not to list all the boring details just for the sake of completeness. The purpose of the methods sections is to enable the reader to replicate exactly what you did, verify or corroborate your results, or maybe find that there are factors you did not consider or that are more relevant than expected. 

To make this section as easy to read as possible, you must clearly connect it to the information you provide in the introduction section before and the results section after, it needs to have a clear structure (chronologically or according to topics), and you need to present your results according to the same structure or topics later in the manuscript. There are also official guidelines and journal instructions to follow and ethical issues to avoid to ensure that your manuscript can quickly reach the publication stage.

Table of Contents:

  • General Methods Structure: What is Your Story? 
  • What Methods Should You Report (and Leave Out)? 
  • Details Frequently Missing from the Methods Section

More Journal Guidelines to Consider 

  • Accurate and Appropriate Language in the Methods

General Methods Section Structure: What Is Your Story? 

You might have conducted a number of experiments, maybe also a pilot before the main study to determine some specific factors or a follow-up experiment to clarify unclear details later in the process. Throwing all of these into your methods section, however, might not help the reader understand how everything is connected and how useful and appropriate your methodological approach is to investigate your specific research question. You therefore need to first come up with a clear outline and decide what to report and how to present that to the reader.

The first (and very important) decision to make is whether you present your experiments chronologically (e.g., Experiment 1, Experiment 2, Experiment 3… ), and guide the reader through every step of the process, or if you organize everything according to subtopics (e.g., Behavioral measures, Structural imaging markers, Functional imaging markers… ). In both cases, you need to use clear subheaders for the different subsections of your methods, and, very importantly, follow the same structure or focus on the same topics/measures in the results section so that the reader can easily follow along (see the two examples below).

If you are in doubt which way of organizing your experiments is better for your study, just ask yourself the following questions:

  • Does the reader need to know the timeline of your study? 
  • Is it relevant that one experiment was conducted first, because the outcome of this experiment determined the stimuli or factors that went into the next?
  • Did the results of your first experiment leave important questions open that you addressed in an additional experiment (that was maybe not planned initially)?
  • Is the answer to all of these questions “no”? Then organizing your methods section according to topics of interest might be the more logical choice.

If you think your timeline, protocol, or setup might be confusing or difficult for the reader to grasp, consider adding a graphic, flow diagram, decision tree, or table as a visual aid.

What Methods Should You Report (and Leave Out)?

The answer to this question is quite simple–you need to report everything that another researcher needs to know to be able to replicate your study. Just imagine yourself reading your methods section in the future and trying to set up the same experiments again without prior knowledge. You would probably need to ask questions such as:

  • Where did you conduct your experiments (e.g., in what kind of room, under what lighting or temperature conditions, if those are relevant)? 
  • What devices did you use? Are there specific settings to report?
  • What specific software (and version of that software) did you use?
  • How did you find and select your participants?
  • How did you assign participants into groups?  
  • Did you exclude participants from the analysis? Why and how?
  • Where did your reagents or antibodies come from? Can you provide a Research Resource Identifier (RRID) ?
  • Did you make your stimuli yourself or did you get them from somewhere?
  • Are the stimuli you used available for other researchers?
  • What kind of questionnaires did you use? Have they been validated?
  • How did you analyze your data? What level of significance did you use?
  • Were there any technical issues and did you have to adjust protocols?

Note that for every experimental detail you provide, you need to tell the reader (briefly) why you used this type of stimulus/this group of participants/these specific amounts of reagents. If there is earlier published research reporting the same methods, cite those studies. If you did pilot experiments to determine those details, describe the procedures and the outcomes of these experiments. If you made assumptions about the suitability of something based on the literature and common practice at your institution, then explain that to the reader.

In a nutshell, established methods need to be cited, and new methods need to be clearly described and briefly justified. However, if the fact that you use a new approach or a method that is not traditionally used for the data or phenomenon you study is one of the main points of your study (and maybe already reflected in the title of your article), then you need to explain your rationale for doing so in the introduction already and discuss it in more detail in the discussion section .

Note that you also need to explain your statistical analyses at the end of your methods section. You present the results of these analyses later, in the results section of your paper, but you need to show the reader in the methods section already that your approach is either well-established or valid, even if it is new or unusual. 

When it comes to the question of what details you should leave out, the answer is equally simple ‒ everything that you would not need to replicate your study in the future. If the educational background of your participants is listed in your institutional database but is not relevant to your study outcome, then don’t include that. Other things you should not include in the methods section:

  • Background information that you already presented in the introduction section.
  • In-depth comparisons of different methods ‒ these belong in the discussion section.
  • Results, unless you summarize outcomes of pilot experiments that helped you determine factors for your main experiment.

Also, make sure your subheadings are as clear as possible, suit the structure you chose for your methods section, and are in line with the target journal guidelines. If you studied a disease intervention in human participants, then your methods section could look similar to this:

materials an methods breakdown

Since the main point of interest here are your patient-centered outcome variables, you would center your results section on these as well and choose your headers accordingly (e.g., Patient characteristics, Baseline evaluation, Outcome variable 1, Outcome variable 2, Drop-out rate ). 

If, instead, you did a series of visual experiments investigating the perception of faces including a pilot experiment to create the stimuli for your actual study, you would need to structure your methods section in a very different way, maybe like this:

materials and methods breakdown

Since here the analysis and outcome of the pilot experiment are already described in the methods section (as the basis for the main experimental setup and procedure), you do not have to mention it again in the results section. Instead, you could choose the two main experiments to structure your results section ( Discrimination and classification, Familiarization and adaptation ), or divide the results into all your test measures and/or potential interactions you described in the methods section (e.g., Discrimination performance, Classification performance, Adaptation aftereffects, Correlation analysis ).

Details Commonly Missing from the Methods Section

Manufacturer information.

For laboratory or technical equipment, you need to provide the model, name of the manufacturer, and company’s location. The usual format for these details is the product name (company name, city, state) for US-based manufacturers and the product name (company name, city/town, country) for companies outside the US.

Sample size and power estimation

Power and sample size estimations are measures for how many patients or participants are needed in a study in order to detect statistical significance and draw meaningful conclusions from the results. Outside of the medical field, studies are sometimes still conducted with a “the more the better” approach in mind, but since many journals now ask for those details, it is better to not skip this important step.

Ethical guidelines and approval

In addition to describing what you did, you also need to assure the editor and reviewers that your methods and protocols followed all relevant ethical standards and guidelines. This includes applying for approval at your local or national ethics committee, providing the name or location of that committee as well as the approval reference number you received, and, if you studied human participants, a statement that participants were informed about all relevant experimental details in advance and signed consent forms before the start of the study. For animal studies, you usually need to provide a statement that all procedures included in your research were in line with the Declaration of Helsinki. Make sure you check the target journal guidelines carefully, as these statements sometimes need to be placed at the end of the main article text rather than in the method section.

Structure & word limitations

While many journals simply follow the usual style guidelines (e.g., APA for the social sciences and psychology, AMA for medical research) and let you choose the headers of your method section according to your preferred structure and focus, some have precise guidelines and strict limitations, for example, on manuscript length and the maximum number of subsections or header levels. Make sure you read the instructions of your target journal carefully and restructure your method section if necessary before submission. If the journal does not give you enough space to include all the details that you deem necessary, then you can usually submit additional details as “supplemental” files and refer to those in the main text where necessary.

Standardized checklists

In addition to ethical guidelines and approval, journals also often ask you to submit one of the official standardized checklists for different study types to ensure all essential details are included in your manuscript. For example, there are checklists for randomized clinical trials, CONSORT (Consolidated Standards of Reporting Trials) , cohort, case-control, cross‐sectional studies, STROBE (STrengthening the Reporting of OBservational studies in Epidemiology ), diagnostic accuracy, STARD (STAndards for the Reporting of Diagnostic accuracy studies) , systematic reviews and meta‐analyses PRISMA (Preferred Reporting Items for Systematic reviews and Meta‐Analyses) , and Case reports, CARE (CAse REport) .

Make sure you check if the manuscript uses a single- or double-blind review procedure , and delete all information that might allow a reviewer to guess where the authors are located from the manuscript text if necessary. This means that your method section cannot list the name and location of your institution, the names of researchers who conducted specific tests, or the name of your institutional ethics committee.  

methods section checklist

Accurate and Appropriate Language in the Methods Section

Like all sections of your research paper, your method section needs to be written in an academic tone . That means it should be formal, vague expressions and colloquial language need to be avoided, and you need to correctly cite all your sources. If you describe human participants in your method section then you should be especially careful about your choice of words. For example, “participants” sounds more respectful than “subjects,” and patient-first language, that is, “patients with cancer,” is considered more appropriate than “cancer patients” by many journals.

Passive voice is often considered the standard for research papers, but it is completely fine to mix passive and active voice, even in the method section, to make your text as clear and concise as possible. Use the simple past tense to describe what you did, and the present tense when you refer to diagrams or tables. Have a look at this article if you need more general input on which verb tenses to use in a research paper . 

Lastly, make sure you label all the standard tests and questionnaires you use correctly (look up the original publication when in doubt) and spell genes and proteins according to the common databases for the species you studied, such as the HUGO Gene Nomenclature Committee database for human studies .  

Visit Wordvice AI’s AI Text Editor to receive a free grammar check and English editing services (including manuscript editing , paper editing , and dissertation editing ) before submitting your manuscript to journal editors.

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Research Method

Home » Research Methods – Types, Examples and Guide

Research Methods – Types, Examples and Guide

Table of Contents

Research Methods

Research Methods


Research Methods refer to the techniques, procedures, and processes used by researchers to collect , analyze, and interpret data in order to answer research questions or test hypotheses. The methods used in research can vary depending on the research questions, the type of data that is being collected, and the research design.

Types of Research Methods

Types of Research Methods are as follows:

Qualitative research Method

Qualitative research methods are used to collect and analyze non-numerical data. This type of research is useful when the objective is to explore the meaning of phenomena, understand the experiences of individuals, or gain insights into complex social processes. Qualitative research methods include interviews, focus groups, ethnography, and content analysis.

Quantitative Research Method

Quantitative research methods are used to collect and analyze numerical data. This type of research is useful when the objective is to test a hypothesis, determine cause-and-effect relationships, and measure the prevalence of certain phenomena. Quantitative research methods include surveys, experiments, and secondary data analysis.

Mixed Method Research

Mixed Method Research refers to the combination of both qualitative and quantitative research methods in a single study. This approach aims to overcome the limitations of each individual method and to provide a more comprehensive understanding of the research topic. This approach allows researchers to gather both quantitative data, which is often used to test hypotheses and make generalizations about a population, and qualitative data, which provides a more in-depth understanding of the experiences and perspectives of individuals.

Key Differences Between Research Methods

The following Table shows the key differences between Quantitative, Qualitative and Mixed Research Methods

Research MethodQuantitativeQualitativeMixed Methods
To measure and quantify variablesTo understand the meaning and complexity of phenomenaTo integrate both quantitative and qualitative approaches
Typically focused on testing hypotheses and determining cause and effect relationshipsTypically exploratory and focused on understanding the subjective experiences and perspectives of participantsCan be either, depending on the research design
Usually involves standardized measures or surveys administered to large samplesOften involves in-depth interviews, observations, or analysis of texts or other forms of dataUsually involves a combination of quantitative and qualitative methods
Typically involves statistical analysis to identify patterns and relationships in the dataTypically involves thematic analysis or other qualitative methods to identify themes and patterns in the dataUsually involves both quantitative and qualitative analysis
Can provide precise, objective data that can be generalized to a larger populationCan provide rich, detailed data that can help understand complex phenomena in depthCan combine the strengths of both quantitative and qualitative approaches
May not capture the full complexity of phenomena, and may be limited by the quality of the measures usedMay be subjective and may not be generalizable to larger populationsCan be time-consuming and resource-intensive, and may require specialized skills
Typically focused on testing hypotheses and determining cause-and-effect relationshipsSurveys, experiments, correlational studiesInterviews, focus groups, ethnographySequential explanatory design, convergent parallel design, explanatory sequential design

Examples of Research Methods

Examples of Research Methods are as follows:

Qualitative Research Example:

A researcher wants to study the experience of cancer patients during their treatment. They conduct in-depth interviews with patients to gather data on their emotional state, coping mechanisms, and support systems.

Quantitative Research Example:

A company wants to determine the effectiveness of a new advertisement campaign. They survey a large group of people, asking them to rate their awareness of the product and their likelihood of purchasing it.

Mixed Research Example:

A university wants to evaluate the effectiveness of a new teaching method in improving student performance. They collect both quantitative data (such as test scores) and qualitative data (such as feedback from students and teachers) to get a complete picture of the impact of the new method.

Applications of Research Methods

Research methods are used in various fields to investigate, analyze, and answer research questions. Here are some examples of how research methods are applied in different fields:

  • Psychology : Research methods are widely used in psychology to study human behavior, emotions, and mental processes. For example, researchers may use experiments, surveys, and observational studies to understand how people behave in different situations, how they respond to different stimuli, and how their brains process information.
  • Sociology : Sociologists use research methods to study social phenomena, such as social inequality, social change, and social relationships. Researchers may use surveys, interviews, and observational studies to collect data on social attitudes, beliefs, and behaviors.
  • Medicine : Research methods are essential in medical research to study diseases, test new treatments, and evaluate their effectiveness. Researchers may use clinical trials, case studies, and laboratory experiments to collect data on the efficacy and safety of different medical treatments.
  • Education : Research methods are used in education to understand how students learn, how teachers teach, and how educational policies affect student outcomes. Researchers may use surveys, experiments, and observational studies to collect data on student performance, teacher effectiveness, and educational programs.
  • Business : Research methods are used in business to understand consumer behavior, market trends, and business strategies. Researchers may use surveys, focus groups, and observational studies to collect data on consumer preferences, market trends, and industry competition.
  • Environmental science : Research methods are used in environmental science to study the natural world and its ecosystems. Researchers may use field studies, laboratory experiments, and observational studies to collect data on environmental factors, such as air and water quality, and the impact of human activities on the environment.
  • Political science : Research methods are used in political science to study political systems, institutions, and behavior. Researchers may use surveys, experiments, and observational studies to collect data on political attitudes, voting behavior, and the impact of policies on society.

Purpose of Research Methods

Research methods serve several purposes, including:

  • Identify research problems: Research methods are used to identify research problems or questions that need to be addressed through empirical investigation.
  • Develop hypotheses: Research methods help researchers develop hypotheses, which are tentative explanations for the observed phenomenon or relationship.
  • Collect data: Research methods enable researchers to collect data in a systematic and objective way, which is necessary to test hypotheses and draw meaningful conclusions.
  • Analyze data: Research methods provide tools and techniques for analyzing data, such as statistical analysis, content analysis, and discourse analysis.
  • Test hypotheses: Research methods allow researchers to test hypotheses by examining the relationships between variables in a systematic and controlled manner.
  • Draw conclusions : Research methods facilitate the drawing of conclusions based on empirical evidence and help researchers make generalizations about a population based on their sample data.
  • Enhance understanding: Research methods contribute to the development of knowledge and enhance our understanding of various phenomena and relationships, which can inform policy, practice, and theory.

When to Use Research Methods

Research methods are used when you need to gather information or data to answer a question or to gain insights into a particular phenomenon.

Here are some situations when research methods may be appropriate:

  • To investigate a problem : Research methods can be used to investigate a problem or a research question in a particular field. This can help in identifying the root cause of the problem and developing solutions.
  • To gather data: Research methods can be used to collect data on a particular subject. This can be done through surveys, interviews, observations, experiments, and more.
  • To evaluate programs : Research methods can be used to evaluate the effectiveness of a program, intervention, or policy. This can help in determining whether the program is meeting its goals and objectives.
  • To explore new areas : Research methods can be used to explore new areas of inquiry or to test new hypotheses. This can help in advancing knowledge in a particular field.
  • To make informed decisions : Research methods can be used to gather information and data to support informed decision-making. This can be useful in various fields such as healthcare, business, and education.

Advantages of Research Methods

Research methods provide several advantages, including:

  • Objectivity : Research methods enable researchers to gather data in a systematic and objective manner, minimizing personal biases and subjectivity. This leads to more reliable and valid results.
  • Replicability : A key advantage of research methods is that they allow for replication of studies by other researchers. This helps to confirm the validity of the findings and ensures that the results are not specific to the particular research team.
  • Generalizability : Research methods enable researchers to gather data from a representative sample of the population, allowing for generalizability of the findings to a larger population. This increases the external validity of the research.
  • Precision : Research methods enable researchers to gather data using standardized procedures, ensuring that the data is accurate and precise. This allows researchers to make accurate predictions and draw meaningful conclusions.
  • Efficiency : Research methods enable researchers to gather data efficiently, saving time and resources. This is especially important when studying large populations or complex phenomena.
  • Innovation : Research methods enable researchers to develop new techniques and tools for data collection and analysis, leading to innovation and advancement in the field.

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Fault probability identification method for distribution networks based on mov-mf distribution.

Jiang Li

  • Shanghai University of Electric Power, Shanghai, China

To address the fault identification challenge in distribution networks, a method leveraging a mixture of the von Mises–Fisher (mov-MF) distribution model for fault probability identification is proposed. Initially, the synchronous phasor measuring unit is employed to gather the post-fault steady-state voltage phase quantities, and then, the voltage phase angle values are combined to form a three-dimensional feature quantity. Subsequently, the mov-MF distribution model is initialized through the spherical K-means algorithm and the minimum message length algorithm. This model is further refined via the expectation–maximization algorithm to iteratively optimize distribution parameters. The test set data are input into the mov-MF distribution model, which has been constructed using typical fault data, to discern fault types. Finally, the efficacy of the proposed method is validated through simulation verification conducted on the IEEE 33-node distribution system. The analysis of the examples demonstrates the accuracy of the mov-MF distribution model-based fault identification method in identifying single-phase ground, two-phase ground, two-phase interphase, and three-phase short-circuit faults.

1 Introduction

The requirements for ensuring power supply quality and reliability of modern distribution networks as the terminal facing users are gradually increasing ( Sheng et al., 2023 ). Currently, the main grounding methods for distribution networks in China are either ungrounded neutral points or grounding through arc suppression coils. Due to the complex structure of distribution networks, various types of faults are likely to occur in practical operation. Single-phase grounding short circuit is the most common type of short circuit fault. If the short circuit is caused by the contact between the line and tree branches or the ground, the transient resistance of this short circuit is high, resulting in a weak fault electrical quantity that is difficult to detect, thereby affecting the normal operation of the distribution network. When faults occur in distribution networks, the primary task is to identify the faults. Therefore, efficient and reliable methods for fault identification in distribution networks are of great significance for the safe operation of distribution networks ( Peng et al., 2023 ).

Zhu et al. (2020) utilized current, voltage, and power data at the maximum power point in the time domain as feature quantities, combined with Pearson’s coefficient similarity and relative Euclidean distance deviation for fault-type differentiation. Jiang et al. (2021) used dynamic time warping (DTW) similarity and electrical volume data sequence similarity, and the combination of both inputs into a classifier significantly outperformed single features. Zhang et al. (2022a) proposed a waveform similarity-based identification method to construct two reconstructed currents by comparing the one-dimensional time-domain sampled values of the currents at the two ends of a transmission line and used the Kendall’s tau coefficient (KTC) waveform similarity algorithm to achieve reliable fault identification. Zhang et al. (2022b) proposed a sparse representation method based on one-dimensional time-domain current signals to construct a fault feature dictionary and calculate the feature residuals to determine the fault category. Liu et al. (2020) built a support vector machine model for high-resistance grounding fault identification using time-domain current-voltage magnitude and frequency as features. Ghaemi et al. (2022) used an integrated learning approach combined with multiple classifiers to accurately identify the fault type and location using one-dimensional time-domain voltage and current measurements, which maintains high classification accuracy even in the presence of measurement errors.

In contrast to the previous paper, which proposes to judge the fault type by constructing the signal similarity or deviation value as a one-dimensional feature quantity, another class of methods automatically proposes multi-dimensional feature quantities and makes the fault-type judgment through intelligent algorithms. Yang and Yu (2022) used a discrete wavelet transform to decompose three-phase voltage and zero-sequence sequences and constructed multidimensional time–frequency matrices to input into the ResNet network, which improved the effect of fault-type identification in distribution networks. Xingquan et al. (2022) converted the time-domain three-phase voltage and current data during faults into a multidimensional time–frequency spectral gray scale map, combined with SVM and a deep convolutional neural network, to improve the accuracy of high-resistance fault classification. Biswas et al. (2023) used variational mode decomposition (VMD) to quickly extract different frequency components of the fault current signal, which is input into the CNN for fault-type identification in the frequency domain to shorten the detection time and ensure the accuracy. Azizi and Seker (2022) processed the current time-domain signal through the Hilbert–Huang transform, formed the multidimensional feature quantity of the frequency-domain signal combination under different frequencies, and used BrownBoost algorithm to classify the data space, which improved the accuracy of fault-type classification. Feng et al. (2022) used the linear discriminant analysis (LDA) algorithm to incorporate the frequency-domain optimal fault features, which constitute two-dimensional and three-dimensional feature quantities, into the Bayesian classification model based on the kernel distribution to achieve fault location identification, in which the three-dimensional feature quantities are better than the two-dimensional feature quantities.

The fault identification methods mentioned in the literature can be broadly categorized into two types:

1. Extraction of time-domain electrical quantities: In this category, time-domain electrical quantities such as voltage and current amplitudes are extracted as one-dimensional features to represent fault types. Fault identification is achieved through methods such as constructing similarity or deviation values and comparing them against thresholds.

2. Time-frequency transformation methods: This category involves transforming the collected time-domain signals into multidimensional time–frequency matrices or forming grayscale images using time–frequency transformation methods. Intelligent algorithms are then employed to automatically extract multidimensional feature sets for fault type identification, resulting in improved accuracy compared to the first category. However, establishing time–frequency matrices or forming grayscale images requires complex preprocessing of time-domain signals, leading to longer computation times. Compared to one-dimensional features, multidimensional feature sets contain richer fault information and exhibit better classification performance. It is worth noting that the signals processed in the literature mostly consist of phasor magnitudes, overlooking the fault information contained in phase angles.

Wang et al. (2021a) utilized an improved VMD combined with fuzzy c-means (FCM) to achieve classification and identification of rolling bearing fault types through FCM clustering. Qi et al. (2021) utilized the von Mises–Fisher (v-MF) distribution combined with the standard Euclidean distance to analyze the similarity between different samples for sample selection. Initialization of different groups requires pre-setting a lower limit for the grouping values but does not implement merging of similar groups. Chen et al. (2015) proposed the combination of the expectation–maximization (EM) algorithm and the v-MF algorithm. By selecting the positioning data on crystal positions to form a v-MF distribution and using cosine similarity as the clustering basis, crystal-type identification is carried out. However, the consideration for the number of groups in mixed distributions is not addressed. Garcia-Fernandez et al. (2019) utilizes the v-MF distribution to construct Gaussian filters for target direction measurement. Angle information is used to form two-dimensional and three-dimensional vectors for tracking target directions, but the establishment of distributions for multiple targets is not implemented. Data clustering is a fundamental step in data analysis. The application of von Mises–Fisher (v-MF) distribution-based clustering methods has shown good utility in sample selection ( Qi et al., 2021 ), crystal-type identification ( Chen et al., 2015 ), direction measurement tracking ( Garcia-Fernandez et al., 2019 ), and other areas.

1.1 Contributions

The main contributions of this paper are summarized below.

• In this paper, we propose a probabilistic fault identification method based on the mixed von Mises–Fisher (v-MF) distribution. The mov-MF distribution of sample data is established, and fault probability is calculated by integrating the data to be measured into the established mov-MF distribution. Fault-type identification is then achieved based on the resulting probability magnitude. The biggest innovation of the mov-MF-based probabilistic fault identification method for distribution networks proposed in this paper is the fault-type identification by establishing the clustering distribution of 3D vector data on the spherical space. In power systems, there are a large number of 3D vectors, so the method is suitable for power system data analysis. Compared with the two types of fault identification methods introduced in the previous paper, the method proposed in this paper can make the accuracy of fault identification higher by using 3D vectors; the use of 3D eigenvectors in the time domain to establish the mov-MF distribution without complex data preprocessing makes the algorithm more concise, ensures accuracy, and at the same time, improves the computational efficiency.

• To establish the mixed von Mises–Fisher (v-MF) distribution of sample data more accurately, we employ the spherical K-means algorithm and minimum message length (MML) for parameter initialization. Subsequently, these parameters are iteratively optimized using the expectation–maximization (EM) algorithm to refine the accuracy of the mov-MF distribution parameters. We validate this approach through simulations conducted on an IEEE 33-node distribution system, where various fault conditions are set. The test results are compared with those reported in Xingquan et al. (2022) and Azizi and Seker (2022) . Our findings demonstrate that the proposed method achieves accurate fault-type identification. Moreover, the acquisition of feature vectors is simplified, and the accuracy is comparable to that of the comparison method. Importantly, our method exhibits robust performance across different fault conditions, highlighting its broad applicability.

1.2 Paper organization

The remainder of the paper is structured as follows: Section 2 provides an introduction to the fundamental theory of von Mises–Fisher (v-MF) distribution and the expectation–maximization (EM) algorithm. Section 3 outlines the initialization method for parameters of the mov-MF distribution, along with the algorithm for fault-type identification based on the mov-MF distribution. Section 4 verifies the effectiveness and applicability of the proposed method through simulation examples.

2 The von Mises–Fisher basic theory

The von Mises–Fisher distribution is the probability distribution of directional statistics for spherical surface data. A d -dimensional unit random vector x (i.e., x ∈ R d and x = 1 ) is said to have the d-variate von Mises–Fisher (v-MF) distribution if its probability density function is given by

In the Eq. 1 , where μ = 1 , κ ≥ 0 , d ≥ 2 . The normalizing constant C d κ is given by

where I d κ represents the first kind-modified Bessel function.

The probability density f x | μ , κ function is determined by the mean direction μ and concentration parameter κ . The mean direction μ represents the central direction of clustering of this type of data on the spherical surface, indicating the direction of clustering. The concentration parameter κ represents the concentration of data in this direction. A higher value indicates a higher degree of clustering of data in this direction. The specific comparison chart is shown in Figure 1

Figure 1 . Clustering effects of different concentration parameters.

2.1 Maximum likelihood estimation

For a given dataset χ , we want to find the maximum likelihood estimates of the parameters: mean direction μ and concentration parameter κ of its probability density function f χ | μ , κ . Assuming these data are independently and identically distributed, the logarithm of the likelihood for χ can be expressed as

To obtain the maximum likelihood estimates of mean direction μ and concentration parameter κ , we introduce Lagrange multipliers and derive the maximum likelihood estimation from Equation 3 , resulting following Eqs 4 , 5 :

Due to the implicit equation involving the ratio of Bessel functions in the calculation process of the above expression, it is impossible to obtain an exact analytical solution directly. Therefore, we must use numerical asymptotic approximation methods to obtain an approximate solution for the concentration parameter κ ^ , expressed using Eq. 6 . We select the best performing approximate solution method proposed in Zhe et al. (2019) :

2.2 Parameter estimation of mov-MF distribution based on the EM algorithm

The process of using v-MF distributions for fault-type identification requires a hybrid model containing multiple v-MF distributions. We now consider a mix of k v-MF (mov-MF) distributions that serves as a generative model for directional data. Let f h x | μ , κ h = 1 k denote the h th v-MF distribution, then a mixture of these k v-MF distributions given by Eq. 7 :

where π h denotes the weights of the different types of components and the sum is 1. We randomly select the h th v-MF distribution with weights π h and sample a point from that distribution f h x | μ h , κ h . Let χ = x 1 , ⋯ , x n be the dataset of n independently sampled points that follow Eq. 7. Let Z = z 1 , ⋯ , z n be the corresponding set of hidden random variables that indicate the particular v-MF distribution from which the points are sampled. In particular, z i = h if x i is sampled from f h x | μ h , κ h . Assuming that the values in the set Z are known, the log-likelihood of the observed data is given by

Equation 8 is actually a random variable dependent on Z, which follows a distribution. This random variable is referred to as the complete data log-likelihood. Given a particular value of χ , μ , κ , the conditional probability expectation of Z | χ , μ , κ is calculated, and this estimation forms the E-step in an EM framework.

Using an EM approach for maximizing the expectation of Eq. 8) , we can summarize the steps for estimating the mov-MF parameters based on the EM algorithm.

Algorithm 1. EM algorithm.

Input : set X of data points

Output : a mov-MF distribution; initialize all π h , μ h , κ h , h = 1 , . . . , k

{ The E-step of EM }

for i = 1 to n do

  for h = 1 to k do

   f h x i | μ h , κ h ← c d κ h e κ h μ h T x i

  end for

   p h | x i , μ , κ ← π h f h x i | μ h , κ h ∑ l = 1 k π l f l x i | μ l , κ l

{ The M-step pf EM }

for h = 1 to k do

   π h = 1 n ∑ i = 1 n p h | x i , μ , κ

   r h = ∑ i = 1 n x i p h | x i , μ , κ

   μ ^ h = r h r h

   κ ^ = r ¯ h d − r ¯ h 3 1 − r ¯ h 2

until convergence

On termination, the algorithm gives the parameters π h , μ h , κ h of the k v-MF distributions that model the dataset χ , as well as the soft-clustering, i.e., the posterior probabilities p h | x i , μ , κ , for all h and i .

3 Steps for designing the fault identification model based on mov-MF distribution

3.1 data preprocessing and dataset construction.

The fault signals of the distribution network are acquired and combined to form a three-dimensional vector Ψ φ 1 , φ 2 , φ 3 , which is converted into directional data by L2 normalization. The dataset consists of voltage phasors measured by the PMU under different fault conditions. After a fault occurs, the positive–negative–zero-sequence voltage phasors of different types of faults vary widely, and the main difference exists between the phase angles. The L2 normalized data are distributed on the unit sphere, and the different types of fault vectors are combined to form a dataset in the form of a matrix.

3.2 Calculation of the parameters of the mov-MF distribution

As the EM algorithm is needed to establish the mov-MF distribution, there is an important problem that in the case of the known distribution χ , we need to solve the distribution of the average direction μ and concentration parameters κ . From Section 2.2, we need to use the log-likelihood function as the objective function to estimate the unknown parameters μ and κ , and the log-likelihood function is non-convex; there are some small local maxima and local minima, so avoiding such problems is essential to improve the performance of the EM algorithm. Therefore, avoiding such problems is crucial to improve the performance of the EM algorithm. The EM algorithm is more sensitive to the initial value, and the clustering result fluctuates greatly with the change in the initial value, so it is chosen to determine the reasonable starting state of the EM by the preliminary clustering of the data.

3.2.1 mov-MF model parameter initialization

The mov-MF parameters are computed by initializing the spherical K-means algorithm, updating the parameters by the EM algorithm, and determining whether the optimality is reached based on the cosine similarity D .

Initialization is performed using the spherical K-means algorithm ( Mashal and Hosseini, 2015 ), where the n × d data matrix is first divided into K clusters, K generally needs to be set in advance, and K data points are selected as the initial cluster centers. Before the algorithm, it is assumed that in the case of a mov-MF distribution, all classified clusters are equal a priori , i.e., for each distribution π h = 1 k , h = 1 , ⋯ , k , while it is further assumed that all classified clusters have equal concentration parameters, which are generally set to κ h = 100 . For the case of mov-MF distribution, some distant data points are selected as initialization parameters μ h for different clusters.

In order to realize the classification of different data points, the distance metric between different points on the unit hypersphere is defined, which can be mainly categorized into Euclidean distance, Manhattan distance, cosine distance, and correlation distance, etc., depending on the clustering requirements. Jianyuan et al. (2023) explained the rationality of using cosine similarity as a distance metric for clustering. Therefore, we choose to calculate the cosine similarity S as the clustering metric.

Thus, the cluster label to which each data point belongs is determined based on the similarity of the data point to the initial cluster center.

From this, we obtain the center of each cluster μ h , initialize again to select a set of cluster centers μ h , and compare the distance between the data points in the cluster and the center point D , D = 1 − S . If the distance D of the current clustering result is smaller than that of the previous generation, then update the clustering result until the distance D does not change anymore to get the optimal clustering result of the K clusters at this time and compute the average direction μ h , concentration parameter κ h , and mixing distribution weight π h of each cluster at this time, which is used as the initial parameter of the mov-MF model. In order to improve the accuracy of the initial parameters, multiple initializations are usually performed, and the group with the smallest distance D is chosen as the initialization parameter.

3.2.2 mov-MF model group score determination

On the basis of step a), the group score of the sample data is determined by the MML algorithm, and according to the log-likelihood l r and the minimum message length I π to determine whether the optimal group score is reached or not and through many iterations of the EM algorithm, the mov-MF distribution of the typical sample data is obtained.

When the mov-MF model group scores are determined, then the EM algorithm is used to estimate the mixture distribution parameters, i.e., the mixture distribution weights and the parameters for each subgroup. Thus, we need to determine the optimal number of subgroups for the mixture distribution and the corresponding distribution parameters.

Therefore, the minimum message length (MML) algorithm is used for group score K determination. First, we need to encode the parameters using MML and calculate the message length corresponding to different parameters. The log-likelihood ratio of the mov-MF distribution for a set of fractions is given by Eq. 11 :

where π h and f h x i ; Θ h , Θ h = μ h , κ h are the weights and probability densities of the h th group component, respectively, under the assumption that the initial number of group scores, K , is determined; K is a number of groupings for the current hypothesis; and the maximum likelihood is estimated to be Φ M L = argmax Φ χ Φ , using the EM algorithm for the estimation of the above mixing parameters.

For step E, rewriting the formulas for calculating the conditional expectation probability of the joint distribution, expressed by Eqs 12 , 13 :

For the M-step, assuming an estimate Φ t for the t th iteration, the local parameters and the maximum log-likelihood estimates used to compute the next one, and the weights of the h th component are updated as π h t + 1 = n h t N .

Based on the expression proposed in Kasarapu and Allison (2015) for encoding the component weights, the message length expression for the hybrid weights π h is redefined on this basis by combining the log-likelihood l r ← E ∑ h = 1 k π h f h x | μ h , κ h obtained from the E-step:

According to the initialization parameters obtained by the spherical K-means algorithm, the log-likelihood l r and the message length of the hybrid weight I π in the initial state. The message length of the hybrid weight expressed by Eq. 14 . Execute the E-step to calculate the initial log-likelihood was executed using the initialization parameters μ h , κ h , and π h , and then the M-step was executed to calculate the parameters at the time of maximization of the expectation; after completing the calculation of the corresponding parameters for each subgroup, the log-likelihood and the message length were updated at this time. If a subgroup of a subgroup is set to 0, the subgroup is removed from the model, and the number of subgroups is reduced. At the end of each E-step and M-step, the log-likelihood is compared with the previous generation by calculating the log-likelihood and judging whether convergence occurs based on the threshold value Δ l r . calculated from Eq. 15 .

Meanwhile, after each iteration of the E–M step to the number of confirmed groups, the new message length I ′ π is recalculated, checking whether the current message length is no longer changing and thus determining whether the optimal result is reached.

It is likely that there are two or even more similar groupings in the initialization phase, and when there are such groupings with very close average directions, group merging is required. Using the mean direction μ h of each group, the similarity between different groups is calculated, the similarity is used to determine if they are similar groups, these groups are merged, and the parameters μ h , κ h , and π h and the number of groups K are updated.

3.3 Fault-type identification

After establishing a mov-MF distribution based on the sample data, the samples to be tested are mixed into the constructed sample mov-MF distribution, and the probabilities of the samples to be tested attributed to different types of faults are calculated. The fault label is then determined according to the size of the probability, thus realizing fault-type identification.

Labeling of fault types h = 1 , 2 , … , k , weights π h are the weights corresponding to different fault types in the mov-MF model obtained from the sample data; r h i is the probability of the fault types of the data to be measured, and according to the size of the probability, the vector of the data to be measured is assigned to the grouping of the fault types with the largest probability to realize the fault-type identification.

Algorithm 2. Fault identification algorithm.

Step 1: Input sample dataset χ , set the initial number of groups K , and set the initial κ h = 100 , π h = 1 K .

Step 2: Select K μ h i as cluster centers, calculate the similarity index D h i between the selected cluster centers and the data in the clusters, and if it is smaller than the previous generation result, then re-select the cluster centers and repeat step 2 until D h i is larger than the previous generation result.

Step 3: After the initial cluster centers μ h are selected, the obtained initialization parameters and dataset χ are used to estimate and update the parameters by the EM algorithm ( Algorithm 1 ).

Step 4: After obtaining the mov-MF distribution of the K subgroups, determine whether to keep the subgroups by judging whether π h is zero or not.

Step 5: Calculate the log-likelihood Δ l r and determine whether convergence has been reached; if not, return to step 3.

Step 6: Calculate the message length of the mixed weights I π and determine whether the message length is no longer changing, otherwise return to step 2.

Step 7: Output μ h , κ h , π h , and K and, get the mixture v-MF distribution of sample dataset χ for. Mix the samples to be tested into this distribution, and realize the fault-type identification by Eq. 16 .

The step-by-step flowchart is shown in Figure 2 :

Figure 2 . Flowchart of fault identification based on the mov-MF algorithm.

4 Example analysis

In order to verify the effectiveness of the fault identification method based on the mov-MF model proposed in this paper, simulation experiments are carried out in MATLAB/Simulink on the IEEE33 node 10-kV distribution system, as shown in Figure 3 , to obtain the fault sample data.

Figure 3 . 10-kV IEEE33 node distribution network model.

4.1 Sample data

Fault points are set between nodes 8–9, 13–14, 18–19, and 23–24, respectively, where nodes 20–21, 11–17, 22–24, and 29–32 are connected by overhead lines, and the rest of the lines are connected by cables, and the parameters of each sequence of the overhead lines and cables are shown in Table 1 , line model parameters ( Wang et al., 2021b ). The system is a 10-kV distribution network. It is set up with transformer grounding methods that are neutral ungrounded and neutral grounded via arcing coil(0.8697H). Only one of the above fault parameters is changed in each simulation, and the duration of each type of fault is 0.1 s. The synchronized phase data are collected using a PMU, and a measuring device is installed at each node, with an update interval of 10 m and a sampling frequency of 6.4 kHz. A total of 560 sets of fault samples are generated, of which 420 sets comprise the training set and 140 sets comprise the test set. The fault conditions are neutral ungrounded; neutral grounded via arcing coil; transition resistance 0Ω, 1Ω, 10Ω, and 1000Ω and has access to distributed power; and the abovementioned seven conditions are grouped into four fault points for single-phase grounded short-circuit faults (AG,BG,CG), two-phase grounded short-circuit faults (ABG,BCG,ACG), three-phase short-circuit faults, and two-phase interphase short-circuit faults (AB,BC,AC); 80 fault samples are generated for each group, and 33 data points are obtained for each set of data, and the mov-MFs are established, respectively, under different conditions.

Table 1 . Line model parameter.

Based on the principle in Section 3.1, the vector dataset suitable for building the mov-MF model is constructed. In the mov-MF model, the main judgment basis for fault-type identification is the average direction μ of the grouped clusters, so the phase angle values of the positive–negative-sequence and zero-sequence voltage phasors at the moment of 0.05 s after the fault are selected to be combined into the three-dimensional feature vectors Ψ φ u 1 , φ u 2 , φ u 0 .

The feature vectors extracted from the typical sample fault dataset are used as initial vectors for L2 normalization to obtain the normalized Ψ ′ φ u 1 , φ u 2 , φ u 0 . The 3D feature vectors of each data point for each fault type obtained after normalization are combined to form a 330 × 3 initial vector matrix Ψ ′ = Ψ ′ 1 Ψ ′ 2 ⋯ Ψ ′ 329 Ψ ′ 330 T , and the corresponding mov-MF distribution is modeled on the basis of this dataset.

4.2 Type identification under different fault conditions

After establishing the mov-MF distribution model based on the historical sample fault dataset, the simulation is then carried out according to different fault conditions, and the test dataset of a particular fault is mixed into the history set of the mov-MF model for different conditions completed in Section 4.1 based on the historical samples for identification in each test.

4.2.1 Different transformer grounding methods

The purpose of changing the transformer grounding method is to verify the applicability of the fault identification method proposed in this paper under this condition. The simulation model is a 10-kV distribution network model, so two small current grounding methods are set. The compensation method of the arc-canceling coil is set to be over-compensation, and the simulation is carried out. Fault-type identification is carried out by establishing the mov-MF model, and the mov-MF model established according to the positive-, negative, and zero-sequence phases is shown in Figure 4 .

Figure 4 . Neutral ungrounded mov-MF distribution of neutral grounded through arc suppression coil.

The small current grounding method does not have much effect on the positive-, negative-, and zero-sequence voltage phase angles, and the obtained mov-MF distributions are similar. Eighty sets of test datasets are mixed into the obtained mov-MF distributions for different neutral grounding methods, and the labeling results are used to determine whether the classification is correct or not. The typical data mean direction matrix when the neutral point is not grounded is:

According to the average direction of typical faults, the cosine similarity was calculated between the test data set and the average direction of a certain type of fault, the probability of belonging to that type of fault was also calculated according to the number of data point labels, and the type of fault with the highest probability was selected to judge that it belongs to that type of fault. The A-phase short-circuit grounding fault was taken as an example under the condition of neutral ungrounded, and the fault probability r h i was calculated, as shown in Figure 5 .

Figure 5 . Fault-type probability diagram (AG, neutral ungrounded).

The overall accuracy results for the 40 test sets are shown in Table 2 .

Table 2 . Fault identification accuracy under different grounding modes.

Transformer neutral point through the arcing coil grounding will limit the fault phase current. The method proposed in this paper does not have much impact, so the 10-kV distribution network applicable to the small current grounding method is applicable to this method.

4.2.2 Fault transition resistance impact analysis

Changing the transition resistance when the fault occurs, the transition resistors with sizes of 0Ω, 1Ω, 10Ω, and 1000Ω are selected, and simulation experiments are carried out by changing the fault type and the initial phase angle of the fault at different fault locations. The mov-MF model is established for fault type identification, and the mov-MF model is also established according to the positive and negative zero sequence phases as shown in Figure 6 .

Figure 6 . mov-MF distribution of different transition resistors (0Ω and 1000Ω).

Varying the transition resistance size, the mov-MF distributions are different due to the fact that 0Ω, 1Ω, and 10Ω all differ from 1000Ω, but the expected results can still be achieved for type differentiation under each condition. The 160 sets of test datasets are mixed into the obtained mov-MF distributions for different neutral grounding methods, and the labeling results are used to determine whether the classification is correct or not. The typical data mean direction matrix for a transition resistance of 0Ω is:

The A-phase short-circuit ground fault under the condition of 0Ω transition resistance is taken as an example, and the fault probability r h i is calculated as shown in Figure 7 :

Figure 7 . Fault-type probability diagram (AG, 0Ω).

The judgment process is the same as shown in section IV.B.a), and the results of 80 sets of test data are shown in Table 3 .

Table 3 . Fault identification accuracy under different transition resistors.

When a single-phase high-resistance grounded short-circuit occurs, the transition resistance will have a certain effect on the fault phase voltage amplitude, and for positive-, negative-, and zero-sequence phase angles, the transition resistance does not have much effect, so the fault-type identification accuracy is not affected under the condition of different fault transition resistances, and it still maintains a high accuracy rate.

4.2.3 Impact analysis of connecting to distributed power sources

DG is connected at nodes 17, 21, 24, and 32, and DG is a 1.5 kW/230 V PV power supply. The transformer grounding method is selected as neutral ungrounded, and the transition resistance is 0 Ω. Simulation experiments are carried out by changing the fault types at different locations. Fault type identification is carried out by establishing a mov-MF model, and the mov-MF model established according to the positive and negative zero sequence phasors is shown in Figure 8 .

Figure 8 . mov-MF distribution after connecting to DG.

After accessing the distributed power supply, the impact on the vectors we use to build the mov-MF distribution will not be significant, so the obtained mov-MF distribution is similar to the previous distribution and still differentiates between different types of faults based on the feature vectors. The 10 sets of test datasets are mixed into the obtained mov-MF distribution, and the labeling results are used to judge whether the classification is correct or not. The typical data mean direction matrix after accessing the DG is:

Take the example of a short-circuit ground fault in phase A after connecting to the DG, and calculate the fault probability r h i as shown in Figure 9 :

Figure 9 . Fault-type probability graph (AG, DG).

The judgment process is the same as shown in section IV.B.a, and the results of 20 sets of test data are shown in Table 4 .

Table 4 . Fault identification accuracy after connecting to DG.

After accessing the distributed power supply, the fault current and voltage amplitude will slightly increase when a fault occurs compared with when it is not connected. For positive-, negative-, and zero-sequence voltage phase angles, access to distributed power supply has little effect on it; as a feature vector can still establish a clearly classified hybrid v MF distribution, the accuracy of fault-type identification is not affected, and the accuracy rate is still high.

4.2.4 Comparative analysis of different algorithms

The algorithm proposed in this paper is compared with the existing algorithms, and in Table 4, with the ensemble algorithm of multilayer classifiers ( Ghaemi et al., 2022 ), the CNN–SVM algorithm ( Xingquan et al., 2022 ), and the BrownBoost–HHT algorithm ( Azizi and Seker, 2022 ), and compared with the algorithms that make use of the one-dimensional feature quantities, there is an improvement in the fault identification rate for two-phase short circuits, two-phase inter-phase, and three-phase short circuits; compared with the fault identification methods that make use of intelligent algorithms, the mov MF distribution of the three-dimensional feature quantity established by the algorithm proposed in this paper is simpler in the model, and the algorithm is clearer. The acquisition of the feature quantity is simpler, and the accuracy of fault-type identification is comparable to the algorithm.

The comprehensive analysis of Table 5 shows that the accuracy of fault-type identification using the method based on the mov-MF distribution is slightly lower than other types of faults when single-phase ground faults and three-phase grounding faults occur. When establishing the mov-MF distribution, a dataset consisting of phase angle values of positive-, negative-, and zero-sequence voltages is chosen, and the mov-MF distribution is able to extract the average direction of the same type of fault vectors as a feature value based on the vector data, so we carry out the fault-type identification based on this characteristic.

Table 5 . Classification accuracy of different fault types.

4.2.5 Simulation test time

The methodology in this paper needs to be applied with consideration of the required hardware base and the time-consuming identification work. As an example, the running time of the MATLAB fault classification program is analyzed to test the time taken to identify different types of faults under ungrounded neutral conditions, and the proposed methodology is applied to identify a single fault. The test hardware is a conventional mainstream PC with AMD Ryzen-5,000 processor and 16 GB RAM, and the time required to build the mov-MF distribution under these conditions is approximately 15 s. When a fault occurs, the probabilistic identification method of distribution network based on hybrid v-MF can achieve classification judgment within 1 s, which is a rapid response, and has engineering application significance and practical value.

5 Conclusion

This paper introduces a novel method for fault-type identification in distribution networks utilizing a mixed von Mises–Fisher (v-MF) distribution. The method involves constructing three-dimensional feature quantities derived from the positive, negative-, and zero-sequence voltage phase angles observed at the time of the fault. Subsequently, the mov-MF distribution is generated to classify the fault type based on the integration of current data with historical distributions. Consequently, the following conclusions can be drawn:

In this paper, we propose a method for fault-type identification utilizing 3D direction vectors to construct a mixed von Mises–Fisher (v-MF) distribution. By leveraging the positive–negative–zero-sequence voltage phasors associated with various fault types, we establish the mov-MF distribution using sample data from diverse fault scenarios. The probability that the faults under test belong to different fault types is estimated by discerning the discrepancy between the mean directions of distinct fault types. Consequently, our method achieves fault-type identification with high accuracy.

The method proposed in this paper remains unaffected by changes in neutral grounding mode, fault transition resistance, and variations in fault locations. It exhibits robust applicability under diverse working conditions.

Data availability statement

The datasets presented in this study can be found in online repositories. The names of the repository/repositories and accession number(s) can be found in the article/Supplementary Material.

Author contributions

JL: writing–review and editing and writing–original draft. ZS: writing–review and editing and writing–original draft. BL: writing–review and editing and supervision.

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

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors, and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

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Keywords: distribution network, fault identification, von Mises–Fisher distribution, maximum expectation algorithm, spherical k-means algorithm

Citation: Li J, Sun Z and Liu B (2024) Fault probability identification method for distribution networks based on mov-MF distribution. Front. Energy Res. 12:1410731. doi: 10.3389/fenrg.2024.1410731

Received: 01 April 2024; Accepted: 30 May 2024; Published: 03 July 2024.

Reviewed by:

Copyright © 2024 Li, Sun and Liu. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: Zhengran Sun, [email protected]

Disclaimer: All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.


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Research on the renewal of multi-story high-density urban landscape based on property rights land—a case study of the self-built liu houses in zherong, fujian province, 1. introduction, 2. materials and methods, 3. results: case study—zherong county, fujian province.

  • ② History of the County
  • (ii) Regional Morphological Feature: Lack of Certain Regularity
  • (iii) Architectural Feature: Significant Diversity Exists
  • (iv) Summary of Early Liu House Features
  • ② Sample B: Mid-term Liu Houses (i) Morphology and Structure of Land Parcels
  • (ii) Regional Morphological Feature: Pattern with Certain Regularity
  • (iii) Architectural Feature: Balanced Similarity and Diversity
  • (iv) Summary of Mid-Term Liu House Features
  • ③ Sample C: Late Liu Houses (i) Morphology and Structure of Land Parcels
  • (ii) Regional Morphological Feature: Strong Regularity
  • (iii) Architectural Features: Highly Unified Similarity
  • (iv) Summary of Late Liu House Features
  • ② Estimation-Based Renovation Framework of Liu House Areas in Zherong

4. Discussion

  • (ii) Individual Construction Driven by the Residents
  • ② Mid-term Liu Houses: Morphological and Architectural Features Affected by both the Government and the Residents (i) Land Parcels Shaped by Administrative Planning
  • (ii) Collective Construction Driven by Spontaneously Formed Resident Groups
  • ③ Late Liu Houses: Unified Morphological and Architectural Features Under Developers’ Direct Control (i) Commercial Real Estate Development
  • (ii) Unified Construction Led by Commercial Developers

5. Conclusions

Author contributions, data availability statement, conflicts of interest.

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Click here to enlarge figure

ContentSub-ContentDetailed ContentIndicatorsWeight Values
Building scaleHeightsAverage floor heightThe average floor height of the target building is added or subtracted from the average of the block and block in which the building is located, and the difference is recorded as H1 and H2, respectively.In the calculation, the weight values k1 and k2 are used, respectively.
Number of floorsAdd or subtract from the average of the blocks and blocks, and the difference is recorded as H1 and H2.In the calculation, the weight values K1 and K2 are used, respectively.
VolumeWidthAdd or subtract from the average of the blocks and blocks, and the difference is recorded as w1 and w2.In the calculation, the weight values q1 and q2 are used, respectively.
LengthAdd or subtract from the average of the blocks and blocks, and the difference is recorded as d1 and d2.In the calculation, the weight values q3 and q4 are used, respectively.
AreaAdd or subtract from the average of the blocks and blocks, and the difference is recorded as a1 and a2.In the calculation, the weight values q5 and q6 are used, respectively.
Concave and convexIf courtyardBool value is ɑ1.The weight value x1 is used in the calculation.
If terraceBool value is ɑ2.The weight value x2 is used in the calculation.
If Bay windowBool value is ɑ3.The weight value x3 is used in the calculation.
If concave and convex over 50 cmBool value is ɑ4.The weight value x4 is used in the calculation.
Plan elementsBuilding setbackBuilding setback scalesBool value is ɑ5.The weight value y1 is used in the calculation.
Facade elementsRoof formIf similarBool value is ɑ6.The weight value u1 is used in the calculation.
Mian formIf similarBool value is ɑ7.The weight value u2 is used in the calculation.
Base formIf similarBool value is ɑ8.The weight value u3 is used in the calculation.
ColorIf similarBool value is ɑ9.The weight value u4 is used in the calculation.
MaterialIf similarBool value is ɑ10.The weight value u5 is used in the calculation
OrnamentIf similarBool value is ɑ11.The weight value u6 is used in the calculation,
Types of Liu HousesTimeArchitectural FeaturesSample Figures
Early Liu House1980–1990(1) The number of floors is no less than 3 and no more than 6 floors.
(2) The pediments of the townhouses are independent of each other, and the construction is led by the residents.
Mid-term Liu House1990–1995(1) The number of floors is no less than 3 and no more than 6 floors.
(3) Townhouse buildings share common pediments.
Late Liu House1995+(1) The number of floors is no less than 3 and no more than 6 floors.
(2) Townhouse buildings share common walls and foundations and are constructed by the developer in a unified manner.
ContentSub-ContentDetailed ContentDifficulty of Renovation ConstructionWeight Values
Building scaleHeightsAverage floor heightHighConsidering the difficulty of the update construction, k1 = k2 = 10
Number of floorsConsidering the difficulty of the update construction, K1 = K2 = 10
VolumeWidthVery highConsidering the difficulty of the update construction, q1 = q2 = 20
LengthConsidering the difficulty of the update construction, q3 = q4 = 20
AreaConsidering the difficulty of the update construction, q5 = q6 = 20
Concave and convexIf courtyardHighx1 = 10 is set to take into account the difficulty of updating the construction
If terracex1 = 10 is set to take into account the difficulty of updating the construction
If Bay windowx1 = 10 is set to take into account the difficulty of updating the construction
If concave and convex over 50 cmx1 = 10 is set to take into account the difficulty of updating the construction
Plan elementsBuilding setbackBuilding setback scalesVery highy1 = 20 is set to take into account the difficulty of updating the construction
Facade elementsRoof formIf similarMediumu1 = 2 is set to take into account the difficulty of updating the construction
Mian formIf similarMediumu2 = 2 is set to take into account the difficulty of updating the construction
Base formIf similarLowu3 = 1 is set to take into account the difficulty of updating the construction
ColorIf similarLowu4 = 1 is set to take into account the difficulty of updating the construction
MaterialIf similarMediumu5 = 2 is set to take into account the difficulty of updating the construction
OrnamentIf similarLowu6 = 1 is set to take into account the difficulty of updating the construction
Control LevelControl TargetRange of Number XControl MethodsRenovation Strategies
Level 1The diversity of form is high >180not much guidance required
Level 2Diversity is comparatively high100–180Certain guidance required
Level 3Diversity is normal50–100Constraints and control needed
Level 4Diversity is comparatively low20–50Strict constraints and control needed
Level 5Diversity is very low <20An overall renovation may be more suitable
The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Share and Cite

Li, N.; Cao, Z.; Wang, K. Research on the Renewal of Multi-Story High-Density Urban Landscape Based on Property Rights Land—A Case Study of the Self-Built Liu Houses in Zherong, Fujian Province. Buildings 2024 , 14 , 1998.

Li N, Cao Z, Wang K. Research on the Renewal of Multi-Story High-Density Urban Landscape Based on Property Rights Land—A Case Study of the Self-Built Liu Houses in Zherong, Fujian Province. Buildings . 2024; 14(7):1998.

Li, Ningyuan, Zhenyu Cao, and Ka Wang. 2024. "Research on the Renewal of Multi-Story High-Density Urban Landscape Based on Property Rights Land—A Case Study of the Self-Built Liu Houses in Zherong, Fujian Province" Buildings 14, no. 7: 1998.

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  • Survey Research | Definition, Examples & Methods

Survey Research | Definition, Examples & Methods

Published on August 20, 2019 by Shona McCombes . Revised on June 22, 2023.

Survey research means collecting information about a group of people by asking them questions and analyzing the results. To conduct an effective survey, follow these six steps:

  • Determine who will participate in the survey
  • Decide the type of survey (mail, online, or in-person)
  • Design the survey questions and layout
  • Distribute the survey
  • Analyze the responses
  • Write up the results

Surveys are a flexible method of data collection that can be used in many different types of research .

Table of contents

What are surveys used for, step 1: define the population and sample, step 2: decide on the type of survey, step 3: design the survey questions, step 4: distribute the survey and collect responses, step 5: analyze the survey results, step 6: write up the survey results, other interesting articles, frequently asked questions about surveys.

Surveys are used as a method of gathering data in many different fields. They are a good choice when you want to find out about the characteristics, preferences, opinions, or beliefs of a group of people.

Common uses of survey research include:

  • Social research : investigating the experiences and characteristics of different social groups
  • Market research : finding out what customers think about products, services, and companies
  • Health research : collecting data from patients about symptoms and treatments
  • Politics : measuring public opinion about parties and policies
  • Psychology : researching personality traits, preferences and behaviours

Surveys can be used in both cross-sectional studies , where you collect data just once, and in longitudinal studies , where you survey the same sample several times over an extended period.

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Before you start conducting survey research, you should already have a clear research question that defines what you want to find out. Based on this question, you need to determine exactly who you will target to participate in the survey.


The target population is the specific group of people that you want to find out about. This group can be very broad or relatively narrow. For example:

  • The population of Brazil
  • US college students
  • Second-generation immigrants in the Netherlands
  • Customers of a specific company aged 18-24
  • British transgender women over the age of 50

Your survey should aim to produce results that can be generalized to the whole population. That means you need to carefully define exactly who you want to draw conclusions about.

Several common research biases can arise if your survey is not generalizable, particularly sampling bias and selection bias . The presence of these biases have serious repercussions for the validity of your results.

It’s rarely possible to survey the entire population of your research – it would be very difficult to get a response from every person in Brazil or every college student in the US. Instead, you will usually survey a sample from the population.

The sample size depends on how big the population is. You can use an online sample calculator to work out how many responses you need.

There are many sampling methods that allow you to generalize to broad populations. In general, though, the sample should aim to be representative of the population as a whole. The larger and more representative your sample, the more valid your conclusions. Again, beware of various types of sampling bias as you design your sample, particularly self-selection bias , nonresponse bias , undercoverage bias , and survivorship bias .

There are two main types of survey:

  • A questionnaire , where a list of questions is distributed by mail, online or in person, and respondents fill it out themselves.
  • An interview , where the researcher asks a set of questions by phone or in person and records the responses.

Which type you choose depends on the sample size and location, as well as the focus of the research.


Sending out a paper survey by mail is a common method of gathering demographic information (for example, in a government census of the population).

  • You can easily access a large sample.
  • You have some control over who is included in the sample (e.g. residents of a specific region).
  • The response rate is often low, and at risk for biases like self-selection bias .

Online surveys are a popular choice for students doing dissertation research , due to the low cost and flexibility of this method. There are many online tools available for constructing surveys, such as SurveyMonkey and Google Forms .

  • You can quickly access a large sample without constraints on time or location.
  • The data is easy to process and analyze.
  • The anonymity and accessibility of online surveys mean you have less control over who responds, which can lead to biases like self-selection bias .

If your research focuses on a specific location, you can distribute a written questionnaire to be completed by respondents on the spot. For example, you could approach the customers of a shopping mall or ask all students to complete a questionnaire at the end of a class.

  • You can screen respondents to make sure only people in the target population are included in the sample.
  • You can collect time- and location-specific data (e.g. the opinions of a store’s weekday customers).
  • The sample size will be smaller, so this method is less suitable for collecting data on broad populations and is at risk for sampling bias .

Oral interviews are a useful method for smaller sample sizes. They allow you to gather more in-depth information on people’s opinions and preferences. You can conduct interviews by phone or in person.

  • You have personal contact with respondents, so you know exactly who will be included in the sample in advance.
  • You can clarify questions and ask for follow-up information when necessary.
  • The lack of anonymity may cause respondents to answer less honestly, and there is more risk of researcher bias.

Like questionnaires, interviews can be used to collect quantitative data: the researcher records each response as a category or rating and statistically analyzes the results. But they are more commonly used to collect qualitative data : the interviewees’ full responses are transcribed and analyzed individually to gain a richer understanding of their opinions and feelings.

Next, you need to decide which questions you will ask and how you will ask them. It’s important to consider:

  • The type of questions
  • The content of the questions
  • The phrasing of the questions
  • The ordering and layout of the survey

Open-ended vs closed-ended questions

There are two main forms of survey questions: open-ended and closed-ended. Many surveys use a combination of both.

Closed-ended questions give the respondent a predetermined set of answers to choose from. A closed-ended question can include:

  • A binary answer (e.g. yes/no or agree/disagree )
  • A scale (e.g. a Likert scale with five points ranging from strongly agree to strongly disagree )
  • A list of options with a single answer possible (e.g. age categories)
  • A list of options with multiple answers possible (e.g. leisure interests)

Closed-ended questions are best for quantitative research . They provide you with numerical data that can be statistically analyzed to find patterns, trends, and correlations .

Open-ended questions are best for qualitative research. This type of question has no predetermined answers to choose from. Instead, the respondent answers in their own words.

Open questions are most common in interviews, but you can also use them in questionnaires. They are often useful as follow-up questions to ask for more detailed explanations of responses to the closed questions.

The content of the survey questions

To ensure the validity and reliability of your results, you need to carefully consider each question in the survey. All questions should be narrowly focused with enough context for the respondent to answer accurately. Avoid questions that are not directly relevant to the survey’s purpose.

When constructing closed-ended questions, ensure that the options cover all possibilities. If you include a list of options that isn’t exhaustive, you can add an “other” field.

Phrasing the survey questions

In terms of language, the survey questions should be as clear and precise as possible. Tailor the questions to your target population, keeping in mind their level of knowledge of the topic. Avoid jargon or industry-specific terminology.

Survey questions are at risk for biases like social desirability bias , the Hawthorne effect , or demand characteristics . It’s critical to use language that respondents will easily understand, and avoid words with vague or ambiguous meanings. Make sure your questions are phrased neutrally, with no indication that you’d prefer a particular answer or emotion.

Ordering the survey questions

The questions should be arranged in a logical order. Start with easy, non-sensitive, closed-ended questions that will encourage the respondent to continue.

If the survey covers several different topics or themes, group together related questions. You can divide a questionnaire into sections to help respondents understand what is being asked in each part.

If a question refers back to or depends on the answer to a previous question, they should be placed directly next to one another.

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Before you start, create a clear plan for where, when, how, and with whom you will conduct the survey. Determine in advance how many responses you require and how you will gain access to the sample.

When you are satisfied that you have created a strong research design suitable for answering your research questions, you can conduct the survey through your method of choice – by mail, online, or in person.

There are many methods of analyzing the results of your survey. First you have to process the data, usually with the help of a computer program to sort all the responses. You should also clean the data by removing incomplete or incorrectly completed responses.

If you asked open-ended questions, you will have to code the responses by assigning labels to each response and organizing them into categories or themes. You can also use more qualitative methods, such as thematic analysis , which is especially suitable for analyzing interviews.

Statistical analysis is usually conducted using programs like SPSS or Stata. The same set of survey data can be subject to many analyses.

Finally, when you have collected and analyzed all the necessary data, you will write it up as part of your thesis, dissertation , or research paper .

In the methodology section, you describe exactly how you conducted the survey. You should explain the types of questions you used, the sampling method, when and where the survey took place, and the response rate. You can include the full questionnaire as an appendix and refer to it in the text if relevant.

Then introduce the analysis by describing how you prepared the data and the statistical methods you used to analyze it. In the results section, you summarize the key results from your analysis.

In the discussion and conclusion , you give your explanations and interpretations of these results, answer your research question, and reflect on the implications and limitations of the research.

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

  • Student’s  t -distribution
  • Normal distribution
  • Null and Alternative Hypotheses
  • Chi square tests
  • Confidence interval
  • Quartiles & Quantiles
  • Cluster sampling
  • Stratified sampling
  • Data cleansing
  • Reproducibility vs Replicability
  • Peer review
  • Prospective cohort study

Research bias

  • Implicit bias
  • Cognitive bias
  • Placebo effect
  • Hawthorne effect
  • Hindsight bias
  • Affect heuristic
  • Social desirability bias

A questionnaire is a data collection tool or instrument, while a survey is an overarching research method that involves collecting and analyzing data from people using questionnaires.

A Likert scale is a rating scale that quantitatively assesses opinions, attitudes, or behaviors. It is made up of 4 or more questions that measure a single attitude or trait when response scores are combined.

To use a Likert scale in a survey , you present participants with Likert-type questions or statements, and a continuum of items, usually with 5 or 7 possible responses, to capture their degree of agreement.

Individual Likert-type questions are generally considered ordinal data , because the items have clear rank order, but don’t have an even distribution.

Overall Likert scale scores are sometimes treated as interval data. These scores are considered to have directionality and even spacing between them.

The type of data determines what statistical tests you should use to analyze your data.

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 sampling methods or criteria for selecting subjects
  • 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 )

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  1. 010 Format Methodology Research Paper ~ Museumlegs

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  2. Research Paper Format

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  3. 😍 Research method paper. Methodology Research Paper Example. 2019-01-22

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  4. Sample student research paper. Download Research Paper Samples For Free

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  5. Research methodology final paper

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  6. Research Methodology Paper Sample

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  1. How to Write an APA Methods Section

    Research papers in the social and natural sciences often follow APA style. This article focuses on reporting quantitative research methods. In your APA methods section, you should report enough information to understand and replicate your study, including detailed information on the sample, measures, and procedures used.

  2. How to Write the Methods Section of a Research Paper

    The methods section of a research paper typically constitutes materials and methods; while writing this section, authors usually arrange the information under each category. The materials category describes the samples, materials, treatments, and instruments, while experimental design, sample preparation, data collection, and data analysis are ...

  3. Research Methods

    Research methods are specific procedures for collecting and analyzing data. Developing your research methods is an integral part of your research design. When planning your methods, there are two key decisions you will make. First, decide how you will collect data. Your methods depend on what type of data you need to answer your research question:

  4. What Is a Research Methodology?

    Step 1: Explain your methodological approach. Step 2: Describe your data collection methods. Step 3: Describe your analysis method. Step 4: Evaluate and justify the methodological choices you made. Tips for writing a strong methodology chapter. Other interesting articles.

  5. Research Paper

    The methods section of a research paper describes the research design, the sample selection, the data collection and analysis procedures, and the statistical methods used to analyze the data. This section should provide sufficient detail for other researchers to replicate the study.

  6. PDF Methodology Section for Research Papers

    The methodology section of your paper describes how your research was conducted. This information allows readers to check whether your approach is accurate and dependable. A good methodology can help increase the reader's trust in your findings. First, we will define and differentiate quantitative and qualitative research.

  7. PDF How to Write the Methods Section of a Research Paper

    The methods section should describe what was done to answer the research question, describe how it was done, justify the experimental design, and explain how the results were analyzed. Scientific writing is direct and orderly. Therefore, the methods section structure should: describe the materials used in the study, explain how the materials ...

  8. Research Methodology Example (PDF + Template)

    In this video, we walk you through a research methodology from a dissertation that earned full distinction, step by step. We start off by discussing the core components of a research methodology by unpacking our free methodology chapter template. We then progress to the sample research methodology to show how these concepts are applied in an ...

  9. Your Step-by-Step Guide to Writing a Good Research Methodology

    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.

  10. Research Methods

    Research methods are ways of collecting and analysing data. Common methods include surveys, experiments, interviews, and observations. ... Compare your paper to billions of pages and articles with Scribbr's Turnitin-powered plagiarism checker. ... A sample is a subset of individuals from a larger population.

  11. Research Methodology

    Include details such as their demographics, sampling method, sample size, and any exclusion criteria used. ... The research methodology is an important section of any research paper or thesis, as it describes the methods and procedures that will be used to conduct the research. It should include details about the research design, data ...

  12. Sample papers

    These sample papers demonstrate APA Style formatting standards for different student paper types. Students may write the same types of papers as professional authors (e.g., quantitative studies, literature reviews) or other types of papers for course assignments (e.g., reaction or response papers, discussion posts), dissertations, and theses.

  13. Sample Paper

    Sample Paper. This paper should be used only as an example of a research paper write-up. Horizontal rules signify the top and bottom edges of pages. For sample references which are not included with this paper, you should consult the Publication Manual of the American Psychological Association, 4th Edition. This paper is provided only to give ...

  14. How to Write a Methods Section for a Research Paper

    Passive voice is often considered the standard for research papers, but it is completely fine to mix passive and active voice, even in the method section, to make your text as clear and concise as possible. Use the simple past tense to describe what you did, and the present tense when you refer to diagrams or tables.

  15. APA Sample Paper

    Media Files: APA Sample Student Paper , APA Sample Professional Paper This resource is enhanced by Acrobat PDF files. Download the free Acrobat Reader. Note: The APA Publication Manual, 7 th Edition specifies different formatting conventions for student and professional papers (i.e., papers written for credit in a course and papers intended for scholarly publication).

  16. PDF Sample of the Qualitative Research Paper

    QUALITATIVE RESEARCH PAPER 45 research problem. For example, the purpose of this study is to examine the prevalence of the use of synthetic marijuana use among preteens which will lead to a prevention and intervention model to be used in community centers citywide. Significance of the Study.

  17. Research Methods

    Quantitative research methods are used to collect and analyze numerical data. This type of research is useful when the objective is to test a hypothesis, determine cause-and-effect relationships, and measure the prevalence of certain phenomena. Quantitative research methods include surveys, experiments, and secondary data analysis.

  18. What Is a Research Design

    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.

  19. Methodology in a Research Paper: Definition and Example

    The methodology section of your research paper allows readers to evaluate the overall validity and reliability of your study and gives important insight into two key elements of your research: your data collection and analysis processes and your rationale for conducting your research. When writing a methodology for a research paper, it's ...

  20. Examples of Methodology in Research Papers (With Definition)

    Example of a methodology in a research paper The following example of a methodology in a research paper provides insight into the structure and content to consider when writing your own: This research article discusses the psychological and emotional impact of a mental health support program for employees. The program provided prolonged and tailored help to job seekers via a job support agency ...

  21. CHAPTER 3

    Within the theoretical-empirical papers, approximately 67% were of qualitative nature, predominantly case studies (55,7%) as the main research method, although it can be suggested there is a ...

  22. How to Write a Research Paper

    Choose a research paper topic. Conduct preliminary research. Develop a thesis statement. Create a research paper outline. Write a first draft of the research paper. Write the introduction. Write a compelling body of text. Write the conclusion. The second draft.

  23. Frontiers

    In this paper, we propose a method for fault-type identification utilizing 3D direction vectors to construct a mixed von Mises-Fisher (v-MF) distribution. By leveraging the positive-negative-zero-sequence voltage phasors associated with various fault types, we establish the mov-MF distribution using sample data from diverse fault scenarios.

  24. Buildings

    Unlike in Western countries, land ownership in China is overwhelmingly vested in the state, and individuals cannot directly own private lands and build houses. Therefore, developers will contract the land to the government and build it into collective apartments. Against this backdrop, a different kind of multi-story, high-density self-built residential buildings is widespread in small towns ...

  25. Survey Research

    Survey research means collecting information about a group of people by asking them questions and analyzing the results. To conduct an effective survey, follow these six steps: Determine who will participate in the survey. Decide the type of survey (mail, online, or in-person) Design the survey questions and layout.