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4 Writing the Materials and Methods (Methodology) Section

The Materials and Methods section briefly describes how you did your research. In other words, what did you do to answer your research question? If there were materials used for the research or materials experimented on you list them in this section. You also describe how you did the research or experiment. The key to a methodology is that another person must be able to replicate your research—follow the steps you take. For example if you used the internet to do a search it is not enough to say you “searched the internet.” A reader would need to know which search engine and what key words you used.

Open this section by describing the overall approach you took or the materials used. Then describe to the readers step-by-step the methods you used including any data analysis performed. See Fig. 2.5 below for an example of materials and methods section.

Writing tips:

• Explain procedures, materials, and equipment used
• Example: “We used an x-ray fluorescence spectrometer to analyze major and trace elements in the mystery mineral samples.”
• Order events chronologically, perhaps with subheadings (Field work, Lab Analysis, Statistical Models)
• Use past tense (you did X, Y, Z)
• Quantify measurements
• Include results in the methods! It’s easy to make this mistake!
• Example: “W e turned on the machine and loaded in our samples, then calibrated the instrument and pushed the start button and waited one hour. . . .”

Technical Writing @ SLCC Copyright © 2020 by Department of English, Linguistics, and Writing Studies at SLCC is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License , except where otherwise noted.

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• Int J Endocrinol Metab
• v.17(1); 2019 Jan

The Principles of Biomedical Scientific Writing: Materials and Methods

Asghar ghasemi.

1 Endocrine Physiology Research Center, Research Institute for Endocrine Sciences, Shahid Beheshti University of Medical Sciences, Tehran, Iran

Zahra Bahadoran

2 Nutrition and Endocrine Research Center, Research Institute for Endocrine Sciences, Shahid Beheshti University of Medical Sciences, Tehran, Iran

Azita Zadeh-Vakili

3 Cellular and Molecular Endocrine Research Center, Research Institute for Endocrine Sciences, Shahid Beheshti University of Medical Sciences, Tehran, Iran

Seyed Ali Montazeri

4 Obesity Research Center, Research Institute for Endocrine Sciences, Shahid Beheshti University of Medical Sciences, Tehran, Iran

Farhad Hosseinpanah

The materials and methods (M&M) section is the heart of a scientific paper and is subject to initial screening of the editor to decide whether the manuscript should be sent for external review. If the M&M section of a scientific paper be considered as a recipe, its ingredients would be who, what, when, where, how, and why. M&M should effectively respond to the study question/hypothesis using the following basic elements including materials, study design, study population/subjects or animals, methods of measurements/assessments, and statistical analysis. A well-organized M&M permits other scientists to evaluate the study findings and repeat the experiments. Although there are several disciplinary differences in the M&M, similar dos and don’ts may be considered to organize a well-written M&M. Briefly, authors need to provide clear-cut, adequate, and detailed information in the M&M section. In this review, the structure, the principles, and the most common recommendations for writing the M&M section are provided, both in general and study-specific; these could help authors effectively prepare the M&M section of a scientific biomedical manuscript.

The principal mission of scientific writing is to convey the researcher’s message clearly and concisely to the scientific community ( 1 ). Although publishing a scientific paper is not the ultimate goal of a research, it contributes much to the progress of science and evidence-based decision-making ( 2 ). During the last decades, efforts have continued to improve the structure and content of research papers, which have resulted in the unified structure and style of scientific writing ( 3 ), that is the IMRAD (Introduction, Materials and Methods, Results, and Discussion) structure.

Although the materials and methods (M&M) section is the heart of a paper, it is very often poorly written ( 4 ). Despite this section seeming to be easier than other parts, the author encounters many challenges ( 5 ). Approximately 30% of rejections by journals are related to the M&M section ( 5 ). A well-written M&M helps the peer review process ( 6 ), enhancing the chances of acceptance of the manuscript ( 5 ); it also increases the chance of inclusion of study findings in secondary analysis of existing data, in systematic reviews and/or meta-analyses ( 7 ).

The M&M section of a scientific paper is a crossroads connecting the introduction to the results section to create a clear story line ( 8 ); it should clearly present the approach to answer the main study question(s) ( 9 ), i.e. questions like who, what, where, when, why, and how ( 10 ). We could also refer to this section as the Experimental section, Method description and Validation, or Patients/subjects and Methods ( 5 , 11 ).

Following our previous report about the writing of the introduction section ( 12 ), in this review, we describe the main principles, general structure and common recommendations that can help authors to prepare the M&M section of a scientific biomedical manuscript more effectively. In addition, specific recommendations will be provided regarding the M&M section of clinical, experimental, epidemiological, and genetic studies.

2. Functions of the Materials and Methods Section

The M&M section of a paper has two main functions ( 13 ): To allow readers to repeat the work and to convince them that the work has been done in an appropriate way. For hypothesis-testing papers, the most important function of the M&M section is to provide information on “what procedures were used to answer the main question(s) stated in the introduction” ( 14 ). The ultimate mission of this section is providing clear and precise descriptions to enable the readers to ascertain exactly how the authors implemented the experimental design ( 15 ). The M&M section should include sufficient details and references to allow other scientists to repeat experiments accurately ( 14 ). The M&M section provides sufficient details on when, where, why, and how the study procedures were performed, what materials were used, and who was included in the study.

Other functions of the M&M section are to facilitate interpretation of study results and convince readers regarding their validity of the results ( 8 , 15 ) and to help them to understand how the results and conclusion were derived from the experiments ( 4 ); in addition, this section must explain how the study avoided or corrected for potential bias in selecting participants/subjects, measuring variables, and estimating associations between variables ( 7 ). In observational human studies, the M&M section also provides justification on how the findings from the sample studied can be generalized to the target population ( 7 ).

3. Components of the Materials and Methods

The basic elements of the M&M section of an original quantitative manuscript include Materials, Study design, Study population/subjects or animals, Methods of measurements/assessments, and Statistical analysis ( Table 1 ). Ethical considerations of research (both for humans and animals) should also be reported in this section, and based on the journal policy, these are reported under the subheading Study population or under a separate heading. This section can be separated under corresponding subheadings to help readers to understand the various stages or components more easily ( 11 ). A common suggestion is that each paragraph or subheading in the M&M section should correspond with the related paragraph/subheading in the results section ( 5 ).

3.1. Materials

3.1.1. chemicals.

In this section, the authors should describe the chemicals (e.g., drugs, culture media, buffers, and gases) used in the research ( 14 ). Specifying the source (manufacturers) is not required for basic laboratory chemicals, but it needs to be clarified for other chemicals ( 16 ). In addition to details on the manufacturer, their location needs to be mentioned when first cited ( 16 ). These details should be used with appropriate punctuation; for example, we used N-(1-naphtyl) ethylene diamine dihydrochloride (NEDD; Sigma-Aldrich Chemical Co., St. Louis, MO).

For drugs, the authors need to mention some essential details including generic name, manufacturer, purity, and concentration; for solutions, the solvent, pH, temperature, total volume infused, and rate of infusion, should be specified if required ( 14 ). If the drug is placed in an organ bath or reservoir, its concentration should be calculated in fluid ( 14 ). For culture media and buffers, the components and their concentrations, temperature, volume, and pH, need to be specified if appropriate ( 14 ).

To avoid advertising, use of generic or chemical names is usually preferred to trade names ( 17 ). In contrast, it is also believed that if the name of the material is registered as trademark, the authors should include the superscript TM or ®, as provided by the supplier ( 16 ). In case of a complicated name of a chemical, its abbreviated name is suggested ( 16 ).

3.1.2. Experimental Materials/Animals/Humans

3.1.2.1. experimental materials.

Experimental materials including molecules, cell lines, and tissues should be described in this section. For plants and micro-organisms, genera, species, and strain designations should be accurately identified ( 17 ). If organisms were collected for the experiment, the dates and locations of collection should also be included.

For cell lines, the sources, species, sex, strains, race, and age of donor should be clarified; whether the cell lines were primary or established and which specific tests were used for their preparation should also be mentioned ( 17 ). Some guidelines for using cell lines are available online ( Table 2 ).

Abbreviations: RCT, randomized clinical trial; STROBE, strengthening the reporting of observational studies in epidemiology; UKCCCR, United Kingdom Coordinating Committee on Cancer Research; WMA, World Medical Association.

3.1.2.2. Experimental Animals

In case of animal studies, source of animals, species, strains, weight, sex, and the number of animals used should be mentioned; conditions of evaluation of experimental animals as well as details of their care and treatment should be specified ( 14 ). Details regarding method and agents used for anesthesia in surgical procedures should be clearly provided ( 5 , 18 ). For treatment/intervention, the authors need to clearly mention chemical names, doses, routes of administration, and duration of treatment ( 5 ). Details should be specified regarding housing of animals, including type of facility, type and size of the cage, breeding program, light/dark cycle, temperature, quality of water, type of food, access to food and water, and environmental enrichment ( 19 ). It is recommended that authors use the name of the animal (e.g., rat or mouse) and specify the type of animal model (e.g., db/db mouse) ( 14 ).

3.1.2.3. Participants/Subjects/Patients

For human observational studies, the eligibility criteria, the sources and methods of selection of participants, and methods of follow-up (in cohort studies) should be described ( 20 ). For case-control studies, the sources and methods of sampling of the control group and the rationale for the choice of cases and controls must be described ( 20 ). The number of exposed and unexposed participants (for cohort studies) and the number of controls per case and the criteria for matching (in case-control studies) should be stated ( 20 , 21 ). For molecular epidemiologic studies, further details including any habits, clinical conditions, physiological factors, working or living conditions that might affect the characteristics or concentrations of the biomarker should also be specified for study populations ( 22 ).

For clinical trials, this section is expected to include the target population, sample size and sampling method, sample representativeness, recruitment and randomization procedures, the basic demographic profile of the study population (e.g., age, gender, and the racial composition), and inclusion and exclusion criteria. Such information are needed to evaluate both the internal and external validity of the study ( 15 , 23 ). Selection criteria and rationale for enrolling patients into the study must be clearly stated ( 15 ). If the study includes a control group, more details on sampling, source of recruitment, and matching (e.g., age, ethnicity, and clinical condition) should be provided ( 24 ).

3.1.3. Ethics Statements

Ethical issues are important components of biomedical studies ( 25 ). The ethics section in a scientific biomedical paper should consist of a statement regarding obtaining approval from the ethics committee with its registration number; otherwise, they need to state that the study was conducted according to the protocols previously outlined such as the Declaration of Helsinki, a set of ethics principles developed by the World Medical Association ( Table 2 ) to provide guidance to scientists and physicians in medical research involving human subjects ( 26 ).

In case of clinical trials, the registration number of study protocol obtained from the clinical trials’ registries ( Table 2 ) should be mentioned. According to the Declaration of Helsinki-2008, “every clinical trial must be registered in an easily accessible database for the public before recruitment of the first participant” ( 27 ). This approach is believed to contribute substantially to the improvement of clinical trial transparency and reduce publication bias and selective reporting ( 28 , 29 ). Practical guidelines for the registration of a clinical trial can be found elsewhere ( 30 , 31 ).

For human studies, a statement regarding informed consent/assent forms should also be mentioned in the ethics approval section. Briefly, informed consent is a process by which an adult human subject confirms his/her willingness to participate in a research after being properly informed of the research protocol ( 25 , 32 ). General principles like potential harm/benefit of the research, study protocols and registration, use of placebo, post-trial provisions (post-trial access to treatment for patients participating in a clinical trial) ( 33 , 34 ), and research publication should be considered in written informed consent forms ( 25 , 35 ). Table 2 provides useful links regarding clinical trial regulations. Assent, as a fundamental part of pediatric research ethics, is given by children in addition to parental consent ( 36 ).

It should be noted that any information that might allow someone to identify human subjects (e.g., names, initials, or hospital identification numbers) is not allowed to be included in the M&M section ( 16 ).

In animal studies, in addition to state approval of the institutional ethics committee ( 19 ), the authors need to determine whether they have applied the 3Rs, namely, replacement, refinement, and reduction of the number of animals used in experiments ( 6 ).

3.2. Methods

3.2.1. study design.

The study design section of a scientific paper is the road map of the study method, which leads to a clear understanding of the data obtaining approach and helps the reader to interpret the results properly ( 37 ). The study design should be the first subsection of the methods in a hypothesis-testing paper ( 37 ). It provides an overview of the procedures used to answer the question(s) and is followed by the relevant details in separate subsections ( 14 ). For hypothesis-testing papers, study question(s), intervention(s), variables measured, and the order of the measurements should be explained ( 14 ). Furthermore, it is expected that this section covers the information including dependent and independent variables, controls (e.g., baseline, control group, and placebo), study duration, and sample size ( 14 ).

The authors should present the specific design of the study, for example, randomized controlled trial, prospective/retrospective cohort study, case-control study, cross-sectional survey, and experimental study, or describe its key components (interventional vs. observational study, longitudinal vs. cross-sectional design) ( 8 ). An overview on observational and interventional study designs can be found elsewhere ( 38 , 39 ).

For observational studies, study location and relevant dates (i.e., period of recruitment, period of exposure, follow-up, and data collection) should be described ( 20 ). An extension of the STROBE statement ( Table 2 ) suggests more details for the study design section in molecular epidemiologic studies ( 22 ); these details describe the specific study designs (nested case-control and case/cohort) ( 40 ) and the setting of the biological sample collection (amount of sample, nature of sample collection procedures, participant conditions, time between sample collection and relevant clinical or physiological endpoints), biological sample storage and processing until biomarker analysis (centrifugation, timing, and additives), and biomarker biochemical characteristics (half-life of the biomarker and chemical and physical characteristics).

For human clinical studies, the authors are requested to specify the trial design (e.g., parallel and factorial), phase of clinical trial (phase I, II, III, or IV), and the allocation ratio (ratio of intended numbers of participants in each of the comparison groups) ( 41 ). More information regarding common terms and designs of clinical trials are provided as useful links in Table 2 .

A further subheading entitled procedures or interventions may also be considered for clinical trials. In this section, authors need to provide detailed information for randomization procedures, including the method used to generate the random allocation sequence (computer-generated random numbers) and mechanisms used to implement the random allocation sequence (sequentially numbered containers), stratification, and random block sizes (if applicable) ( 41 ). According to the CONSORT statement ( Table 2 ), it also should be described who generated the random allocation sequence, who enrolled participants, and who randomly assigned participants to interventions ( 41 ).

If applicable, the authors should state which type of blinding was used (single or double) and who was blinded (participants, care providers, or data analyzer) ( 41 ). Details of interventions, including how and when the interventions were implemented for each group should be specified. Information about the assessment of compliance and adverse events throughout the study should be included ( 41 ). When applicable, it is expected that any interim analysis and cessation of the trial be clarified ( 41 ).

According to ARRIVE (Animal in Research: Reporting In Vivo Experiments) statement ( Table 2 ), for animal studies, the number of groups, randomization procedure, blinding, and experimental unit (i.e., single animal, group, or cage of animal) should be mentioned ( 19 ); for complex designs, a time-line diagram or flowchart can be useful ( 19 ).

For genetic studies, the authors need to consider nomenclatures of genes and variants ( Table 2 ) and follow recommendations for the description of sequence variants ( 42 ). For genetic association studies, an extension of the STROBE statement, namely STREGA, advises authors on how to provide further details in the study design section; details on the criteria and methods for the selection of subsets of participants from a larger study should also be described in this section. Furthermore, genetic exposures (genetic variants) and variables associated with population stratification should be clarified ( 43 ).

3.2.2. Methods of Measurements/Assessments

Although describing details in the M&M section depends on the type of study and the target audience, authors need to maintain a balance. As a rule of thumb, the details of the procedures should be included if the study replication would fail without them. All that reader needs to understand is how the key findings in this paper were derived. However, this section should not be like a procedure manual or a cookbook ( 4 ).

The term “condensed” or “extended” has been used to describe levels of details used in the methods section ( 44 ). In the condensed methods, little elaboration or justification is provided, whereas in the extended methods, authors need to provide a rationale of why and how the procedures were performed ( 44 ). In practice, depending on the novelty of the methods used in the study, different levels of details may need to be described ( Table 3 ). To summarize documented methods, authors may begin with “in brief”; use of “briefly” instead is a common mistake because “briefly” describes the following verb and does not indicate the author’s intention to be brief ( 16 ).

The rationale for method choices and characteristics of the study design may also be provided in the methods section ( 10 , 11 ). From an editor’s point of view, advantages and disadvantages, values and limitations of the techniques and methods, especially new ones, are better to be described using a general background of the field ( 45 ).

In this section, the authors need to clearly describe how study variables (i.e., exposures or independent variables, outcomes or dependent variables, covariates, or potential modifiers) were measured ( 8 , 15 ). If applicable, diagnostic criteria need to be clarified for the variables (i.e., exposure, outcome and/or confounder); moreover, sources of data and details of methods of assessments (measurements) should be described for each variable of interest.

In animal studies, details of how, when (time of day), where (home cage and laboratory), and why (rationale for dose and route of administration) for each procedure should be reported ( 19 ).

According to minimum information for publication of quantitative real-time PCR experiments (MIQE), details about sample processing and storage, RNA and DNA extraction and quantification, primer and probe characteristics, reverse transcription details, sample normalization, PCR efficiency, and data analysis should be provided in real-time quantitative PCR (qPCR) experiments ( 46 ).

For genetic association studies, authors need to describe laboratory methods, including source and storage of DNA, genotyping methods and platforms (including the allele calling algorithm used and its version), and error and call rates. The name of the laboratory or center where genotyping was performed and comparability of laboratory methods (if there is more than one group) needs to be clarified. According to the STREGA statement, authors should specify whether genotypes were assigned using all the data from the study simultaneously or separately in smaller batches ( 43 ).

To describe instruments, the manufacturer and model as well as the calibration procedures should be described; in addition, it should be clearly described how measurements were taken ( 10 , 15 ). Details of measurement characteristics (i.e., reproducibility, validity, and responsiveness) that influence the interpretation of the main results should also be described ( 8 ); validity and reliability, key indicators of the quality of measurement instruments (e.g., equipment and questionnaires) used for data collection or measurement should be appropriately reported ( 18 ).

3.2.3. Statistical Analysis

The basic requirement of writing the statistical section is providing description and justification for the statistical approaches and selection of statistical tests ( 14 ). General considerations for preliminary, primary, and supplementary analyses derived from statistical reporting guidelines ( 47 , 48 ) and the common pitfalls ( 49 , 50 ) in writing the statistical section are provided in Box 1 . The Vancouver guideline states “describe statistical methods with enough details to enable a knowledgeable reader with access to the original data to verify the reported results” ( 51 ).

Statistical tests should be discussed in order to be applicable for data analysis ( 52 ). Typically, this section is initiated by preliminary analysis and descriptive statistics, describing the study population, and then it is followed by specific tests describing the association of variables or assessing the effect of experiments ( 52 ).

The exact value of sample size, e.g., the number of human subjects, animals, or cells for each analysis and how the data were presented (mean, median, standard deviation, standard error, or confidence intervals) should be specified. Furthermore, the statistical methods used to determine strategies for randomization/stratification and sample size estimation need to be clarified ( 14 ). Appropriate identification (i.e., name, version, company, city, state, and country) for the statistical package or program used for analysis must be mentioned.

4. General Considerations for Materials and Methods Section

4.1. length.

Typical length of the M&M section is 2 - 3 pages (each page is considered one page in a word processor, with conventional margins, 1.5 line spacing, and font size of 11), consisting of 6 - 9 paragraphs (each paragraph usually contains 100 - 200 words, not exceeding 750 words) ( 19 ); however, depending on the discipline and field of study, the length of this section may vary from the condensed to the extended form ( 44 ). Method sections of chemistry, mycology, and molecular biology may be categorized as condensed-form, whereas public health and medical research are considered as intermediate, and psychology, sociology, and education are organized in the extended-form ( 44 ). To keep the M&M more concise, some details of materials and methods may be allowed as appendix or supplementary documents that are published online ( 45 ).

To organize paragraphs, topic sentences can be used to signal the topic of a paragraph, especially when a subsection has more than one paragraph ( 14 ). Use of linking or transition phrases/clauses (purpose phrases, time-related linking phrases, or causal linking phrases) to signal the topic of a paragraph is highly recommended ( Table 4 ) ( 11 , 14 , 44 ).

The M&M section may include up to 5 - 15 references ( 19 ). Never reference a document that you have not read ( 53 ).

4.2. Tables and Figures in Methods: Yes or No?

Use of appropriate tables and figures helps authors to summarize large amounts of complex information of the study procedures; a common recommendation to reduce the word count ( 11 ). Flowchart of the study design may be a common form of figure referenced within the M&M section. Some guidelines are available to organize study flowcharts for different study designs, for instance, the CONSORT flow diagram for clinical trials ( 54 ) and the STROBE flowchart of study participants for observational designs like cohort studies ( 21 ), as shown in Table 2 . This section does not include results ( 14 , 55 ), although intermediate results such those used for calculations that are used for obtaining results for the study question such as standard curves are recommended to be included in this section ( 14 ).

4.3. Ordering Procedures in the Materials and Methods Section

Several parts of the M&M section should be written in a logical or chronological order; presenting the methods in a logical order helps the text to make complete sense; however, the actions should be mentioned in chronological order within a paragraph or sentence. Some believe that the use of numbers or bullets to describe a sequential procedure, provided that be acceptable by the journal, make the M&M section easier to read ( 11 ). As a general suggestion, no more than two actions should be presented in a sentence. To increase readability, the subject and verb in a sentence should preferably be close together ( 11 ).

4.4. Tenses and Voices

A general recommendation is that the M&M section should be written in the past tense, either in active or passive voice ( 5 ). Depending on the author’s field, the journal style, or the action described in the M&M section, the present simple tense may also be used, for example, this tense is required when a standard method is described or when the authors present their procedure, model, software, or device ( 11 ).

Although passive voice (e.g., was/were investigated, was/were evaluated, or was/were performed) is the more common form of verbs in this section, using the active voice to show the ownership of the investigators (e.g., we performed, we evaluated, or we implemented) have recently taken priority ( 5 ). However, there is a belief that the active voice is not appropriate for the M&M section because the focus would be shifted from the research to the researchers ( 11 , 56 ).

4.5. Self-Assessing the Quality of the Materials and Methods Section

Self-assessment of the quality of the M&M section may be the last, but it is certainly not the least important step in the writing of the M&M section. Authors need to ask themselves “would a researcher be able to reproduce the study with the information provided in the method section?” ( 8 ). Using this approach, the authors would be reassured that all the critical information has been included, and unnecessary and redundant data have been excluded from this section; this process is useful to keep the paper’s storyline ( 8 ). In Box 2 , a checklist comprised of the most important questions for general quality assessment of the method section is provided.

To ensure all the necessary information is included in the methods section, referring to reporting guidelines that are available for the most common study types (e.g., CONSORT for clinical trials, STROBE for observational studies, STARD for diagnostic research, PRISMA for systematic reviews and meta-analyses, and ARRIVE for animal studies) is highly recommended ( Table 2 ).

5. Conclusions

The M&M section is the most important part of a research paper because it provides detailed information to other scientists/researchers to reproduce the study and judge the validity of the study’s findings. In the M&M section, “materials” refers to what was examined (e.g., humans, animals, cell lines, or tissues) and various chemicals and treatments (e.g., drugs, culture media, and gases), and the instruments used in the study. “methods” presents how subjects or objects were employed to answer the study question, that is, how measurements and calculations were made and how data analysis was carried out. Useful tips and common pitfalls in the M&M section are briefly reviewed in Box 3 .

Acknowledgments

The authors wish to acknowledge Ms. Niloofar Shiva for critical editing of English grammar and syntax of the manuscript.

How to Write the Methods Section of a Scientific Article

What Is the Methods Section of a Research Paper?

The Methods section of a research article includes an explanation of the procedures used to conduct the experiment. For authors of scientific research papers, the objective is to present their findings clearly and concisely and to provide enough information so that the experiment can be duplicated.

Research articles contain very specific sections, usually dictated by either the target journal or specific style guides. For example, in the social and behavioral sciences, the American Psychological Association (APA) style guide is used to gather information on how the manuscript should be arranged . As with most styles, APA’s objectives are to ensure that manuscripts are written with minimum distractions to the reader. Every research article should include a detailed Methods section after the Introduction.

Why is the Methods Section Important?

The Methods section (also referred to as “Materials and Methods”) is important because it provides the reader enough information to judge whether the study is valid and reproducible.

Structure of the Methods Section in a Research Paper

While designing a research study, authors typically decide on the key points that they’re trying to prove or the “ cause-and-effect relationship ” between objects of the study. Very simply, the study is designed to meet the objective. According to APA, a Methods section comprises of the following three subsections: participants, apparatus, and procedure.

How do You Write a Method Section in Biology?

In biological sciences, the Methods section might be more detailed, but the objectives are the same—to present the study clearly and concisely so that it is understandable and can be duplicated.

If animals (including human subjects) were used in the study, authors should ensure to include statements that they were treated according to the protocols outlined to ensure that treatment is as humane as possible.

• The Declaration of Helsinki is a set of ethical principles developed by The World Medical Association to provide guidance to scientists and physicians in medical research involving human subjects.

Research conducted at an institution using human participants is overseen by the Institutional Review Board (IRB) with which it is affiliated. IRB is an administrative body whose purpose is to protect the rights and welfare of human subjects during their participation in the study.

Literature Search

Literature searches are performed to gather as much information as relevant from previous studies. They are important for providing evidence on the topic and help validate the research. Most are accomplished using keywords or phrases to search relevant databases. For example, both MEDLINE and PubMed provide information on biomedical literature. Google Scholar, according to APA, is “one of the best sources available to an individual beginning a literature search.” APA also suggests using PsycINFO and refers to it as “the premier database for locating articles in psychological science and related literature.”

Authors must make sure to have a set of keywords (usually taken from the objective statement) to stay focused and to avoid having the search move far from the original objective. Authors will benefit by setting limiting parameters, such as date ranges, and avoiding getting pulled into the trap of using non-valid resources, such as social media, conversations with people in the same discipline, or similar non-valid sources, as references.

Related: Ready with your methods section and looking forward to manuscript submission ? Check these journal selection guidelines now!

What Should be Included in the Methods Section of a Research Paper?

One commonly misused term in research papers is “methodology.” Methodology refers to a branch of the Philosophy of Science which deals with scientific methods, not to the methods themselves, so authors should avoid using it. Here is the list of main subsections that should be included in the Methods section of a research paper ; authors might use subheadings more clearly to describe their research.

• Literature search : Authors should cite any sources that helped with their choice of methods. Authors should indicate timeframes of past studies and their particular parameters.
• Study participants : Authors should cite the source from where they received any non-human subjects. The number of animals used, the ages, sex, their initial conditions, and how they were housed and cared for, should be listed. In case of human subjects, authors should provide the characteristics, such as geographical location; their age ranges, sex, and medical history (if relevant); and the number of subjects. In case hospital records were used, authors should include the subjects’ basic health information and vital statistics at the beginning of the study. Authors should also state that written informed consent was provided by each subject.
• Inclusion/exclusion criteria : Authors should describe their inclusion and exclusion criteria, how they were determined, and how many subjects were eliminated.
• Group characteristics (could be combined with “Study participants”) : Authors should describe how the chosen group was divided into subgroups and their characteristics, including the control. Authors should also describe any specific equipment used, such as housing needs and feed (usually for animal studies). If patient records are reviewed and assessed, authors should mention whether the reviewers were blinded to them.
• Procedures : Authors should describe their study design. Any necessary preparations (e.g., tissue samples, drugs) and instruments must be explained. Authors should describe how the subjects were “ manipulated to answer the experimental question .” Timeframes should be included to ensure that the procedures are clear (e.g., “Rats were given XX drug for 14 d”). For animals sacrificed, the methods used and the protocols followed should be outlined.
• Statistical analyses: The type of data, how they were measured, and which statistical tests were performed, should be described. (Note: This is not the “results” section; any relevant tables and figures should be referenced later.) Specific software used must be cited.

What Should not be Included in Your Methods Section?

Common pitfalls can make the manuscript cumbersome to read or might make the readers question the validity of the research. The University of Southern California provides some guidelines .

• Background information that is not helpful must be avoided.
• Authors must avoid providing a lot of detail.
• Authors should focus more on how their method was used to meet their objective and less on mechanics .
• Any obstacles faced and how they were overcome should be described (often in your “Study Limitations”). This will help validate the results.

According to the University of Richmond , authors must avoid including extensive details or an exhaustive list of equipment that have been used as readers could quickly lose attention. These unnecessary details add nothing to validate the research and do not help the reader understand how the objective was satisfied. A well-thought-out Methods section is one of the most important parts of the manuscript. Authors must make a note to always prepare a draft that lists all parts, allow others to review it, and revise it to remove any superfluous information.

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Research Paper Writing: 5. Methods / Materials

• 1. Getting Started
• 2. Abstract
• 3. Introduction
• 4. Literature Review
• 5. Methods / Materials
• 6. Results / Analysis
• 7. Discussion
• 8. Conclusion
• 9. Reference

Methods / Materials Overview

These sections of the research paper should be concise. The audience reading the paper will always want to know what materials or methods that were used. The methods and materials may be under subheadings in the section or incorporated together. The main objective for these sections is to provide specialized materials, general procedures, and methods to judge the scientific value of the paper.

What to include in the sections

• Described separately
• Include the chemicals, biological, and any equipment
• Do not include common supplies, such as test tubes, pipette tips, beakers, etc. or standard lab equipment
• Single out sources like a specific type of equipment, enzyme, or a culture
• These should be mentioned in a separate paragraph with its own heading or highlighted in the procedure section if there is one
• Refer to solutions by name and describe
• Describes in detail how the analysis was conducted
• Be brief when presenting methods under the title devoted to a specific technique or groups of procedures
• Simplify and report what the procedure was
• Report the method by name
• Use third person passive voice, and avoid using first person
• Use normal text in these sections
• Avoid informal lists
• Use complete sentences

Example of a Methods Section

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Materials and Methods Examples and Writing Tips

Abstract | Introduction | Literature Review | Research question | Materials & Methods | Results | Discussion | Conclusion

In this blog, we look at how to write the materials and methods section of a research paper. In most research papers, the materials and methods section follows the literature review section. This is generally the easiest section to write because you are simply reproducing what you did in your experiments. It is always a good idea to start writing your research paper with the materials and methods section.

1. What is the purpose of the materials and methods section?

Materials and methods should describe how you did your research and detail the experimental procedure. One of the most important things to bear in mind while writing the materials and methods section is that it should have enough detail so that other researchers in your field can replicate your experiments and reproduce your results.  You should provide all the steps in a logical order so that your readers can follow your description easily.

2. Materials and Methods Examples

The structure of the methods section will very much depend on your discipline. If you are not sure about the structure, then the best place to start will be to go through the methods section of some previously published papers from your chosen journal. We will look at some examples of materials and methods structure in different disciplines. 

2.1. Materials & methods example #1 (Engineering paper)

If you are writing an engineering sciences research paper in which you are introducing a new method, your materials and methods section would typically include the following information.

You can start with the top-level summary of the method. You can try to answer these questions. Are you proposing a new method? Or,  Are you using a standard method from the literature?  Or, Are you extending a previously published method? If so, is it your previous work? or work published by a different author?

Then you can talk about the reasons for choosing this method. You can quote previous papers that have used this method successfully to support your arguments. Then, you can talk about the actual implementation details of the methods.

Then you can talk about how the methods were validated to confirm that they are suitable for your research. You can also include information about any pilot or preliminary studies you conducted before the full study. Then you can explain how you propose to test and evaluate the methods to prove that they are better than the existing methods. Here, you can talk about metrics and statistical tests you will be using to evaluate your method.

2.2. Materials & methods example #2 (Measurement paper)

If you are writing a paper that deals with measurements, you would typically include the following information in your materials and methods section.

You can start by talking about the experimental setup. You can try to answer these questions. What equipment was used to perform the measurements? What was the make and the model of the equipment?  How many technicians took the measurements?  How experienced were the technicians?

Then you can talk about the parameters that were measured during the experiment. Then you can talk about the actual measurement procedure. How were the samples prepared for the measurements?  How many measurements were taken? Were the measurements repeated for consistency? Was there a time interval between successive measurements?

Then you can talk about measurement conditions and constraints. Were the measurements performed at room temperature or under special conditions? Were there any practical difficulties while performing the measurements, if so, how did you overcome them?

Most importantly, you must list all the calculations in the form of detailed equations and formulas so that readers know exactly how the data was produced.

2.3. Materials & methods example #3 (Survey questionnaire paper)

If you are writing a survey questionnaire paper , you would typically include the following information in your materials and methods section.

You can start by talking about your participants. Who is your target population? What are their demographics? How did you recruit them?  How did participants provide consent for your study? What sampling method did you use to select the participants?

Then you can talk about the survey type. Was it a phone interview? Was it a personal interview? Was it an online survey? Or, Was it a written survey?

Then you can talk about the questionnaire design. How did you choose the questions? How many questions were there? What type of questions were they? Were they open ended questions, or close ended questions, or rating scale questions, or a mixture of different types of questions?

Then you can talk about how the questionnaire was administered. If it is an online survey, how did you get the questionnaire to the participants? Did you email them? Or did you post the survey forms?

If you are doing a personal interview. How did you conduct the interviews? Was it one to one interview, or was it done in batches, or did you use focus groups? How did the participants behave during the interview?

Then you can talk about questionnaire testing. Did you test your questionnaire before the main study? Did you have to make any changes after initial testing?  Did you have to translate the questionnaire into multiple languages? Then finally you can talk about different types of statistical tests you used to analyze the survey responses.

2.4. Materials & methods example #4 (Medical clinical trial paper)

If you are writing a medical research paper , your materials and methods section would typically include the following information.

You can start by providing information about the study design. Was it a randomized trial, or an observational trial? Was it a prospective study, or a retrospective study? Was the study double-blinded, or single-blinded?

Then, you can talk about how the ethical approval was obtained for the study and clarify if the clinical trial was registered. if so, then provide the registration number.

Then, you can talk about how the participants were recruited for the study, and explain the inclusion and exclusion criteria. Then, you can talk about how the participants were grouped into control and placebo groups, and explain how the medication was administered.

Then, you can talk about what outcomes were measured. What was the primary outcome? What was the secondary outcome? What was the follow up period? You can try to answer these questions. Then you can finish off with some information about the statistical tests you used to analyze the data.

3. Frequently Asked Questions

One of the common mistakes people make is using vague language in materials and methods. Reviewers won’t like it, and they will reject the paper on the basis that the section is not elaborate enough for other researchers to reproduce your experiments.

Make sure you write the materials and methods section in past tense, since you are reporting something that has already happened.

Acronyms & Abbrevations: Try to use acronyms and abbreviations for long method names. Abbreviations and acronyms are a great way to make your writing concise and save time. Define the acronyms and abbreviations during their first occurrence then use the short form in the rest of the text. The common practice is to put the acronym and abbreviations in parentheses after the full term.

Use different layouts: Another problem you are likely to face is that your methods section can sound like manual if you have too much text in it. In particular, if you are dealing with a very complex procedure, the readers might find it dry and tedious. So try to provide some variety to the layout. Try to use bullet points and numberings instead of long paragraphs to make it easy for the readers to understand the procedure. You can use flow diagrams to illustrate the process rather than describing it.

When you are using a standard method that is well described in literature, the standard practice is to reference the paper rather than repeating the entire procedure. You can also provide a brief summary of the procedure in your own words.

For example, you can say something like this, “The details of the procedure have been reported previously in…”, and reference the previous paper. And then, you can follow it up with a brief summary of the method from the previous paper.

If you are extending a previous method, then you can do something like this. You can say that, “Some minor modifications were made to the method described in…” and reference the previous paper.  And then, you can follow it up with the list of refinements you made to the previous method in order to adapt it to your work.

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How to Write a Methods Section for a Psychology Paper

Tips and Examples of an APA Methods Section

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

Emily is a board-certified science editor who has worked with top digital publishing brands like Voices for Biodiversity, Study.com, GoodTherapy, Vox, and Verywell.

Verywell / Brianna Gilmartin 

The methods section of an APA format psychology paper provides the methods and procedures used in a research study or experiment . This part of an APA paper is critical because it allows other researchers to see exactly how you conducted your research.

Method refers to the procedure that was used in a research study. It included a precise description of how the experiments were performed and why particular procedures were selected. While the APA technically refers to this section as the 'method section,' it is also often known as a 'methods section.'

The methods section ensures the experiment's reproducibility and the assessment of alternative methods that might produce different results. It also allows researchers to replicate the experiment and judge the study's validity.

This article discusses how to write a methods section for a psychology paper, including important elements to include and tips that can help.

What to Include in a Method Section

So what exactly do you need to include when writing your method section? You should provide detailed information on the following:

• Research design
• Participants
• Participant behavior

The method section should provide enough information to allow other researchers to replicate your experiment or study.

Components of a Method Section

The method section should utilize subheadings to divide up different subsections. These subsections typically include participants, materials, design, and procedure.

Participants 

In this part of the method section, you should describe the participants in your experiment, including who they were (and any unique features that set them apart from the general population), how many there were, and how they were selected. If you utilized random selection to choose your participants, it should be noted here.

For example: "We randomly selected 100 children from elementary schools near the University of Arizona."

At the very minimum, this part of your method section must convey:

• Basic demographic characteristics of your participants (such as sex, age, ethnicity, or religion)
• The population from which your participants were drawn
• Any restrictions on your pool of participants
• How many participants were assigned to each condition and how they were assigned to each group (i.e., randomly assignment , another selection method, etc.)
• Why participants took part in your research (i.e., the study was advertised at a college or hospital, they received some type of incentive, etc.)

Information about participants helps other researchers understand how your study was performed, how generalizable the result might be, and allows other researchers to replicate the experiment with other populations to see if they might obtain the same results.

In this part of the method section, you should describe the materials, measures, equipment, or stimuli used in the experiment. This may include:

• Testing instruments
• Technical equipment
• Any psychological assessments that were used
• Any special equipment that was used

For example: "Two stories from Sullivan et al.'s (1994) second-order false belief attribution tasks were used to assess children's understanding of second-order beliefs."

For standard equipment such as computers, televisions, and videos, you can simply name the device and not provide further explanation.

Specialized equipment should be given greater detail, especially if it is complex or created for a niche purpose. In some instances, such as if you created a special material or apparatus for your study, you might need to include an illustration of the item in the appendix of your paper.

In this part of your method section, describe the type of design used in the experiment. Specify the variables as well as the levels of these variables. Identify:

• The independent variables
• Dependent variables
• Control variables
• Any extraneous variables that might influence your results.

Also, explain whether your experiment uses a  within-groups  or between-groups design.

For example: "The experiment used a 3x2 between-subjects design. The independent variables were age and understanding of second-order beliefs."

The next part of your method section should detail the procedures used in your experiment. Your procedures should explain:

• What the participants did
• How data was collected
• The order in which steps occurred

For example: "An examiner interviewed children individually at their school in one session that lasted 20 minutes on average. The examiner explained to each child that he or she would be told two short stories and that some questions would be asked after each story. All sessions were videotaped so the data could later be coded."

Keep this subsection concise yet detailed. Explain what you did and how you did it, but do not overwhelm your readers with too much information.

Tips for How to Write a Methods Section

In addition to following the basic structure of an APA method section, there are also certain things you should remember when writing this section of your paper. Consider the following tips when writing this section:

• Use the past tense : Always write the method section in the past tense.
• Be descriptive : Provide enough detail that another researcher could replicate your experiment, but focus on brevity. Avoid unnecessary detail that is not relevant to the outcome of the experiment.
• Use an academic tone : Use formal language and avoid slang or colloquial expressions. Word choice is also important. Refer to the people in your experiment or study as "participants" rather than "subjects."
• Use APA format : Keep a style guide on hand as you write your method section. The Publication Manual of the American Psychological Association is the official source for APA style.
• Make connections : Read through each section of your paper for agreement with other sections. If you mention procedures in the method section, these elements should be discussed in the results and discussion sections.
• Proofread : Check your paper for grammar, spelling, and punctuation errors.. typos, grammar problems, and spelling errors. Although a spell checker is a handy tool, there are some errors only you can catch.

After writing a draft of your method section, be sure to get a second opinion. You can often become too close to your work to see errors or lack of clarity. Take a rough draft of your method section to your university's writing lab for additional assistance.

A Word From Verywell

The method section is one of the most important components of your APA format paper. The goal of your paper should be to clearly detail what you did in your experiment. Provide enough detail that another researcher could replicate your study if they wanted.

Finally, if you are writing your paper for a class or for a specific publication, be sure to keep in mind any specific instructions provided by your instructor or by the journal editor. Your instructor may have certain requirements that you need to follow while writing your method section.

Frequently Asked Questions

While the subsections can vary, the three components that should be included are sections on the participants, the materials, and the procedures.

• Describe who the participants were in the study and how they were selected.
• Define and describe the materials that were used including any equipment, tests, or assessments
• Describe how the data was collected

To write your methods section in APA format, describe your participants, materials, study design, and procedures. Keep this section succinct, and always write in the past tense. The main heading of this section should be labeled "Method" and it should be centered, bolded, and capitalized. Each subheading within this section should be bolded, left-aligned and in title case.

The purpose of the methods section is to describe what you did in your experiment. It should be brief, but include enough detail that someone could replicate your experiment based on this information. Your methods section should detail what you did to answer your research question. Describe how the study was conducted, the study design that was used and why it was chosen, and how you collected the data and analyzed the results.

Erdemir F. How to write a materials and methods section of a scientific article ? Turk J Urol . 2013;39(Suppl 1):10-5. doi:10.5152/tud.2013.047

Kallet RH. How to write the methods section of a research paper . Respir Care . 2004;49(10):1229-32. PMID: 15447808.

American Psychological Association.  Publication Manual of the American Psychological Association  (7th ed.). Washington DC: The American Psychological Association; 2019.

American Psychological Association. APA Style Journal Article Reporting Standards . Published 2020.

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

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• How to Write Your Methods

Ensure understanding, reproducibility and replicability

What should you include in your methods section, and how much detail is appropriate?

Why Methods Matter

The methods section was once the most likely part of a paper to be unfairly abbreviated, overly summarized, or even relegated to hard-to-find sections of a publisher’s website. While some journals may responsibly include more detailed elements of methods in supplementary sections, the movement for increased reproducibility and rigor in science has reinstated the importance of the methods section. Methods are now viewed as a key element in establishing the credibility of the research being reported, alongside the open availability of data and results.

A clear methods section impacts editorial evaluation and readers’ understanding, and is also the backbone of transparency and replicability.

For example, the Reproducibility Project: Cancer Biology project set out in 2013 to replicate experiments from 50 high profile cancer papers, but revised their target to 18 papers once they understood how much methodological detail was not contained in the original papers.

What to include in your methods section

What you include in your methods sections depends on what field you are in and what experiments you are performing. However, the general principle in place at the majority of journals is summarized well by the guidelines at PLOS ONE : “The Materials and Methods section should provide enough detail to allow suitably skilled investigators to fully replicate your study. ” The emphases here are deliberate: the methods should enable readers to understand your paper, and replicate your study. However, there is no need to go into the level of detail that a lay-person would require—the focus is on the reader who is also trained in your field, with the suitable skills and knowledge to attempt a replication.

A constant principle of rigorous science

A methods section that enables other researchers to understand and replicate your results is a constant principle of rigorous, transparent, and Open Science. Aim to be thorough, even if a particular journal doesn’t require the same level of detail . Reproducibility is all of our responsibility. You cannot create any problems by exceeding a minimum standard of information. If a journal still has word-limits—either for the overall article or specific sections—and requires some methodological details to be in a supplemental section, that is OK as long as the extra details are searchable and findable .

Imagine replicating your own work, years in the future

As part of PLOS’ presentation on Reproducibility and Open Publishing (part of UCSF’s Reproducibility Series ) we recommend planning the level of detail in your methods section by imagining you are writing for your future self, replicating your own work. When you consider that you might be at a different institution, with different account logins, applications, resources, and access levels—you can help yourself imagine the level of specificity that you yourself would require to redo the exact experiment. Consider:

• Which details would you need to be reminded of? 
• Which cell line, or antibody, or software, or reagent did you use, and does it have a Research Resource ID (RRID) that you can cite?
• Which version of a questionnaire did you use in your survey? 
• Exactly which visual stimulus did you show participants, and is it publicly available? 
• What participants did you decide to exclude? 
• What process did you adjust, during your work? 

Tip: Be sure to capture any changes to your protocols

You yourself would want to know about any adjustments, if you ever replicate the work, so you can surmise that anyone else would want to as well. Even if a necessary adjustment you made was not ideal, transparency is the key to ensuring this is not regarded as an issue in the future. It is far better to transparently convey any non-optimal methods, or methodological constraints, than to conceal them, which could result in reproducibility or ethical issues downstream.

Visual aids for methods help when reading the whole paper

Consider whether a visual representation of your methods could be appropriate or aid understanding your process. A visual reference readers can easily return to, like a flow-diagram, decision-tree, or checklist, can help readers to better understand the complete article, not just the methods section.

Ethical Considerations

In addition to describing what you did, it is just as important to assure readers that you also followed all relevant ethical guidelines when conducting your research. While ethical standards and reporting guidelines are often presented in a separate section of a paper, ensure that your methods and protocols actually follow these guidelines. Read more about ethics .

Existing standards, checklists, guidelines, partners

While the level of detail contained in a methods section should be guided by the universal principles of rigorous science outlined above, various disciplines, fields, and projects have worked hard to design and develop consistent standards, guidelines, and tools to help with reporting all types of experiment. Below, you’ll find some of the key initiatives. Ensure you read the submission guidelines for the specific journal you are submitting to, in order to discover any further journal- or field-specific policies to follow, or initiatives/tools to utilize.

Tip: Keep your paper moving forward by providing the proper paperwork up front

Be sure to check the journal guidelines and provide the necessary documents with your manuscript submission. Collecting the necessary documentation can greatly slow the first round of peer review, or cause delays when you submit your revision.

Randomized Controlled Trials – CONSORT The Consolidated Standards of Reporting Trials (CONSORT) project covers various initiatives intended to prevent the problems of  inadequate reporting of randomized controlled trials. The primary initiative is an evidence-based minimum set of recommendations for reporting randomized trials known as the CONSORT Statement . 

Systematic Reviews and Meta-Analyses – PRISMA The Preferred Reporting Items for Systematic Reviews and Meta-Analyses ( PRISMA ) is an evidence-based minimum set of items focusing  on the reporting of  reviews evaluating randomized trials and other types of research.

Research using Animals – ARRIVE The Animal Research: Reporting of In Vivo Experiments ( ARRIVE ) guidelines encourage maximizing the information reported in research using animals thereby minimizing unnecessary studies. (Original study and proposal , and updated guidelines , in PLOS Biology .) 

Laboratory Protocols Protocols.io has developed a platform specifically for the sharing and updating of laboratory protocols , which are assigned their own DOI and can be linked from methods sections of papers to enhance reproducibility. Contextualize your protocol and improve discovery with an accompanying Lab Protocol article in PLOS ONE .

Consistent reporting of Materials, Design, and Analysis – the MDAR checklist A cross-publisher group of editors and experts have developed, tested, and rolled out a checklist to help establish and harmonize reporting standards in the Life Sciences . The checklist , which is available for use by authors to compile their methods, and editors/reviewers to check methods, establishes a minimum set of requirements in transparent reporting and is adaptable to any discipline within the Life Sciences, by covering a breadth of potentially relevant methodological items and considerations. If you are in the Life Sciences and writing up your methods section, try working through the MDAR checklist and see whether it helps you include all relevant details into your methods, and whether it reminded you of anything you might have missed otherwise.

Summary Writing tips

The main challenge you may find when writing your methods is keeping it readable AND covering all the details needed for reproducibility and replicability. While this is difficult, do not compromise on rigorous standards for credibility!

• Keep in mind future replicability, alongside understanding and readability.
• Follow checklists, and field- and journal-specific guidelines.
• Consider a commitment to rigorous and transparent science a personal responsibility, and not just adhering to journal guidelines.
• Establish whether there are persistent identifiers for any research resources you use that can be specifically cited in your methods section.
• Deposit your laboratory protocols in Protocols.io, establishing a permanent link to them. You can update your protocols later if you improve on them, as can future scientists who follow your protocols.
• Consider visual aids like flow-diagrams, lists, to help with reading other sections of the paper.
• Be specific about all decisions made during the experiments that someone reproducing your work would need to know.

Don’t

• Summarize or abbreviate methods without giving full details in a discoverable supplemental section.
• Presume you will always be able to remember how you performed the experiments, or have access to private or institutional notebooks and resources.
• Attempt to hide constraints or non-optimal decisions you had to make–transparency is the key to ensuring the credibility of your research.
• How to Write a Great Title
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Materials and methods

The study’s methods are one of the most important parts used to judge the overall quality of the paper. In addition the Methods section should give readers enough information so that they can repeat the experiments. Reviewers should look for potential sources of bias in the way the study was designed and carried out, and for places where more explanation is needed.

The specific types of information in a Methods section will vary from field to field and from study to study. However, some general rules for Methods sections are:

• It should be clear from the Methods section how all of the data in the Results section were obtained.
• The study system should be clearly described. In medicine, for example, researchers need to specify the number of study subjects; how, when, and where the subjects were recruited, and that the study obtained appropriate ‘informed consent’ documents; and what criteria subjects had to meet to be included in the study.
• In most cases, the experiments should include appropriate controls or comparators. The conditions of the controls should be specified.
• The outcomes of the study should be defined, and the outcome measures should be objectively validated.
• The methods used to analyze the data must be statistically sound.
• For qualitative studies, an established qualitative research method (e.g. grounded theory is often used in sociology) must be used as appropriate for the study question.
• If the authors used a technique from a published study, they should include a citation and a summary of the procedure in the text. The method also needs to be appropriate to the present experiment.
• All materials and instruments should be identified, including the supplier’s name and location. For example, “Tests were conducted with a Vulcanizer 2.0 (XYZ Instruments, Mumbai, India).”
• The Methods section should not have information that belongs in another section (such as the Introduction or Results).

You may suggest if additional experiments would greatly improve the quality of the manuscript. Your suggestions should be in line with the study’s aims. Remember that almost any study could be strengthened by further experiments, so only suggest further work if you believe that the manuscript is not publishable without it.

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Writing the materials and methods

Affiliation.

• 1 Department of Biomedical Imaging, Biomedical Imaging and Interventional Journal, University of Malaya, Kuala Lumpur, Malaysia. [email protected]
• PMID: 19037549

When writing scientific papers to share their research findings with their peers, it is not enough for researchers to just communicate the results of their study; it is equally important to explain the process by which they arrived at their results, so that the study can be replicated to validate the observations. The materials and methods section is used to describe the experimental design and provide sufficient details so that a competent colleague can repeat the experiment. A good materials and methods section will enable readers to evaluate the research performed and replicate the study, if necessary.

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Home » Research Paper – Structure, Examples and Writing Guide

Research Paper – Structure, Examples and Writing Guide

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Research Paper

Definition:

Research Paper is a written document that presents the author’s original research, analysis, and interpretation of a specific topic or issue.

It is typically based on Empirical Evidence, and may involve qualitative or quantitative research methods, or a combination of both. The purpose of a research paper is to contribute new knowledge or insights to a particular field of study, and to demonstrate the author’s understanding of the existing literature and theories related to the topic.

Structure of Research Paper

The structure of a research paper typically follows a standard format, consisting of several sections that convey specific information about the research study. The following is a detailed explanation of the structure of a research paper:

The title page contains the title of the paper, the name(s) of the author(s), and the affiliation(s) of the author(s). It also includes the date of submission and possibly, the name of the journal or conference where the paper is to be published.

The abstract is a brief summary of the research paper, typically ranging from 100 to 250 words. It should include the research question, the methods used, the key findings, and the implications of the results. The abstract should be written in a concise and clear manner to allow readers to quickly grasp the essence of the research.

Introduction

The introduction section of a research paper provides background information about the research problem, the research question, and the research objectives. It also outlines the significance of the research, the research gap that it aims to fill, and the approach taken to address the research question. Finally, the introduction section ends with a clear statement of the research hypothesis or research question.

Literature Review

The literature review section of a research paper provides an overview of the existing literature on the topic of study. It includes a critical analysis and synthesis of the literature, highlighting the key concepts, themes, and debates. The literature review should also demonstrate the research gap and how the current study seeks to address it.

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.

The results section presents the findings of the research, using tables, graphs, and figures to illustrate the data. The findings should be presented in a clear and concise manner, with reference to the research question and hypothesis.

The discussion section of a research paper interprets the findings and discusses their implications for the research question, the literature review, and the field of study. It should also address the limitations of the study and suggest future research directions.

The conclusion section summarizes the main findings of the study, restates the research question and hypothesis, and provides a final reflection on the significance of the research.

The references section provides a list of all the sources cited in the paper, following a specific citation style such as APA, MLA or Chicago.

How to Write Research Paper

You can write Research Paper by the following guide:

• Choose a Topic: The first step is to select a topic that interests you and is relevant to your field of study. Brainstorm ideas and narrow down to a research question that is specific and researchable.
• Conduct a Literature Review: The literature review helps you identify the gap in the existing research and provides a basis for your research question. It also helps you to develop a theoretical framework and research hypothesis.
• Develop a Thesis Statement : The thesis statement is the main argument of your research paper. It should be clear, concise and specific to your research question.
• Plan your Research: Develop a research plan that outlines the methods, data sources, and data analysis procedures. This will help you to collect and analyze data effectively.
• Collect and Analyze Data: Collect data using various methods such as surveys, interviews, observations, or experiments. Analyze data using statistical tools or other qualitative methods.
• Organize your Paper : Organize your paper into sections such as Introduction, Literature Review, Methods, Results, Discussion, and Conclusion. Ensure that each section is coherent and follows a logical flow.
• Write your Paper : Start by writing the introduction, followed by the literature review, methods, results, discussion, and conclusion. Ensure that your writing is clear, concise, and follows the required formatting and citation styles.
• Edit and Proofread your Paper: Review your paper for grammar and spelling errors, and ensure that it is well-structured and easy to read. Ask someone else to review your paper to get feedback and suggestions for improvement.
• Cite your Sources: Ensure that you properly cite all sources used in your research paper. This is essential for giving credit to the original authors and avoiding plagiarism.

Research Paper Example

Note : The below example research paper is for illustrative purposes only and is not an actual research paper. Actual research papers may have different structures, contents, and formats depending on the field of study, research question, data collection and analysis methods, and other factors. Students should always consult with their professors or supervisors for specific guidelines and expectations for their research papers.

Research Paper Example sample for Students:

Title: The Impact of Social Media on Mental Health among Young Adults

Abstract: This study aims to investigate the impact of social media use on the mental health of young adults. A literature review was conducted to examine the existing research on the topic. A survey was then administered to 200 university students to collect data on their social media use, mental health status, and perceived impact of social media on their mental health. The results showed that social media use is positively associated with depression, anxiety, and stress. The study also found that social comparison, cyberbullying, and FOMO (Fear of Missing Out) are significant predictors of mental health problems among young adults.

Introduction: Social media has become an integral part of modern life, particularly among young adults. While social media has many benefits, including increased communication and social connectivity, it has also been associated with negative outcomes, such as addiction, cyberbullying, and mental health problems. This study aims to investigate the impact of social media use on the mental health of young adults.

Literature Review: The literature review highlights the existing research on the impact of social media use on mental health. The review shows that social media use is associated with depression, anxiety, stress, and other mental health problems. The review also identifies the factors that contribute to the negative impact of social media, including social comparison, cyberbullying, and FOMO.

Methods : A survey was administered to 200 university students to collect data on their social media use, mental health status, and perceived impact of social media on their mental health. The survey included questions on social media use, mental health status (measured using the DASS-21), and perceived impact of social media on their mental health. Data were analyzed using descriptive statistics and regression analysis.

Results : The results showed that social media use is positively associated with depression, anxiety, and stress. The study also found that social comparison, cyberbullying, and FOMO are significant predictors of mental health problems among young adults.

Discussion : The study’s findings suggest that social media use has a negative impact on the mental health of young adults. The study highlights the need for interventions that address the factors contributing to the negative impact of social media, such as social comparison, cyberbullying, and FOMO.

Conclusion : In conclusion, social media use has a significant impact on the mental health of young adults. The study’s findings underscore the need for interventions that promote healthy social media use and address the negative outcomes associated with social media use. Future research can explore the effectiveness of interventions aimed at reducing the negative impact of social media on mental health. Additionally, longitudinal studies can investigate the long-term effects of social media use on mental health.

Limitations : The study has some limitations, including the use of self-report measures and a cross-sectional design. The use of self-report measures may result in biased responses, and a cross-sectional design limits the ability to establish causality.

Implications: The study’s findings have implications for mental health professionals, educators, and policymakers. Mental health professionals can use the findings to develop interventions that address the negative impact of social media use on mental health. Educators can incorporate social media literacy into their curriculum to promote healthy social media use among young adults. Policymakers can use the findings to develop policies that protect young adults from the negative outcomes associated with social media use.

References :

• Twenge, J. M., & Campbell, W. K. (2019). Associations between screen time and lower psychological well-being among children and adolescents: Evidence from a population-based study. Preventive medicine reports, 15, 100918.
• Primack, B. A., Shensa, A., Escobar-Viera, C. G., Barrett, E. L., Sidani, J. E., Colditz, J. B., … & James, A. E. (2017). Use of multiple social media platforms and symptoms of depression and anxiety: A nationally-representative study among US young adults. Computers in Human Behavior, 69, 1-9.
• Van der Meer, T. G., & Verhoeven, J. W. (2017). Social media and its impact on academic performance of students. Journal of Information Technology Education: Research, 16, 383-398.

Appendix : The survey used in this study is provided below.

Social Media and Mental Health Survey

• How often do you use social media per day?
• Less than 30 minutes
• 30 minutes to 1 hour
• 1 to 2 hours
• 2 to 4 hours
• More than 4 hours
• Which social media platforms do you use?
• Others (Please specify)
• How often do you experience the following on social media?
• Social comparison (comparing yourself to others)
• Cyberbullying
• Fear of Missing Out (FOMO)
• Have you ever experienced any of the following mental health problems in the past month?
• Do you think social media use has a positive or negative impact on your mental health?
• Very positive
• Somewhat positive
• Somewhat negative
• Very negative
• In your opinion, which factors contribute to the negative impact of social media on mental health?
• Social comparison
• In your opinion, what interventions could be effective in reducing the negative impact of social media on mental health?
• Education on healthy social media use
• Counseling for mental health problems caused by social media
• Social media detox programs
• Regulation of social media use

Thank you for your participation!

Applications of Research Paper

Research papers have several applications in various fields, including:

• Advancing knowledge: Research papers contribute to the advancement of knowledge by generating new insights, theories, and findings that can inform future research and practice. They help to answer important questions, clarify existing knowledge, and identify areas that require further investigation.
• Informing policy: Research papers can inform policy decisions by providing evidence-based recommendations for policymakers. They can help to identify gaps in current policies, evaluate the effectiveness of interventions, and inform the development of new policies and regulations.
• Improving practice: Research papers can improve practice by providing evidence-based guidance for professionals in various fields, including medicine, education, business, and psychology. They can inform the development of best practices, guidelines, and standards of care that can improve outcomes for individuals and organizations.
• Educating students : Research papers are often used as teaching tools in universities and colleges to educate students about research methods, data analysis, and academic writing. They help students to develop critical thinking skills, research skills, and communication skills that are essential for success in many careers.
• Fostering collaboration: Research papers can foster collaboration among researchers, practitioners, and policymakers by providing a platform for sharing knowledge and ideas. They can facilitate interdisciplinary collaborations and partnerships that can lead to innovative solutions to complex problems.

When to Write Research Paper

Research papers are typically written when a person has completed a research project or when they have conducted a study and have obtained data or findings that they want to share with the academic or professional community. Research papers are usually written in academic settings, such as universities, but they can also be written in professional settings, such as research organizations, government agencies, or private companies.

Here are some common situations where a person might need to write a research paper:

• For academic purposes: Students in universities and colleges are often required to write research papers as part of their coursework, particularly in the social sciences, natural sciences, and humanities. Writing research papers helps students to develop research skills, critical thinking skills, and academic writing skills.
• For publication: Researchers often write research papers to publish their findings in academic journals or to present their work at academic conferences. Publishing research papers is an important way to disseminate research findings to the academic community and to establish oneself as an expert in a particular field.
• To inform policy or practice : Researchers may write research papers to inform policy decisions or to improve practice in various fields. Research findings can be used to inform the development of policies, guidelines, and best practices that can improve outcomes for individuals and organizations.
• To share new insights or ideas: Researchers may write research papers to share new insights or ideas with the academic or professional community. They may present new theories, propose new research methods, or challenge existing paradigms in their field.

Purpose of Research Paper

The purpose of a research paper is to present the results of a study or investigation in a clear, concise, and structured manner. Research papers are written to communicate new knowledge, ideas, or findings to a specific audience, such as researchers, scholars, practitioners, or policymakers. The primary purposes of a research paper are:

• To contribute to the body of knowledge : Research papers aim to add new knowledge or insights to a particular field or discipline. They do this by reporting the results of empirical studies, reviewing and synthesizing existing literature, proposing new theories, or providing new perspectives on a topic.
• To inform or persuade: Research papers are written to inform or persuade the reader about a particular issue, topic, or phenomenon. They present evidence and arguments to support their claims and seek to persuade the reader of the validity of their findings or recommendations.
• To advance the field: Research papers seek to advance the field or discipline by identifying gaps in knowledge, proposing new research questions or approaches, or challenging existing assumptions or paradigms. They aim to contribute to ongoing debates and discussions within a field and to stimulate further research and inquiry.
• To demonstrate research skills: Research papers demonstrate the author’s research skills, including their ability to design and conduct a study, collect and analyze data, and interpret and communicate findings. They also demonstrate the author’s ability to critically evaluate existing literature, synthesize information from multiple sources, and write in a clear and structured manner.

Characteristics of Research Paper

Research papers have several characteristics that distinguish them from other forms of academic or professional writing. Here are some common characteristics of research papers:

• Evidence-based: Research papers are based on empirical evidence, which is collected through rigorous research methods such as experiments, surveys, observations, or interviews. They rely on objective data and facts to support their claims and conclusions.
• Structured and organized: Research papers have a clear and logical structure, with sections such as introduction, literature review, methods, results, discussion, and conclusion. They are organized in a way that helps the reader to follow the argument and understand the findings.
• Formal and objective: Research papers are written in a formal and objective tone, with an emphasis on clarity, precision, and accuracy. They avoid subjective language or personal opinions and instead rely on objective data and analysis to support their arguments.
• Citations and references: Research papers include citations and references to acknowledge the sources of information and ideas used in the paper. They use a specific citation style, such as APA, MLA, or Chicago, to ensure consistency and accuracy.
• Peer-reviewed: Research papers are often peer-reviewed, which means they are evaluated by other experts in the field before they are published. Peer-review ensures that the research is of high quality, meets ethical standards, and contributes to the advancement of knowledge in the field.
• Objective and unbiased: Research papers strive to be objective and unbiased in their presentation of the findings. They avoid personal biases or preconceptions and instead rely on the data and analysis to draw conclusions.

Advantages of Research Paper

Research papers have many advantages, both for the individual researcher and for the broader academic and professional community. Here are some advantages of research papers:

• Contribution to knowledge: Research papers contribute to the body of knowledge in a particular field or discipline. They add new information, insights, and perspectives to existing literature and help advance the understanding of a particular phenomenon or issue.
• Opportunity for intellectual growth: Research papers provide an opportunity for intellectual growth for the researcher. They require critical thinking, problem-solving, and creativity, which can help develop the researcher’s skills and knowledge.
• Career advancement: Research papers can help advance the researcher’s career by demonstrating their expertise and contributions to the field. They can also lead to new research opportunities, collaborations, and funding.
• Academic recognition: Research papers can lead to academic recognition in the form of awards, grants, or invitations to speak at conferences or events. They can also contribute to the researcher’s reputation and standing in the field.
• Impact on policy and practice: Research papers can have a significant impact on policy and practice. They can inform policy decisions, guide practice, and lead to changes in laws, regulations, or procedures.
• Advancement of society: Research papers can contribute to the advancement of society by addressing important issues, identifying solutions to problems, and promoting social justice and equality.

Limitations of Research Paper

Research papers also have some limitations that should be considered when interpreting their findings or implications. Here are some common limitations of research papers:

• Limited generalizability: Research findings may not be generalizable to other populations, settings, or contexts. Studies often use specific samples or conditions that may not reflect the broader population or real-world situations.
• Potential for bias : Research papers may be biased due to factors such as sample selection, measurement errors, or researcher biases. It is important to evaluate the quality of the research design and methods used to ensure that the findings are valid and reliable.
• Ethical concerns: Research papers may raise ethical concerns, such as the use of vulnerable populations or invasive procedures. Researchers must adhere to ethical guidelines and obtain informed consent from participants to ensure that the research is conducted in a responsible and respectful manner.
• Limitations of methodology: Research papers may be limited by the methodology used to collect and analyze data. For example, certain research methods may not capture the complexity or nuance of a particular phenomenon, or may not be appropriate for certain research questions.
• Publication bias: Research papers may be subject to publication bias, where positive or significant findings are more likely to be published than negative or non-significant findings. This can skew the overall findings of a particular area of research.
• Time and resource constraints: Research papers may be limited by time and resource constraints, which can affect the quality and scope of the research. Researchers may not have access to certain data or resources, or may be unable to conduct long-term studies due to practical limitations.

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Saul Mcleod, PhD

Editor-in-Chief for Simply Psychology

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

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

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Associate Editor for Simply Psychology

BSc (Hons) Psychology, MSc Psychology of Education

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

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In psychology, a lab report outlines a study’s objectives, methods, results, discussion, and conclusions, ensuring clarity and adherence to APA (or relevant) formatting guidelines.

A typical lab report would include the following sections: title, abstract, introduction, method, results, and discussion.

The title page, abstract, references, and appendices are started on separate pages (subsections from the main body of the report are not). Use double-line spacing of text, font size 12, and include page numbers.

The report should have a thread of arguments linking the prediction in the introduction to the content of the discussion.

This must indicate what the study is about. It must include the variables under investigation. It should not be written as a question.

Title pages should be formatted in APA style .

The abstract provides a concise and comprehensive summary of a research report. Your style should be brief but not use note form. Look at examples in journal articles . It should aim to explain very briefly (about 150 words) the following:

• Start with a one/two sentence summary, providing the aim and rationale for the study.
• Describe participants and setting: who, when, where, how many, and what groups?
• Describe the method: what design, what experimental treatment, what questionnaires, surveys, or tests were used.
• Describe the major findings, including a mention of the statistics used and the significance levels, or simply one sentence summing up the outcome.
• The final sentence(s) outline the study’s “contribution to knowledge” within the literature. What does it all mean? Mention the implications of your findings if appropriate.

The abstract comes at the beginning of your report but is written at the end (as it summarises information from all the other sections of the report).

Introduction

The purpose of the introduction is to explain where your hypothesis comes from (i.e., it should provide a rationale for your research study).

Ideally, the introduction should have a funnel structure: Start broad and then become more specific. The aims should not appear out of thin air; the preceding review of psychological literature should lead logically into the aims and hypotheses.

• Start with general theory, briefly introducing the topic. Define the important key terms.
• Explain the theoretical framework.
• Summarise and synthesize previous studies – What was the purpose? Who were the participants? What did they do? What did they find? What do these results mean? How do the results relate to the theoretical framework?
• Rationale: How does the current study address a gap in the literature? Perhaps it overcomes a limitation of previous research.
• Aims and hypothesis. Write a paragraph explaining what you plan to investigate and make a clear and concise prediction regarding the results you expect to find.

There should be a logical progression of ideas that aids the flow of the report. This means the studies outlined should lead logically to your aims and hypotheses.

Do be concise and selective, and avoid the temptation to include anything in case it is relevant (i.e., don’t write a shopping list of studies).

USE THE FOLLOWING SUBHEADINGS:

Participants

• How many participants were recruited?
• Say how you obtained your sample (e.g., opportunity sample).
• Give relevant demographic details (e.g., gender, ethnicity, age range, mean age, and standard deviation).
• State the experimental design .
• What were the independent and dependent variables ? Make sure the independent variable is labeled and name the different conditions/levels.
• For example, if gender is the independent variable label, then male and female are the levels/conditions/groups.
• How were the IV and DV operationalized?
• Identify any controls used, e.g., counterbalancing and control of extraneous variables.
• List all the materials and measures (e.g., what was the title of the questionnaire? Was it adapted from a study?).
• You do not need to include wholesale replication of materials – instead, include a ‘sensible’ (illustrate) level of detail. For example, give examples of questionnaire items.
• Include the reliability (e.g., alpha values) for the measure(s).
• Describe the precise procedure you followed when conducting your research, i.e., exactly what you did.
• Describe in sufficient detail to allow for replication of findings.
• Be concise in your description and omit extraneous/trivial details, e.g., you don’t need to include details regarding instructions, debrief, record sheets, etc.
• Assume the reader has no knowledge of what you did and ensure that he/she can replicate (i.e., copy) your study exactly by what you write in this section.
• Write in the past tense.
• Don’t justify or explain in the Method (e.g., why you chose a particular sampling method); just report what you did.
• Only give enough detail for someone to replicate the experiment – be concise in your writing.
• The results section of a paper usually presents descriptive statistics followed by inferential statistics.
• Report the means, standard deviations, and 95% confidence intervals (CIs) for each IV level. If you have four to 20 numbers to present, a well-presented table is best, APA style.
• Name the statistical test being used.
• Report appropriate statistics (e.g., t-scores, p values ).
• Report the magnitude (e.g., are the results significant or not?) as well as the direction of the results (e.g., which group performed better?).
• It is optional to report the effect size (this does not appear on the SPSS output).
• Avoid interpreting the results (save this for the discussion).
• Make sure the results are presented clearly and concisely. A table can be used to display descriptive statistics if this makes the data easier to understand.
• DO NOT include any raw data.
• Follow APA style.

Use APA Style

• Numbers reported to 2 d.p. (incl. 0 before the decimal if 1.00, e.g., “0.51”). The exceptions to this rule: Numbers which can never exceed 1.0 (e.g., p -values, r-values): report to 3 d.p. and do not include 0 before the decimal place, e.g., “.001”.
• Percentages and degrees of freedom: report as whole numbers.
• Statistical symbols that are not Greek letters should be italicized (e.g., M , SD , t , X 2 , F , p , d ).
• Include spaces on either side of the equals sign.
• When reporting 95%, CIs (confidence intervals), upper and lower limits are given inside square brackets, e.g., “95% CI [73.37, 102.23]”
• Outline your findings in plain English (avoid statistical jargon) and relate your results to your hypothesis, e.g., is it supported or rejected?
• Compare your results to background materials from the introduction section. Are your results similar or different? Discuss why/why not.
• How confident can we be in the results? Acknowledge limitations, but only if they can explain the result obtained. If the study has found a reliable effect, be very careful suggesting limitations as you are doubting your results. Unless you can think of any c onfounding variable that can explain the results instead of the IV, it would be advisable to leave the section out.
• Suggest constructive ways to improve your study if appropriate.
• What are the implications of your findings? Say what your findings mean for how people behave in the real world.
• Suggest an idea for further research triggered by your study, something in the same area but not simply an improved version of yours. Perhaps you could base this on a limitation of your study.
• Concluding paragraph – Finish with a statement of your findings and the key points of the discussion (e.g., interpretation and implications) in no more than 3 or 4 sentences.

Reference Page

The reference section lists all the sources cited in the essay (alphabetically). It is not a bibliography (a list of the books you used).

In simple terms, every time you refer to a psychologist’s name (and date), you need to reference the original source of information.

If you have been using textbooks this is easy as the references are usually at the back of the book and you can just copy them down. If you have been using websites then you may have a problem as they might not provide a reference section for you to copy.

References need to be set out APA style :

Author, A. A. (year). Title of work . Location: Publisher.

Journal Articles

Author, A. A., Author, B. B., & Author, C. C. (year). Article title. Journal Title, volume number (issue number), page numbers

A simple way to write your reference section is to use Google scholar . Just type the name and date of the psychologist in the search box and click on the “cite” link.

Next, copy and paste the APA reference into the reference section of your essay.

Once again, remember that references need to be in alphabetical order according to surname.

Psychology Lab Report Example

Quantitative paper template.

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 ( https://doi.org/10.1037/xge0000729 ). Copyright 2020 by the American Psychological Association.

Qualitative paper template

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 ( https://doi.org/10.1037/ppm0000278 ). Copyright 2020 by the American Psychological Association.

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Crafting a comprehensive research paper can be daunting. Understanding diverse citation styles and various subject areas presents a challenge for many.

Without clear examples, students often feel lost and overwhelmed, unsure of how to start or which style fits their subject.

Explore our collection of expertly written research paper examples. We’ve covered various citation styles and a diverse range of subjects.

So, read on!

• 1. Research Paper Example for Different Formats
• 2. Examples for Different Research Paper Parts
• 3. Research Paper Examples for Different Fields
• 4. Research Paper Example Outline

Research Paper Example for Different Formats

Following a specific formatting style is essential while writing a research paper . Knowing the conventions and guidelines for each format can help you in creating a perfect paper. Here we have gathered examples of research paper for most commonly applied citation styles :

Social Media and Social Media Marketing: A Literature Review

APA Research Paper Example

APA (American Psychological Association) style is commonly used in social sciences, psychology, and education. This format is recognized for its clear and concise writing, emphasis on proper citations, and orderly presentation of ideas.

Here are some research paper examples in APA style:

Research Paper Example APA 7th Edition

Research Paper Example MLA

MLA (Modern Language Association) style is frequently employed in humanities disciplines, including literature, languages, and cultural studies. An MLA research paper might explore literature analysis, linguistic studies, or historical research within the humanities. 

Here is an example:

Found Voices: Carl Sagan

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• Published: 07 June 2024

Measures of fragmentation of rest activity patterns: mathematical properties and interpretability based on accelerometer real life data

• Ian Meneghel Danilevicz 1 ,
• Vincent Theodoor van Hees 2 ,
• Frank C. T. van der Heide 1 ,
• Louis Jacob 1 ,
• Benjamin Landré 1 ,
• Mohamed Amine Benadjaoud 3   na1 &
• Séverine Sabia 1 , 4   na1  

BMC Medical Research Methodology volume  24 , Article number:  132 ( 2024 ) Cite this article

Metrics details

Accelerometers, devices that measure body movements, have become valuable tools for studying the fragmentation of rest-activity patterns, a core circadian rhythm dimension, using metrics such as inter-daily stability (IS), intradaily variability (IV), transition probability (TP), and self-similarity parameter (named \(\alpha\) ). However, their use remains mainly empirical. Therefore, we investigated the mathematical properties and interpretability of rest-activity fragmentation metrics by providing mathematical proofs for the ranges of IS and IV, proposing maximum likelihood and Bayesian estimators for TP, introducing the activity balance index (ABI) metric, a transformation of \(\alpha\) , and describing distributions of these metrics in real-life setting. Analysis of accelerometer data from 2,859 individuals (age=60-83 years, 21.1% women) from the Whitehall II cohort (UK) shows modest correlations between the metrics, except for ABI and \(\alpha\) . Sociodemographic (age, sex, education, employment status) and clinical (body mass index (BMI), and number of morbidities) factors were associated with these metrics, with differences observed according to metrics. For example, a difference of 5 units in BMI was associated with all metrics (differences ranging between -0.261 (95% CI -0.302, -0.220) to 0.228 (0.18, 0.268) for standardised TP rest to activity during the awake period and TP activity to rest during the awake period, respectively). These results reinforce the value of these rest-activity fragmentation metrics in epidemiological and clinical studies to examine their role for health. This paper expands on a set of methods that have previously demonstrated empirical value, improves the theoretical foundation for these methods, and evaluates their empirical use in a large dataset.

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Introduction

A large number of human behaviours and physiological functions follow a circadian rhythmicity, such as for examples sleep/wake cycles, body temperature, and hormonal levels [ 1 ]. Circadian regulation of these processes is critical to maintaining homeostasis; prolonged disruptions are detrimental to health [ 2 , 3 ], highlighting the importance of precise, scalable measures of human circadian rhythm (CR). Accelerometers, devices that record acceleration of the part of the body to which they are attached, have emerged as valuable tools to measure dimensions of CR based on movements in free-living conditions [ 4 , 5 ].

An important dimension of CR is the fragmentation of rest-activity patterns over several consecutive days [ 6 , 7 ]. Over time several metrics have been proposed to quantity the rest-activity fragmentation using accelerometry data. The first and now commonly used metrics are inter-daily stability (IS) and intradaily variability (IV). IS provides information on how constant the rest-activity pattern is between days and IV quantifies the fragmentation of activity pattern between consecutive hours over the observation period [ 6 , 8 ]. Later the transition probability (TP) has been proposed to measure the likelihood of transitioning from a state of rest to a state of activity, or vice versa [ 7 , 9 ]. Overall, the metrics described above are increasingly used in the context of fragmentation of rest-activity patterns but they can be used in different contexts involving series of dichotomous states, apart for IS and IV that are more specific to organisation of activity during a period of time. In parallel, the detrended fluctuation analysis (DFA) [ 10 ] initially used in genomics has been used to identify hidden patterns where activity fluctuations are used as proxy for rest-activity fragmentation [ 11 , 12 ]. In DFA, the self-similarity parameter, also known as the scaling exponent or \(\alpha\) , is a key metric for description of time series, such as stationary and non-stationary time series, random noise and fractal noise, among others [ 13 ].

Although metrics of rest-activity fragmentation are increasingly used in the literature, mathematical properties of these metrics and their interpretation have not been entirely described. First, although the range of IS in [0, 1] and IV in [0, 2] has been suggested by van Someren et al. (1999) [ 14 ], no proper mathematical proof is available, limiting confidence in interpretability, particularly for extreme values. Second, Lim et al. (2011) [ 7 ] and Di et al. (2017) [ 9 ] have proposed different estimations of TP, both based on heuristic estimators, limiting their mathematical properties as compared to estimators based on maximum likelihood (ML) or Bayesian inference. In addition, the properties of these two estimators have not been compared. Third, interpretation of DFA-derived metrics is not straightforward. Finally, to our knowledge, only one study has shown the correlation between IS, IV, TP (based on Lim et al. (2011) definition [ 7 ]) and DFA within a unique sample, older adults living in residential facilities, limiting generalisability of findings [ 7 ].

In order to overcome limitations of the current evidence on rest-activity fragmentation metrics, the present study aims to 1) provide mathematical proof of the range of IS and IV, 2) propose a ML estimator, the gold standard of estimation, and a Bayesian estimator, with good properties, for TP, and 3) propose a new metric, that is a transformation of DFA-derived self-similarity parameter, named activity balance index (ABI), that reflects how balanced is the activity over several days, and 4) describe these metrics using data from the population-based Whitehall II accelerometer sub-study.

Materials and methods

Preliminary definitions.

Rest-activity fragmentation metrics are calculated based on different time series derived from raw acceleration signals (Table  1 ). These time series differ as a function of units (eg minute or hour) and outcomes considered (acceleration, dichotomous state (rest/activity), or proportion of the epoch in a state). Here are some preliminary definitions of these time series.

Definition 1

For each individual, a discrete stochastic process representing the intensity of movement over a time period [0,  T ] is defined as \(\{X_t\}_{t \in T}\) , with \(X_t \in [0, \delta _x]\) , \(\delta _x<\infty\) , and t corresponds to an epoch. The observed time series is a vector represented as \(\varvec{x} = (x_1, \dots , x_T)'\) . In the case of accelerometry data, \(x_t\) corresponds to the acceleration recorded at the \(t^{th}\) epoch and \(\delta _x\) is the maximum measurable record for \(x_t\) .

Definition 2

For each individual, a second stochastic process representing the active ( a ) and rest ( r ) states is defined as \(\{Y_t\}_{t \in T}\) , with \(Y_t \in \{r,a\}\) , where \(Y_t = a\) if \(X_t > \delta _y\) , and \(\delta _y\) is the threshold which separates active and rest based on the amount of acceleration per epoch. The observed time series is a vector represented as \(\varvec{y} = (y_1, \dots , y_T)'\) .

Definition 3

For each individual, a third stochastic process representing the proportion of active states per hour is defined as \(\{Z_p\}_{p \in P}\) , with \(Z_p \in [0, 1]\) , where \(Z_p = \delta _z^{-1}\sum \nolimits _{t=1}^{\delta _z} I(y_{t + \delta _z(p-1)}=a)\) , \(I(\cdot )\) is an indicator function equal to one if the condition is true and zero otherwise, \(\delta _z\) is the number of epochs which build 1 hour (eg if one epoch corresponds to 1 minute then \(\delta _z = 60\) ), p corresponds to a period of 1 hour, and P is the total number of hours during the period [0,  T ]. The observed time series is a vector represented as \(\varvec{z} = (z_1, \dots , z_P)'\) .

The Whitehall II study is an ongoing prospective cohort study established in 1985-1988 among 10308 British civil servants with clinical examinations every four-five years since inception. A written informed consent for participation was obtained at each contact. Research ethics approval was obtained from the University College London ethics committee (latest reference number 85/0938). An accelerometer measure was added to the 2012-2013 wave of data collection (age range 60 to 83 years) for participants seen at the London clinic and those living in the south-eastern regions of England who underwent clinical examination at home. Participants were requested to wear a tri-axial accelerometer (GENEActiv Original; Activinsights Ltd, Kimbolton, UK) on their non-dominant arm for nine consecutive 24-hour days. Accelerometer data, sampled at 85.7Hz and expressed relative to gravity ( \(1g = 9.81m/s^2\) ), were processed using GGIR v2.9-0 [ 15 ]. The Euclidean norm minus one (ENMO) of raw acceleration was calculated and corrected for calibration error and non-wear time. These acceleration values were averaged over 60-second epochs and we used a 40 m g cut-point to differentiate between rest and active periods as previously done in studies using wrist-worn raw acceleration devices [ 16 , 17 ]. This cut-point was proposed in a study to differentiate between inactive periods and activities of light or moderate-to-vigorous intensities where adult participants undertook series of activities in a laboratory and mimic postures and behaviours from free-living conditions [ 18 ]. This cut-point is in agreement with a more recent study among older adults that showed good classification accuracy based on oxygen consumption during nine laboratory-based activities of daily living [ 19 ].

Waking periods (ie, periods between waking and sleep onset) for each day were identified using an algorithm for sleep detection based on wrist movement along with self-reported sleep onset and waking time using a sleep diary. This algorithm has been previously described and evaluated against polysomnography data [ 20 ]. Data from waking onset on day 2 to same time on day 8 were retained, resulting in seven days of data. Non-wear time was detected using an algorithm that has been previously described [ 21 ], and for the present study 2859 participants who wore the accelerometer over the full seven consecutive days were included in analyses.

For each individual, three time series were considered: the time series corresponding to the 1-minute epoch acceleration over seven days \(x_t\) , \(t = 1, \dots , 10080\) (the number of minutes over seven days), see Definition  1 ; the time series corresponding to the 1-minute epoch active state over seven days, \(y_t\) , \(t = 1, \dots , 10080\) , see Definition  2 ; and the time series corresponding to 1-hour proportion of active state over seven days, \(z_p\) , \(p = 1, \dots , 168\) (the number of hours over seven days), see Definition  3 . A summary of the three considered time series is available in Table  1 , and an illustration is displayed in Fig.  1 . For illustrative purposes, ten participant profiles were selected to highlight differences in metrics observed in real-life situations (six of them are displayed in Figs.  4 , 5 , 6 , 7 , 8 , and 9 and four in the Supplementary material (figures S2-S5)). They were chosen based on their lowest or highest value in the metrics.

Example of three time series from the same individual

Measures of socio-demographic (age, sex, education) and health-related (body mass index (BMI), prevalent morbidities) factors were collected along with the accelerometer data in 2012-2013. Education was categorised as zero if the individual has less than secondary school education and one otherwise. BMI was based on measured weight and height (kg/m \(^2\) ), and the number of prevalent morbidities was assessed using clinical examinations in the study and linkage to electronic health records and includes coronary heart disease, stroke, heart failure.

A total of 4,880 individuals were invited to participate to the Whitehall accelerometer sub-study. Out of these, 4,282 agreed to wear the accelerometer and had no contraindications (allergy to plastic or travelling abroad). Among them, 2,859 individuals had complete data without any non-wear period for a continuous period of seven days corresponding to a total of 10,080 one-minute epochs. The mean age of the participants was 69.2 years, with a standard deviation (SD) of 5.7 years. A total of 602 were women (21.1%), 1170 (40.9%) had less than secondary school education level, 495 (17.3%) were currently employed, and 1140 (39.9%) had at least one morbidity. The mean body mass index (BMI) in the study sample was 26.7 (SD=4.3) kg/m \(^2\) .

Inter-daily stability and intradaily variability

Properties of is and iv.

IS measures how constant the rest-activity pattern is between days [ 8 ]. Considering that we measure H hours over D days, we have a total number of hours \(P = H \times D\) over a full observation period. For IS, it is useful to organize the vector \(\varvec{z}\) from Definition  3 in a matrix form as

where \(z_{d,h}\) is an element for the \(d^{th}\) line and \(h^{th}\) column, where \(d = 1,\dots , D\) and \(h = 1,\dots , H\) . IS is computed as

where \(\bar{z}_h = \frac{1}{D} \sum \nolimits _{d=1}^{D} z_{d,h}\) is the hour mean over the D days of measurement, and \(\bar{z} = \frac{1}{P} \sum \nolimits _{p=1}^{P} z_p\) is the general mean over the full observed period.

IV represents the fragmentation of the rest-activity pattern over a long period, it measures the variability between consecutive hours (Fig.  1 c) [ 8 ]. IV is calculated as

Some mild conditions should be established to derive the properties of IS and IV metrics. They are:

\(Z_p\) follows an autoregressive model of order 1 (AR(1) model) as

where \(\mu\) is the mean of the stochastic process, \(\phi\) is a fixed but unknown parameter with \(|\phi |<1\) , \(\epsilon _p\) is a Gaussian noise.

\(0 \le \phi < 1\) and \(P \rightarrow \infty\) .

The assumption (A1) is required to define the IV range, because we need to determine the relationship between \(Z_p\) and \(Z_{p-1}\) , and the AR(1) model is a very simple and flexible model, which can fit several different real situations. Although, we assume a stationary process, see unit root conditions in Dickey and Fuller (1979) [ 22 ]. The assumption (A2) is imposed to guarantee a positive auto-correlation \(0 \le \phi\) , and a long period of observation, P , of the time series.

Given a stochastic process \(\{Z_p\}_{p \in P}\) , \(\text {IS}(\varvec{z}) \in [0,1]\) .

Given a stochastic process \(\{Z_p\}_{p \in P}\) and under assumption (A1), \(\text {IV}(\varvec{z}) \in [0,\infty )\) .

Given a stochastic process \(\{Z_p\}_{p \in P}\) and under assumptions (A1) and (A2), \(\lim _{P \rightarrow \infty }(\text {IV}(\varvec{z})) \in [0,2]\) .

The proofs of these theorems are provided in the Supplementary material (Section 1).

Interpretation of IS and IV

In the demonstration of Theorem 1 (Supplementary material - Section 1), we showed that a higher value of IS reflects a rest-active pattern that is more constant between days, see (Table  2 ).

In the demonstration of Theorem 2 (Supplementary material - Section 1), we showed that 1) if \(\phi\) goes to one (perfect autocorrelation), then IV goes to zero, reflecting a low rest-activity fragmentation between hours; 2) if \(\phi\) goes to zero (uncorrelated random noise), then IV goes to two, representing a high rest-activity fragmentation between hours; 3) in some specific cases, IV can be greater than two, this can occur when the sample size P is too small, or \(\phi < 0\) which may be seen in ultradian rhythm, which means that the rhythm cycle lasts less than a day [ 14 ], or in the case of use of high frequency data [ 23 ]. These statements agree with the previous claims given by van Someren et al. (1999) about IS and IV [ 14 ]. Some authors use IV based on the \(\varvec{x}\) time series [ 24 , 25 , 26 ]. In that case, the present properties do not hold anymore as the assumptions (A1) and (A2) are verified exclusively for \(\varvec{z}\) .

• Transition probability

Properties of TP

The TP in dichotomous stochastic processes represents the probability of a state change given a period of time spent in a specific state. A formal characterization of TP of changes in rest/activity state is given in Definition  4 .

Definition 4

For each individual, given a stochastic process determined by Definition  2 the TP from r to a given an uninterrupted period of rest with length equal to s is

and the TP from a to r given an uninterrupted period of activity with length equal to s is

The two conditional probabilities from Definition  4 are proposed by Lim et al. (2011) [ 7 ]. The specific cases of \(s=1\) returns two probabilities proposed by Di et al. (2017) [ 9 ]. We aim to propose a ML estimator to TP because if the model assumptions are aligned, there is no better estimation than ML, being a gold standard. Although, if there is available knowledge, we can aggregate this information and build a Bayesian estimator that is even more accurate than ML. Beforehand, some notations need to be introduced for readability.

Definition 5

\(\varvec{r} = (r_1, \dots , r_{n_{r}})'\) is a \(n_{r}\) -vector that records the length of each consecutive bout of rest, where \(n_r\) is the number of bouts of rest \((n_r \le T)\) so that \(r_1\) is the length of the first bout of rest, \(r_2\) of the 2 \(^{nd}\) bout of the rest, and \(r_{n_r}\) the length of the last bout of rest. \(T_{r} = \sum \nolimits _{i=1}^{n_{r}}r_i\) is the total length of rest (in epochs unit), \(r_i \in \{1, \dots , S_r\}\) , \(S_r\) is the duration of the longest bout of rest.

Definition 6

\(\varvec{a} = (a_1, \dots , a_{n_{a}})'\) is a \(n_{a}\) -vector that records the length of each consecutive bout of activity, where \(n_a\) is the number of bouts of activity \((n_a \le T)\) . \(T_{a} = \sum \nolimits _{i=1}^{n_{a}}a_i = T -T_{r}\) is the total length of activity (in epochs unit), \(a_i \in \{1, \dots , S_a\}\) , \(S_a\) is the duration of the longest bout of activity.

Here are two assumptions:

The stochastic process \(\{Y_t\}_{t \in T}\) is stationary.

The stochastic process \(\{Y_t\}_{t \in T}\) has a finite memory equal to \(s \ge 1\) .

Given a stochastic process \(\{Y_t\}_{t \in T}\) , under assumptions (B1) and (B2), the ML estimators of \(\pi _{ra}(s)\) and \(\pi _{ar}(s)\) are \(\hat{\pi }_{ra}(s)_{ML} = \frac{\sum \nolimits _{i=1}^{n_{r}} I(r_i \ge s)-I(y_T=r)}{\sum \nolimits _{i=1}^{n_{r}}(r_i-s+1) I(r_i \ge s)-I(y_T=r)}\) and \(\hat{\pi }_{ar}(s)_{ML} = \frac{\sum \nolimits _{i=1}^{n_{a}} I(a_i \ge s)-I(y_T=a)}{\sum \nolimits _{i=1}^{n_{a}}(a_i-s+1) I(a_i \ge s)-I(y_T=a)}\) , for \(s=1,\dots ,S_r - 1\) , and \(s=1,\dots ,S_a - 1\) , respectively.

Corollary 1

Given a stochastic process \(\{Y_t\}_{t \in T}\) , under assumptions (B1) and (B2), the ML estimators of \(\pi _{ra}(1)\) and \(\pi _{ar}(1)\) are \(\hat{\pi }_{ra}(1)_{ML} = \frac{n_{r}-I(y_T=r)}{T_{r}-I(y_T=r)}\) and \(\hat{\pi }_{ar}(1)_{ML} = \frac{n_{a}-I(y_T=a)}{T_{a}-I(y_T=a)}\) .

Corollary 2

Given a stochastic process \(\{Y_t\}_{t \in T}\) , under assumptions (B1) and (B2), the Bayesian estimators of \(\pi _{ra}(1)\) and \(\pi _{ar}(1)\) are \(\hat{\pi }_{ra}(1)_{B} = \frac{n_{r}-I(y_T=r)+\lambda }{T_{r}-I(y_T=r)+\lambda }\) and \(\hat{\pi }_{ar}(1)_{B} = \frac{n_{a}-I(y_T=a)+\lambda }{T_{a}-I(y_T=a)+\lambda }\) , for any hyperparameter \(\lambda >0\) .

The proof of Theorem 4 is provided in Supplementary material - Section 1 using as a main argument the properties of a Bernoulli stochastic process [ 27 ]. Also the proof of Corollary  1 is given in Supplementary material - Section 1. The proof of the Corollary  2 is a direct application from Corollary  1 for a Binomial model. Then the Beta-Binomial posterior estimator is a well-known result ([ 28 ], page 104).

Corollary  1 makes evident the intuitive relation between the number of transitions per total time in a specific state, which is a gain in terms of interpretability. In the Bayesian estimator introduced in Corollary  2 , \(\lambda\) , present both in the numerator and denominator, is a pre-specified hyperparameter to the Beta prior distribution for the transition probability. This parameter allows the Bayesian estimator to always exist even if any of \(T_{r}\) or \(T_{a}\) is zero. If \(\lambda =1\) , corresponding to the Uniform distribution prior, we assume that in a sequence of nights there is at least one epoch of activity and in a sequence of days there is at least one epoch of rest. Other values might be explored such as \(\lambda =0.5\) corresponding to the Horseshoe prior [ 29 ], or \(\lambda =10^{-6}\) which returns a numerically insignificant difference between ML and Bayesian estimators. Larger values than one for \(\lambda\) may not be relevant in this context as they are likely to deviate too much from the ML estimators.

Even without any assumption about the stochastic process in terms of memory and stationary, some nonparametric measures are avaliable as the reciprocal average duration (RAD) of rest, \(\text {RAD}_r\) , and the RAD of activity, \(\text {RAD}_a\) , which are defined as

This metric appears in previous work [ 30 ], but it was used to approximate the target probabilities \(\pi _{ra}(1)\) and \(\pi _{ar}(1)\) [ 9 ]. If \(y_T = r\) , then \(\text {RAD}_{a} = \hat{\pi }_{ar}(1)_{ML}\) and \(\text {RAD}_{r} > \hat{\pi }_{ra}(1)_{ML}\) as \(T_{r} > n_{r}\) ; if \(y_T = a\) , then \(\text {RAD}_{r} = \hat{\pi }_{ra}(1)_{ML}\) and \(\text {RAD}_{a} > \hat{\pi }_{ar}(1)_{ML}\) as \(T_{a} > n_{a}\) .

Let us give a hypothetical example for a small sample size \(T=15\) as \(\varvec{y} = (a,a,a,r,r,a,r,a,a,a,r,r,a, r,r)'\) to illustrate the difference between \(\hat{\pi }_{ra}(1)_{ML}\) , \(\hat{\pi }_{ra}(1)_{B}\) and \(\text {RAD}_{r}\) , as well as \(\hat{\pi }_{ar}(1)_{ML}\) , \(\hat{\pi }_{ar}(1)_{B}\) and \(\text {RAD}_{a}\) , with hyperparameter \(\lambda =0.5\) . Here we have \(\varvec{r} = (2,1,2,2)'\) and \(\varvec{a} = (3,1,3,1)'\) , this corresponds to \(n_r=4\) , \(n_r-I(y_T=r)=3\) , \(n_a=4\) , \(n_a-I(y_T=a)=4\) , \(T_r=7\) , \(T_r-I(y_T=r)=6\) , \(T_a=8\) , \(T_a-I(y_T=a)=8\) . So we have three changes ( \(n_r-I(y_T=r)\) ) in six opportunities ( \(T_r-I(y_T=r)\) ) ie 50% of transitions from r to a by the ML estimator, the \(\text {RAD}_{r}\) inflates this result to 57% by adding a transition for the last observation, but actually we don’t know what would happen in \(y_{16}\) . From a to r , \(\text {RAD}_a\) and ML estimators are the same, and Bayesian estimator is also really close. For convenience, these values are available in Table  3 .

The conditional probabilities \(\pi _{ar}(1)\) and \(\pi _{ra}(1)\) are more convenient to interpret than \(\pi _{ar}(s)\) and \(\pi _{ra}(s)\) . In the aim of summarizing TP, Lim et al. (2011) proposed a bounded average calculated by LOWESS smoothing over a range of s values [ 7 ]. This method requires to determine the boundary of the s values for which there is not a straightforward method. In the application part of this paper, we chose \(s=1\) and partitioned the observed vector \(\varvec{y}\) in waking and sleep periods as described in Remark  2 .

We propose a Bayesian estimator that compared to ML or RAD, avoids to have values that cannot be computed in case of no time spent in a state (denominator null). For an epidemiological motivation, we split these metrics by wake and sleep windows (that is the period between waking and sleep onset (wake), and between sleep and next waking for the day to start (sleep), respectively), as

the TP from rest to active period during the waking window, and the TP from rest to active period during the sleep window, respectively, and

the TP from active to rest period during the waking window, and the TP from active to rest period during the sleep window, respectively, where \(\lambda \in (0,1]\) , \(n_{a, \texttt{w}}\) is the number of bouts of activity during the awake time, \(n_{a, \texttt{s}}\) is the number of bouts of activity during the sleep time, \(n_{r, \texttt{w}}\) is the number of bouts of rest during the awake time, \(n_{r, \texttt{s}}\) is the number of bouts of rest during the sleep time, \(T_{r, \texttt{w}}\) is the total rest time during the awake time, \(T_{r, \texttt{s}}\) is the total rest time during the sleep time, \(T_{a, \texttt{w}}\) is the total activity time during the awake time, and \(T_{a, \texttt{s}}\) is the total activity time during the sleep time.

Interpretation of TP

When using a small \(\lambda\) and a long period of observation, higher \(\text {TP}_{ra, \texttt{w}}\) corresponds to more transitions from rest to active periods during the awake window, reflecting a more fragmented pattern of rest, higher \(\text {TP}_{ar, \texttt{w}}\) corresponds to more transitions from active to rest periods during the awake window, denoting a more fragmented pattern of activity. A similar interpretation applies to the metrics defined during the sleep window (Table  2 ). In case of one state not being observed during a window as for example no activity at all during the sleep window, the TP exists and transition from this unobserved state to the observed state is equal to 1. This means that in case this person moves to this unobserved state, it is highly likely that he or she will return to the observed state quickly.

• Detrended fluctuation analysis

Introduction to DFA

The DFA is a powerful analytical tool for time series analysis initially proposed by Peng et al. (1994) to analyse long-term correlation of nucleotides [ 10 ]. More recently it has been used in the context of movement behaviour to quantity fractal fluctuations in activity over a range of time scales [ 12 , 31 ]. In practise, it aims to evaluate to which extent the activity pattern (in terms of temporal and structural properties) is similar at different time scales. Estimating the self-similarity parameter allows differentiating stationary and nonstationary stochastic processes and identifying white, pink (fractal), or brown noise patterns. These key properties might be hidden in complex time series, but DFA is a way to reveal them.

Let us consider a bounded stochastic process \(\{X_t\}_{t \in T}\) from Definition  1 . Take the accumulated signal with zero mean as

where \(\bar{x} = T^{-1}\sum \nolimits _{t=1}^{T}x_t\) . Divide \(\varvec{c} = (c_1, \dots , c_T)'\) in B nonoverlapping boxes of equal n -size as \(\varvec{c}_1 = (c_1, \dots , c_n)'\) , \(\varvec{c}_2 = (c_{n+1}, \dots , c_{2n})'\) , until \(\varvec{c}_B = (c_{(B-1)n+1}, \dots , c_{Bn})'\) . For each box, we fit a polynomial of order l , eg, the polynomial for the \(j^{th}\) box is fit using an ordinary least squares regression as

where \(t= (j-1)n+1, \dots , jn\) . In the application section of this paper, we restricted our analysis to \(l=1\) as in previous works [ 26 , 32 ]. In the Supplementary material (Section 3), we replicated the analysis using \(l=2\) for comparison. A polynomial order higher than two is not expected to change the results [ 33 ]. Note that \(\varvec{\beta }=(\beta _0, \dots , \beta _l)'\) is different to each \(j^{th}\) box and each n -size, consequently \(f_t(n)\) depends of t and n . To detrend the integrated time series, ie, remove the trend of \(c_t\) , we take the difference of each pair \(c_t\) and \(f_t(n)\) . For a given n -size box, the root mean square fluctuation is

Repeat the operation for a broad range of n -size boxes, eg, Mesquita et al. (2020) recommend taking a sample on the grid between \(4 \le n \le T/4\) [ 34 , 35 ]. The Fig.  2 displays the steps of DFA for two n -size boxes, the first with 60 minutes (Fig.  2 c) and the second with 30 minutes (Fig.  2 d).

Example of DFA procedure

Summary statistic for DFA and interpretation

Instead of displaying a function of F ( n ) for a grid of n , we can summarize this information by the self-similarity parameter. The root mean square fluctuation in ( 4 ) is proportional to the n -size, \(F(n) \propto n^\alpha\) , where \(\alpha\) is called the scaling exponent or self-similarity parameter, which is estimated using

where \(\epsilon _n\) follows an independent Gaussian error, \(\mu\) is an intercept, and an ordinary least squares regression (OLS) is used to calculate \(\hat{\alpha }\) .

The interpretation of \(\alpha\) is quite precise, but requires much mathematical jargon. Given a stochastic process as determined by Definition  1 , the self-similarity parameter belongs to the range \(0< \alpha <1\) for stationary stochastic processes, and \(1< \alpha <2\) for nonstationary as proofed by Løvsletten (2017) [ 36 ]. Some critical values of the scaling exponent are of distinct mathematical importance as \(\alpha =0.5\) means that the stochastic processes is white noise, \(\alpha =1\) is related to pink or fractal noise, \(\alpha =1.5\) is the case of a random walk [ 32 ].

Activity balance index: a new DFA-derived metric

Given previous empirical results, Hausdorff et al. (1996) hypothesized that many biological systems present a fractal nature, ie, \(\alpha =1\) [ 37 ]. A further hypothesis that healthy people presents fractal noise for heart and walking rates has been elaborated by Peng et al. (2000) [ 38 ]. In the context of activity behaviour, we have introduced a novel metric named activity balance index (ABI), that measures how the activity over the observed period is balanced, higher values reflect a more balanced pattern of activity. It is a transformation of \(\hat{\alpha }\) as

where \(\hat{\alpha } \in (0,2)\) . If \(\hat{\alpha }\) goes to one, then \(|\hat{\alpha }-1|\) goes to zero and \(\text {ABI}(\hat{\alpha })\) goes to one. On the other direction, as \(\hat{\alpha }\) goes to two or zero, which are the extremes for \(\alpha\) [ 36 ], \(|\hat{\alpha }-1|\) goes to one and \(\text {ABI}(\hat{\alpha })\) goes to 0.0006. The ABI has two advantages: it penalizes the scattering of \(\hat{\alpha }\) in both directions and spreads its values over a large range between (0.0006, 1] or (0, 1] for simplicity.

We introduced the ABI that focusses on the fractal noise nature of the signal to evaluate how the activity is balanced over the observation period. If fractal noise represents an optimum balance for activity behaviour, then healthy individuals would present higher values for their ABI metric than unhealthy people (Table  2 ). Both \(\hat{\alpha }\) and ABI are influenced by the choice of the epoch lengths, larger epoch values will naturally tend to smooth acceleration signal, implying lower chance of observing a fractal noise (that is \(\hat{\alpha }\) and ABI closer to one).

Strengths and limitations of IS, IV, TP and DFA

The strengths and limitations of rest-activity fragmentation metrics are summarized in Table  2 .

The metrics mentioned above rely on transitions between rest and active states and do not capture other dimensions of the circadian rhythm. These metrics can be used in complement to other circadian rhythm variables that capture different aspects of the rhythm such as timing or amplitude.

Figure  3 shows the distribution of IS, IV, TP, \(\hat{\alpha }\) and ABI in the total sample. All empirical ranges are within the theoretical ones proposed in Table  2 . For IV, two individuals have a value that exceeds two, these outliers correspond to two of the three individuals whose \(\hat{\phi }\) value is not within the [0, 1] interval, suggesting a minority of cases with ultradian rhythm in the dataset.

Boxplot of inter-daily stability (IS), intradaily variability (IV), estimated autocorrelation parameter of AR(1) model ( \(\hat{\phi }\) ), transition probability (TP) from activity to rest during the awake period ( \(\text {TP}_{ar,\texttt{w}}\) ), TP from activity to rest during the sleep period ( \(\text {TP}_{ar,\texttt{s}}\) ), TP from rest to activity during the awake period ( \(\text {TP}_{ra,\texttt{w}}\) ), TP from rest to activity during the sleep period ( \(\text {TP}_{ra,\texttt{s}}\) ), estimated self-similarity ( \(\hat{\alpha }\) ), and activity balance index (ABI)

When examining how rest-activity fragmentation metrics differ by sex (Table 4 ), we found that men have on average a less constant rest-activity pattern as denoted by smaller IS compared to women (0.529 vs 0.546, \(p=0.001\) ). During the day, men tend to transition less from rest to active periods while during the night men are more likely to transition from active to rest periods as indicated by lower \(\text {TP}_{ra,\texttt{w}}\) ( \(p<0.001\) ) and higher \(\text {TP}_{ar,\texttt{s}}\) ( \(p<0.001\) ) than in women. Finally, on average they tend to have a less balanced activity behaviour than women as shown by lower \(\hat{\alpha }\) ( \(p=0.022\) ) and ABI ( \(p<0.001\) ).

Fewer differences were observed as a function of age, although we found that older people tend to have a more fragmented rest-activity pattern (IV 1.039 vs 0.946 for age \(\ge\) 70 vs <70), to transition more from activity to rest during waking periods ( \(\text {TP}_{ar,\texttt{w}}\) 0.305 vs 0.273), and to transition less from rest to active periods during the day ( \(\text {TP}_{ra,\texttt{w}}\) 0.098 vs 0.109), but more during the night ( \(\text {TP}_{ra,\texttt{s}}\) 0.08 vs 0.007); all \(p<0.001\) .

Table 5 shows one fitted multivariate regression for each standardized rest-activity fragmentation metric. Being a woman, aged around 70 years old (see Figure S1 in Supplementary additional results for association with age), with lower educational level, not currently employed, having lower BMI and less prevalence morbidities were associated with a more constant rest-activity pattern (all \(p<0.05\) ). The same variables (except for sex) were associated with IV, but in the opposite direction, denoting a less fragmented rest-activity pattern. \(\text {TP}_{ar,\texttt{w}}\) was associated with all socio-demographic and health-related factors (except for sex and employment status), and \(\text {TP}_{ar,\texttt{s}}\) , in a complementary way, was only significantly associated with sex and employment status. Higher \(\text {TP}_{ra,\texttt{w}}\) was associated with being a woman, lower BMI and less morbidities while higher \(\text {TP}_{ra,\texttt{s}}\) was associated with higher BMI and more prevalent morbidities. Both \(\hat{\alpha }\) and ABI were associated with all socio-demographic (except education) and health-related factors.

Table 6 presents Pearson’s correlation coefficients between IS, IV, TPs, \(\hat{\alpha }\) , and ABI metrics. We observe one moderate correlation between \(\hat{\alpha }\) and ABI that is expected as ABI is a transformation of \(\hat{\alpha }\) . All the remaining correlations are considered fair or poor [ 39 ].

The sensitivity analysis on the impact of the l parameter for the DFA-derived metrics is presented in Supplementary material (Section 3). Although both \(\hat{\alpha }\) and ABI values for \(l=1\) and \(l=2\) were highly correlated ( \(|r| > 0.8\) ), associations with sociodemographic and health-related factors were more consistent when using \(l=1\) than \(l=2\) .

Figures 4 , 5 , 6 , 7 , 8 , and 9 show the time series processes of individuals with extreme IS, IV, TP, and DFA values. In footnotes, a short description of what characterized these time series is provided. More figures are available in the Supplementary material (Section 2, Figures S2 to S5).

The sedentary: this individual presents the highest \(\text {TP}_{ar,\texttt{w}}\) . Note that the black blocks in the non-blue region of figure ( b ) are short, ie, this individual has short bouts of activity

The active: this individual presents the lowest \(\text {TP}_{ar,\texttt{w}}\) . Note that the black blocks in the non-blue region of figure ( b ) are very long, ie, this individual has long bouts of activity

The good sleeper: this individual presents the lowest \(\text {TP}_{ra,\texttt{s}}\) and a high \(\text {TP}_{ar,\texttt{s}}\) . Note that the black (white) blocks in the blue region of figure ( b ) are very brief (long), ie, during the night this individual almost does not display activity

The insomniac: this individual presents the lowest \(\text {TP}_{ar,\texttt{s}}\) . Note some large black blocks in the blue region of figure ( b ), specially at the third and fifth sleep windows, ie, during the night this individual presents long periods of activity

The unbalanced rest-activity person, this individual presents the lowest IS, a high IV, both \(\hat{\alpha }\) and ABI low. Note the flat time series in figure ( c ) displays a weak rest-activity pattern and high rhythm fragmentation. Note that the time series in figure ( a ) seems very random (constant spikes without clear difference between day and night), denoting a stationary random noise, ie, low \(\hat{\alpha }\) and ABI

The balanced rest-activity person, this individual presents the highest IS, a low IV and a high ABI. Note the very regular waves in figure ( c ) denoting a high IS and low IV, ie, strong rest-activity pattern and low rhythm fragmentation. Note that the time series in figure ( a ) is very well balanced between smoothness and spikes, display a fractal noise and balanced motion, ie, \(\hat{\alpha }\) and ABI close to one

This study provides theoretical ranges and guidance on the interpretation of rest-activity fragmentation metrics. We extended previous research on TP [ 7 , 40 ] by proposing ML and Bayesian estimators for TP. We also proposed a transformation of DFA-derived self-similarity parameter, the ABI, to reflect the balance of activity behaviours over the observation period. This metric is complementary to the \(\alpha\) metric that ought to be used when interest is in characterising the stationarity of the activity pattern. Finally, using accelerometer data from around 2,859 individuals aged 60 to 83 years, we showed that most of the correlations between IS, IV, TP, and ABI were modest. We also found sociodemographic and health-related differences in some of the rest-activity fragmentation metrics but not all, highlighting the fact that they measure different features.

We proposed Bayesian estimators of TP to estimate the probability of change from rest to active period and reversely, defined separately during the awake (day) and the sleep (night) windows. We observed, as expected, a higher TP from activity to rest during the sleep window than during the awake window and, on the reverse, a higher TP from rest to activity during the awake window than during sleep window [ 41 ]. We applied these metrics to rest/activity states defined by a threshold of acceleration [ 17 , 18 ]. These metrics might also be relevant using methods that differentiate sleep and wake states instead of rest and activity states to evaluate the fragmentation of sleep during the night.

When comparing rest-activity fragmentation metrics using data from adults aged 60 to 83 years, we found low to moderate correlations among the variables( \(|r|<0.6\) ), except for \(\hat{\alpha }\) and ABI ( \(r=0.789\) ). Although calculated differently, these estimated correlations are in accordance with those found in the previous studies [ 7 , 25 , 26 , 42 , 43 , 44 ]. These modest correlations suggest that these metrics capture distinct features of individuals’ rest-activity patterns. The graphical analysis of the extreme cases of each metric (see Figs. 4 , 5 , 6 , 7 , 8 , and 9 and Figures S2 to S5 in Section 2 of the Supplementary material) displays several behaviour profiles: sedentary, active, good sleeper, insomniac, (un)balanced rest-activity person, tireless person, and a person with ultradian rhythm. We examined the robustness of our findings regarding the parameter l for the DFA-derived metrics ( \(\alpha\) and ABI) and found that although values for \(l=1\) and \(l=2\) were highly correlated, associations with sociodemographic and health-related factors were more consistent when using \(l=1\) , as previously done in other studies [ 33 , 45 ].

Few studies have examined factors associated with specific rest-activity fragmentation metrics among older adults using data from the Rush Memory and Aging Project [ 7 , 31 , 43 ], the National Health and Nutrition Examination Survey (NHANES) [ 46 , 47 ], and the Rotterdam study [ 42 ]. In these studies, women tended to have higher IS [ 42 , 43 , 47 ] and lower IV [ 42 , 43 ], higher TP from rest to active state and lower TP from activity to rest [ 7 ], while women were found to have a higher \(\alpha\) in the NHANES [ 46 ] but not in the Rush Memory and Aging Project [ 31 ]. Overall, older age was associated with higher IS [ 42 , 43 ], higher IV [ 42 , 43 , 47 ], higher TPs [ 7 ] and lower \(\alpha\) [ 31 ], although not systematically [ 47 ]. In the Rotterdam study, being in employment was associated with lower IS and IV [ 42 ] while we found the reverse for IV. Health-related factors such as higher BMI and prevalence of chronic diseases were consistently found associated with lower IS [ 42 , 47 , 48 ], higher IV [ 42 , 47 , 48 ], and higher TP from activity to rest [ 7 ], as in the present study. Differences in some of the reported associations might arise from differences in the methods to derive the different metrics and in the sample characteristics. Overall, there is evidence of differences in the rest-activity fragmentation metrics by sociodemographic and health-related factors, supporting future studies to investigate their association with further health outcomes.

The study has several strengths, including the use of both theoretical and empirical demonstrations of the range of the rest-activity fragmentation metrics, using a large sample size. The combination of the approaches increases the validity of our findings. Second, using multiple metrics in the same study population allows for a comprehensive comparison of these metrics. The study has also limitations. We used data from participants who had complete data for seven days. This may have resulted in a selection of the participants, highlighting the need to further investigate the impact of non-wear time on these metrics to allow the use of these metrics in a large sample. In addition, participants were aged between 60 and 83 years and most of them were Caucasian and relatively healthy; whether results are valid in other age and ethnic subgroups requires further investigations. The empirical application is restricted to one type of device, a specific cut-point, 40 m g , to differentiate rest from activity, and a specific algorithm to differentiate the sleep from the waking window, and should be replicated in studies using different settings.

This study provided properties of rest-activity fragmentation metrics previously used and proposed new metrics. Their properties were evaluated using both theorical and empirical approaches among more than 2800 older adults. Overall this study shows that the rest-activity fragmentation metrics examined in this paper - IS, IV, TPs ( \(\text {TP}_{ra, \texttt{w}}\) , \(\text {TP}_{ra, \texttt{s}}\) , \(\text {TP}_{ar, \texttt{w}}\) , \(\text {TP}_{ar, \texttt{s}}\) ), \(\hat{\alpha }\) and ABI - are modestly correlated, apart for ABI and \(\hat{\alpha }\) . Additionally, these metrics are differently associated with socio-demographic and health-related factors. Thus, they might reflect different aspects of individual behaviours. However, consideration should be given to their strengths and limitations, as summarized in Table  2 . We encourage the use of these metrics in future studies in order to get insight into the role of rest-activity fragmentation for health in complementarity to other circadian rhythm features such as phase and amplitude.

Availability of data and materials

Data, protocols, and other metadata of the Whitehall II study are available to the scientific community either via the Whitehall II study data sharing portal ( https://www.ucl.ac.uk/psychiatry/research/mental-health-older-people/whitehall-ii/data-sharing ). All metrics discussed here were calculated using R software and the codes are available on GitHub ( https://github.com/iandanilevicz/frag_metrics ), they are available on GGIR ( \(\ge\) 3.0-9) R package ( https://cran.r-project.org/web/packages/GGIR/index.html ), and DFA- \(\alpha\) and DFA-ABI are available on DFA ( \(\ge\) 1.0-0) R package ( https://cran.r-project.org/web/packages/DFA/index.html ).

Abbreviations

Activity balance index

Autoregressive model of order 1

Body mass index

Confidence interval

• Circadian rhythm

Euclidean norm minus one

• Inter-daily stability
• Intradaily variability

Maximum likelihood

National Health and Nutrition Examination Survey

Reciprocal average duration

Standard deviation

United Kingdom

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Acknowledgements

We thank all of the participating civil service departments and their welfare, personnel, and establishment officers; the British Occupational Health and Safety Agency; the British Council of Civil Service Unions; all participating civil servants in the Whitehall II study; and all members of the Whitehall II study team. The Whitehall II Study team comprises research scientists, statisticians, study coordinators, nurses, data managers, administrative assistants and data entry staff, who make the study possible.

The Whitehall II study is and was supported by grants from the National Institute on Aging, NIH (R01AG056477, R01AG062553); UK Medical Research Council (R024227, S011676), and the Wellcome Trust (221854/Z/20/Z). SS is supported by the French National Research Agency (ANR-19-CE36-0004-01) and by the European Union (ERC grant number101043884). The funding agencies had no role in the study design, data collection, analyses, and interpretation of the data or writing of the manuscript. Views and opinions expressed are however those of the authors only and do not necessarily reflect those of the funding agencies. Neither the European Union nor the granting authority can be held responsible for them.

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Mohamed Amine Benadjaoud and Séverine Sabia contributed equally to this work.

Authors and Affiliations

Université Paris Cité, INSERM, U1153, CRESS, Epidemiology of Ageing and Neurodegenerative Diseases, 10 Av de Verdun, 75010, Paris, France

Ian Meneghel Danilevicz, Frank C. T. van der Heide, Louis Jacob, Benjamin Landré & Séverine Sabia

Accelting, Almere, the Netherlands

Vincent Theodoor van Hees

Institut de Radioprotection et de Sûreté Nucléaire (IRSN), 31 Av Division Leclerc, 92260, Fontenay-Aux-Roses, France

Mohamed Amine Benadjaoud

Department of Epidemiology and Public Health, University College London, London, UK

Séverine Sabia

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Contributions

IMD and SS developed the hypothesis and study design. IMD and VTvH conducted data analysis. IMD and MAB demonstrated the theorems. IMD and SS wrote the first and successive drafts of the manuscript. IMD, VTvH, FvdH, LJ, BL, MAB and SS were involved in the conception, and design of the study, analysis and interpretation of the data, and drafting or critically revising the manuscript for important intellectual content, or, in addition, acquired data. All authors have read and approved the final manuscript. MAB and SS contributed equally.

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Correspondence to Séverine Sabia .

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Danilevicz, I., van Hees, V., van der Heide, F. et al. Measures of fragmentation of rest activity patterns: mathematical properties and interpretability based on accelerometer real life data. BMC Med Res Methodol 24 , 132 (2024). https://doi.org/10.1186/s12874-024-02255-w

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Received : 02 November 2023

Accepted : 24 May 2024

Published : 07 June 2024

DOI : https://doi.org/10.1186/s12874-024-02255-w

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