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Introduction to Research Statistical Analysis: An Overview of the Basics

Christian vandever.

1 HCA Healthcare Graduate Medical Education


This article covers many statistical ideas essential to research statistical analysis. Sample size is explained through the concepts of statistical significance level and power. Variable types and definitions are included to clarify necessities for how the analysis will be interpreted. Categorical and quantitative variable types are defined, as well as response and predictor variables. Statistical tests described include t-tests, ANOVA and chi-square tests. Multiple regression is also explored for both logistic and linear regression. Finally, the most common statistics produced by these methods are explored.


Statistical analysis is necessary for any research project seeking to make quantitative conclusions. The following is a primer for research-based statistical analysis. It is intended to be a high-level overview of appropriate statistical testing, while not diving too deep into any specific methodology. Some of the information is more applicable to retrospective projects, where analysis is performed on data that has already been collected, but most of it will be suitable to any type of research. This primer will help the reader understand research results in coordination with a statistician, not to perform the actual analysis. Analysis is commonly performed using statistical programming software such as R, SAS or SPSS. These allow for analysis to be replicated while minimizing the risk for an error. Resources are listed later for those working on analysis without a statistician.

After coming up with a hypothesis for a study, including any variables to be used, one of the first steps is to think about the patient population to apply the question. Results are only relevant to the population that the underlying data represents. Since it is impractical to include everyone with a certain condition, a subset of the population of interest should be taken. This subset should be large enough to have power, which means there is enough data to deliver significant results and accurately reflect the study’s population.

The first statistics of interest are related to significance level and power, alpha and beta. Alpha (α) is the significance level and probability of a type I error, the rejection of the null hypothesis when it is true. The null hypothesis is generally that there is no difference between the groups compared. A type I error is also known as a false positive. An example would be an analysis that finds one medication statistically better than another, when in reality there is no difference in efficacy between the two. Beta (β) is the probability of a type II error, the failure to reject the null hypothesis when it is actually false. A type II error is also known as a false negative. This occurs when the analysis finds there is no difference in two medications when in reality one works better than the other. Power is defined as 1-β and should be calculated prior to running any sort of statistical testing. Ideally, alpha should be as small as possible while power should be as large as possible. Power generally increases with a larger sample size, but so does cost and the effect of any bias in the study design. Additionally, as the sample size gets bigger, the chance for a statistically significant result goes up even though these results can be small differences that do not matter practically. Power calculators include the magnitude of the effect in order to combat the potential for exaggeration and only give significant results that have an actual impact. The calculators take inputs like the mean, effect size and desired power, and output the required minimum sample size for analysis. Effect size is calculated using statistical information on the variables of interest. If that information is not available, most tests have commonly used values for small, medium or large effect sizes.

When the desired patient population is decided, the next step is to define the variables previously chosen to be included. Variables come in different types that determine which statistical methods are appropriate and useful. One way variables can be split is into categorical and quantitative variables. ( Table 1 ) Categorical variables place patients into groups, such as gender, race and smoking status. Quantitative variables measure or count some quantity of interest. Common quantitative variables in research include age and weight. An important note is that there can often be a choice for whether to treat a variable as quantitative or categorical. For example, in a study looking at body mass index (BMI), BMI could be defined as a quantitative variable or as a categorical variable, with each patient’s BMI listed as a category (underweight, normal, overweight, and obese) rather than the discrete value. The decision whether a variable is quantitative or categorical will affect what conclusions can be made when interpreting results from statistical tests. Keep in mind that since quantitative variables are treated on a continuous scale it would be inappropriate to transform a variable like which medication was given into a quantitative variable with values 1, 2 and 3.

Categorical vs. Quantitative Variables

Both of these types of variables can also be split into response and predictor variables. ( Table 2 ) Predictor variables are explanatory, or independent, variables that help explain changes in a response variable. Conversely, response variables are outcome, or dependent, variables whose changes can be partially explained by the predictor variables.

Response vs. Predictor Variables

Choosing the correct statistical test depends on the types of variables defined and the question being answered. The appropriate test is determined by the variables being compared. Some common statistical tests include t-tests, ANOVA and chi-square tests.

T-tests compare whether there are differences in a quantitative variable between two values of a categorical variable. For example, a t-test could be useful to compare the length of stay for knee replacement surgery patients between those that took apixaban and those that took rivaroxaban. A t-test could examine whether there is a statistically significant difference in the length of stay between the two groups. The t-test will output a p-value, a number between zero and one, which represents the probability that the two groups could be as different as they are in the data, if they were actually the same. A value closer to zero suggests that the difference, in this case for length of stay, is more statistically significant than a number closer to one. Prior to collecting the data, set a significance level, the previously defined alpha. Alpha is typically set at 0.05, but is commonly reduced in order to limit the chance of a type I error, or false positive. Going back to the example above, if alpha is set at 0.05 and the analysis gives a p-value of 0.039, then a statistically significant difference in length of stay is observed between apixaban and rivaroxaban patients. If the analysis gives a p-value of 0.91, then there was no statistical evidence of a difference in length of stay between the two medications. Other statistical summaries or methods examine how big of a difference that might be. These other summaries are known as post-hoc analysis since they are performed after the original test to provide additional context to the results.

Analysis of variance, or ANOVA, tests can observe mean differences in a quantitative variable between values of a categorical variable, typically with three or more values to distinguish from a t-test. ANOVA could add patients given dabigatran to the previous population and evaluate whether the length of stay was significantly different across the three medications. If the p-value is lower than the designated significance level then the hypothesis that length of stay was the same across the three medications is rejected. Summaries and post-hoc tests also could be performed to look at the differences between length of stay and which individual medications may have observed statistically significant differences in length of stay from the other medications. A chi-square test examines the association between two categorical variables. An example would be to consider whether the rate of having a post-operative bleed is the same across patients provided with apixaban, rivaroxaban and dabigatran. A chi-square test can compute a p-value determining whether the bleeding rates were significantly different or not. Post-hoc tests could then give the bleeding rate for each medication, as well as a breakdown as to which specific medications may have a significantly different bleeding rate from each other.

A slightly more advanced way of examining a question can come through multiple regression. Regression allows more predictor variables to be analyzed and can act as a control when looking at associations between variables. Common control variables are age, sex and any comorbidities likely to affect the outcome variable that are not closely related to the other explanatory variables. Control variables can be especially important in reducing the effect of bias in a retrospective population. Since retrospective data was not built with the research question in mind, it is important to eliminate threats to the validity of the analysis. Testing that controls for confounding variables, such as regression, is often more valuable with retrospective data because it can ease these concerns. The two main types of regression are linear and logistic. Linear regression is used to predict differences in a quantitative, continuous response variable, such as length of stay. Logistic regression predicts differences in a dichotomous, categorical response variable, such as 90-day readmission. So whether the outcome variable is categorical or quantitative, regression can be appropriate. An example for each of these types could be found in two similar cases. For both examples define the predictor variables as age, gender and anticoagulant usage. In the first, use the predictor variables in a linear regression to evaluate their individual effects on length of stay, a quantitative variable. For the second, use the same predictor variables in a logistic regression to evaluate their individual effects on whether the patient had a 90-day readmission, a dichotomous categorical variable. Analysis can compute a p-value for each included predictor variable to determine whether they are significantly associated. The statistical tests in this article generate an associated test statistic which determines the probability the results could be acquired given that there is no association between the compared variables. These results often come with coefficients which can give the degree of the association and the degree to which one variable changes with another. Most tests, including all listed in this article, also have confidence intervals, which give a range for the correlation with a specified level of confidence. Even if these tests do not give statistically significant results, the results are still important. Not reporting statistically insignificant findings creates a bias in research. Ideas can be repeated enough times that eventually statistically significant results are reached, even though there is no true significance. In some cases with very large sample sizes, p-values will almost always be significant. In this case the effect size is critical as even the smallest, meaningless differences can be found to be statistically significant.

These variables and tests are just some things to keep in mind before, during and after the analysis process in order to make sure that the statistical reports are supporting the questions being answered. The patient population, types of variables and statistical tests are all important things to consider in the process of statistical analysis. Any results are only as useful as the process used to obtain them. This primer can be used as a reference to help ensure appropriate statistical analysis.

Funding Statement

This research was supported (in whole or in part) by HCA Healthcare and/or an HCA Healthcare affiliated entity.

Conflicts of Interest

The author declares he has no conflicts of interest.

Christian Vandever is an employee of HCA Healthcare Graduate Medical Education, an organization affiliated with the journal’s publisher.

This research was supported (in whole or in part) by HCA Healthcare and/or an HCA Healthcare affiliated entity. The views expressed in this publication represent those of the author(s) and do not necessarily represent the official views of HCA Healthcare or any of its affiliated entities.

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  • How to Report Statistics

How to Report Statistics

Ensure appropriateness and rigor, avoid flexibility and above all never manipulate results

In many fields, a statistical analysis forms the heart of both the methods and results sections of a manuscript. Learn how to report statistical analyses, and what other context is important for publication success and future reproducibility.

A matter of principle

First and foremost, the statistical methods employed in research must always be:

Checklist icon

Appropriate for the study design

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Rigorously reported in sufficient detail for others to reproduce the analysis

Fairness icon

Free of manipulation, selective reporting, or other forms of “spin”

Just as importantly, statistical practices must never be manipulated or misused . Misrepresenting data, selectively reporting results or searching for patterns  that can be presented as statistically significant, in an attempt to yield a conclusion that is believed to be more worthy of attention or publication is a serious ethical violation. Although it may seem harmless, using statistics to “spin” results can prevent publication, undermine a published study, or lead to investigation and retraction.

Supporting public trust in science through transparency and consistency

Along with clear methods and transparent study design, the appropriate use of statistical methods and analyses impacts editorial evaluation and readers’ understanding and trust in science.

In 2011  False-Positive Psychology: Undisclosed Flexibility in Data Collection and Analysis Allows Presenting Anything as Significant exposed that “flexibility in data collection, analysis, and reporting dramatically increases actual false-positive rates” and demonstrated “how unacceptably easy it is to accumulate (and report) statistically significant evidence for a false hypothesis”.

Arguably, such problems with flexible analysis lead to the “ reproducibility crisis ” that we read about today. 

A constant principle of rigorous science The appropriate, rigorous, and transparent use of statistics 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. Trust in science is all of our responsibility. You cannot create any problems by exceeding a minimum standard of information and reporting.

research paper for statistical analysis

Sound statistical practices

While it is hard to provide statistical guidelines that are relevant for all disciplines, types of research, and all analytical techniques,  adherence to rigorous and appropriate principles remains key. Here are some ways to ensure your statistics are sound.

Define your analytical methodology before you begin Take the time to consider and develop a thorough study design that defines your line of inquiry, what you plan to do, what data you will collect, and how you will analyze it. (If you applied for research grants or ethical approval, you probably already have a plan in hand!) Refer back to your study design at key moments in the research process, and above all, stick to it.

To avoid flexibility and improve the odds of acceptance, preregister your study design with a journal Many journals offer the option to submit a study design for peer review before research begins through a practice known as preregistration. If the editors approve your study design, you’ll receive a provisional acceptance for a future research article reporting the results. Preregistering is a great way to head off any intentional or unintentional flexibility in analysis.  By declaring your analytical approach in advance you’ll increase the credibility and reproducibility of your results and help address publication bias, too. Getting peer review feedback on your study design and analysis plan before it has begun (when you can still make changes!) makes your research even stronger AND increases your chances of publication—even if the results are negative or null. Never underestimate how much you can help increase the public’s trust in science by planning your research in this way.

Imagine replicating or extending your own work, years in the future Imagine that you are describing your approach to statistical analysis for your future self, in exactly the same way as we have described for writing your methods section . What would you need to know to replicate or extend your own work? When you consider that you might be at a different institution, working with different colleagues,  using different programs, applications, resources — or maybe even adopting new statistical techniques that have emerged — you can help yourself imagine the level of reporting specificity that you yourself would require to redo or extend your work. Consider:

  • Which details would you need to be reminded of? 
  • What did you do to the raw data before analysis?
  • Did the purpose of the analysis change before or during the experiments?
  • What participants did you decide to exclude? 
  • What process did you adjust, during your work? 

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 techniques or constraints than to conceal them, which could result in reproducibility or ethical issues downstream.

Existing standards, checklists, guidelines for specific disciplines

You can apply the Open Science practices outlined above no matter what your area of expertise—but in many cases, you may still need more detailed guidance specific to your own field. Many  disciplines, fields, and projects have worked hard to develop guidelines and resources  to help with statistics, and to identify and avoid bad statistical practices. Below, you’ll find some of the key materials. 

TIP: Do you have a specific journal in mind?

Be sure to read the submission guidelines for the specific journal you are submitting to, in order to discover any journal- or field-specific policies, initiatives or tools to utilize.

Articles on statistical methods and reporting

Makin, T.R.,  Orban de Xivry, J. Science Forum: Ten common statistical mistakes to watch out for when writing or reviewing a manuscript . eLife 2019;8:e48175 (2019).  https://doi.org/10.7554/eLife.48175  

Munafò, M., Nosek, B., Bishop, D. et al. A manifesto for reproducible science . Nat Hum Behav 1, 0021 (2017). https://doi.org/10.1038/s41562-016-0021    

Writing tips

Your use of statistics should be rigorous, appropriate, and uncompromising in avoidance of analytical flexibility. While this is difficult, do not compromise on rigorous standards for credibility!

What to do

  • Remember that trust in science is everyone’s responsibility.
  • Keep in mind future replicability.
  • Consider preregistering your analysis plan to have it (i) reviewed before results are collected to check problems before they occur and (ii) to avoid any analytical flexibility.
  • Follow principles, but also checklists and field- and journal-specific guidelines.
  • Consider a commitment to rigorous and transparent science a personal responsibility, and not simple adhering to journal guidelines.
  • Be specific about all decisions made during the experiments that someone reproducing your work would need to know.
  • Consider a course in advanced and new statistics, if you feel you have not focused on it enough during your research training.

What not to do


  • Misuse statistics to influence significance or other interpretations of results
  • Conduct your statistical analyses if you are unsure of what you are doing—seek feedback (e.g. via preregistration) from a statistical specialist first.
  • How to Write a Great Title
  • How to Write an Abstract
  • How to Write Your Methods
  • How to Write Discussions and Conclusions
  • How to Edit Your Work

The contents of the Peer Review Center are also available as a live, interactive training session, complete with slides, talking points, and activities. …

The contents of the Writing Center are also available as a live, interactive training session, complete with slides, talking points, and activities. …

There’s a lot to consider when deciding where to submit your work. Learn how to choose a journal that will help your study reach its audience, while reflecting your values as a researcher…

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  • Data Descriptor
  • Open access
  • Published: 03 May 2024

A dataset for measuring the impact of research data and their curation

  • Libby Hemphill   ORCID: orcid.org/0000-0002-3793-7281 1 , 2 ,
  • Andrea Thomer 3 ,
  • Sara Lafia 1 ,
  • Lizhou Fan 2 ,
  • David Bleckley   ORCID: orcid.org/0000-0001-7715-4348 1 &
  • Elizabeth Moss 1  

Scientific Data volume  11 , Article number:  442 ( 2024 ) Cite this article

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  • Research data
  • Social sciences

Science funders, publishers, and data archives make decisions about how to responsibly allocate resources to maximize the reuse potential of research data. This paper introduces a dataset developed to measure the impact of archival and data curation decisions on data reuse. The dataset describes 10,605 social science research datasets, their curation histories, and reuse contexts in 94,755 publications that cover 59 years from 1963 to 2022. The dataset was constructed from study-level metadata, citing publications, and curation records available through the Inter-university Consortium for Political and Social Research (ICPSR) at the University of Michigan. The dataset includes information about study-level attributes (e.g., PIs, funders, subject terms); usage statistics (e.g., downloads, citations); archiving decisions (e.g., curation activities, data transformations); and bibliometric attributes (e.g., journals, authors) for citing publications. This dataset provides information on factors that contribute to long-term data reuse, which can inform the design of effective evidence-based recommendations to support high-impact research data curation decisions.

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Background & summary.

Recent policy changes in funding agencies and academic journals have increased data sharing among researchers and between researchers and the public. Data sharing advances science and provides the transparency necessary for evaluating, replicating, and verifying results. However, many data-sharing policies do not explain what constitutes an appropriate dataset for archiving or how to determine the value of datasets to secondary users 1 , 2 , 3 . Questions about how to allocate data-sharing resources efficiently and responsibly have gone unanswered 4 , 5 , 6 . For instance, data-sharing policies recognize that not all data should be curated and preserved, but they do not articulate metrics or guidelines for determining what data are most worthy of investment.

Despite the potential for innovation and advancement that data sharing holds, the best strategies to prioritize datasets for preparation and archiving are often unclear. Some datasets are likely to have more downstream potential than others, and data curation policies and workflows should prioritize high-value data instead of being one-size-fits-all. Though prior research in library and information science has shown that the “analytic potential” of a dataset is key to its reuse value 7 , work is needed to implement conceptual data reuse frameworks 8 , 9 , 10 , 11 , 12 , 13 , 14 . In addition, publishers and data archives need guidance to develop metrics and evaluation strategies to assess the impact of datasets.

Several existing resources have been compiled to study the relationship between the reuse of scholarly products, such as datasets (Table  1 ); however, none of these resources include explicit information on how curation processes are applied to data to increase their value, maximize their accessibility, and ensure their long-term preservation. The CCex (Curation Costs Exchange) provides models of curation services along with cost-related datasets shared by contributors but does not make explicit connections between them or include reuse information 15 . Analyses on platforms such as DataCite 16 have focused on metadata completeness and record usage, but have not included related curation-level information. Analyses of GenBank 17 and FigShare 18 , 19 citation networks do not include curation information. Related studies of Github repository reuse 20 and Softcite software citation 21 reveal significant factors that impact the reuse of secondary research products but do not focus on research data. RD-Switchboard 22 and DSKG 23 are scholarly knowledge graphs linking research data to articles, patents, and grants, but largely omit social science research data and do not include curation-level factors. To our knowledge, other studies of curation work in organizations similar to ICPSR – such as GESIS 24 , Dataverse 25 , and DANS 26 – have not made their underlying data available for analysis.

This paper describes a dataset 27 compiled for the MICA project (Measuring the Impact of Curation Actions) led by investigators at ICPSR, a large social science data archive at the University of Michigan. The dataset was originally developed to study the impacts of data curation and archiving on data reuse. The MICA dataset has supported several previous publications investigating the intensity of data curation actions 28 , the relationship between data curation actions and data reuse 29 , and the structures of research communities in a data citation network 30 . Collectively, these studies help explain the return on various types of curatorial investments. The dataset that we introduce in this paper, which we refer to as the MICA dataset, has the potential to address research questions in the areas of science (e.g., knowledge production), library and information science (e.g., scholarly communication), and data archiving (e.g., reproducible workflows).

We constructed the MICA dataset 27 using records available at ICPSR, a large social science data archive at the University of Michigan. Data set creation involved: collecting and enriching metadata for articles indexed in the ICPSR Bibliography of Data-related Literature against the Dimensions AI bibliometric database; gathering usage statistics for studies from ICPSR’s administrative database; processing data curation work logs from ICPSR’s project tracking platform, Jira; and linking data in social science studies and series to citing analysis papers (Fig.  1 ).

figure 1

Steps to prepare MICA dataset for analysis - external sources are red, primary internal sources are blue, and internal linked sources are green.

Enrich paper metadata

The ICPSR Bibliography of Data-related Literature is a growing database of literature in which data from ICPSR studies have been used. Its creation was funded by the National Science Foundation (Award 9977984), and for the past 20 years it has been supported by ICPSR membership and multiple US federally-funded and foundation-funded topical archives at ICPSR. The Bibliography was originally launched in the year 2000 to aid in data discovery by providing a searchable database linking publications to the study data used in them. The Bibliography collects the universe of output based on the data shared in each study through, which is made available through each ICPSR study’s webpage. The Bibliography contains both peer-reviewed and grey literature, which provides evidence for measuring the impact of research data. For an item to be included in the ICPSR Bibliography, it must contain an analysis of data archived by ICPSR or contain a discussion or critique of the data collection process, study design, or methodology 31 . The Bibliography is manually curated by a team of librarians and information specialists at ICPSR who enter and validate entries. Some publications are supplied to the Bibliography by data depositors, and some citations are submitted to the Bibliography by authors who abide by ICPSR’s terms of use requiring them to submit citations to works in which they analyzed data retrieved from ICPSR. Most of the Bibliography is populated by Bibliography team members, who create custom queries for ICPSR studies performed across numerous sources, including Google Scholar, ProQuest, SSRN, and others. Each record in the Bibliography is one publication that has used one or more ICPSR studies. The version we used was captured on 2021-11-16 and included 94,755 publications.

To expand the coverage of the ICPSR Bibliography, we searched exhaustively for all ICPSR study names, unique numbers assigned to ICPSR studies, and DOIs 32 using a full-text index available through the Dimensions AI database 33 . We accessed Dimensions through a license agreement with the University of Michigan. ICPSR Bibliography librarians and information specialists manually reviewed and validated new entries that matched one or more search criteria. We then used Dimensions to gather enriched metadata and full-text links for items in the Bibliography with DOIs. We matched 43% of the items in the Bibliography to enriched Dimensions metadata including abstracts, field of research codes, concepts, and authors’ institutional information; we also obtained links to full text for 16% of Bibliography items. Based on licensing agreements, we included Dimensions identifiers and links to full text so that users with valid publisher and database access can construct an enriched publication dataset.

Gather study usage data

ICPSR maintains a relational administrative database, DBInfo, that organizes study-level metadata and information on data reuse across separate tables. Studies at ICPSR consist of one or more files collected at a single time or for a single purpose; studies in which the same variables are observed over time are grouped into series. Each study at ICPSR is assigned a DOI, and its metadata are stored in DBInfo. Study metadata follows the Data Documentation Initiative (DDI) Codebook 2.5 standard. DDI elements included in our dataset are title, ICPSR study identification number, DOI, authoring entities, description (abstract), funding agencies, subject terms assigned to the study during curation, and geographic coverage. We also created variables based on DDI elements: total variable count, the presence of survey question text in the metadata, the number of author entities, and whether an author entity was an institution. We gathered metadata for ICPSR’s 10,605 unrestricted public-use studies available as of 2021-11-16 ( https://www.icpsr.umich.edu/web/pages/membership/or/metadata/oai.html ).

To link study usage data with study-level metadata records, we joined study metadata from DBinfo on study usage information, which included total study downloads (data and documentation), individual data file downloads, and cumulative citations from the ICPSR Bibliography. We also gathered descriptive metadata for each study and its variables, which allowed us to summarize and append recoded fields onto the study-level metadata such as curation level, number and type of principle investigators, total variable count, and binary variables indicating whether the study data were made available for online analysis, whether survey question text was made searchable online, and whether the study variables were indexed for search. These characteristics describe aspects of the discoverability of the data to compare with other characteristics of the study. We used the study and series numbers included in the ICPSR Bibliography as unique identifiers to link papers to metadata and analyze the community structure of dataset co-citations in the ICPSR Bibliography 32 .

Process curation work logs

Researchers deposit data at ICPSR for curation and long-term preservation. Between 2016 and 2020, more than 3,000 research studies were deposited with ICPSR. Since 2017, ICPSR has organized curation work into a central unit that provides varied levels of curation that vary in the intensity and complexity of data enhancement that they provide. While the levels of curation are standardized as to effort (level one = less effort, level three = most effort), the specific curatorial actions undertaken for each dataset vary. The specific curation actions are captured in Jira, a work tracking program, which data curators at ICPSR use to collaborate and communicate their progress through tickets. We obtained access to a corpus of 669 completed Jira tickets corresponding to the curation of 566 unique studies between February 2017 and December 2019 28 .

To process the tickets, we focused only on their work log portions, which contained free text descriptions of work that data curators had performed on a deposited study, along with the curators’ identifiers, and timestamps. To protect the confidentiality of the data curators and the processing steps they performed, we collaborated with ICPSR’s curation unit to propose a classification scheme, which we used to train a Naive Bayes classifier and label curation actions in each work log sentence. The eight curation action labels we proposed 28 were: (1) initial review and planning, (2) data transformation, (3) metadata, (4) documentation, (5) quality checks, (6) communication, (7) other, and (8) non-curation work. We note that these categories of curation work are very specific to the curatorial processes and types of data stored at ICPSR, and may not match the curation activities at other repositories. After applying the classifier to the work log sentences, we obtained summary-level curation actions for a subset of all ICPSR studies (5%), along with the total number of hours spent on data curation for each study, and the proportion of time associated with each action during curation.

Data Records

The MICA dataset 27 connects records for each of ICPSR’s archived research studies to the research publications that use them and related curation activities available for a subset of studies (Fig.  2 ). Each of the three tables published in the dataset is available as a study archived at ICPSR. The data tables are distributed as statistical files available for use in SAS, SPSS, Stata, and R as well as delimited and ASCII text files. The dataset is organized around studies and papers as primary entities. The studies table lists ICPSR studies, their metadata attributes, and usage information; the papers table was constructed using the ICPSR Bibliography and Dimensions database; and the curation logs table summarizes the data curation steps performed on a subset of ICPSR studies.

Studies (“ICPSR_STUDIES”): 10,605 social science research datasets available through ICPSR up to 2021-11-16 with variables for ICPSR study number, digital object identifier, study name, series number, series title, authoring entities, full-text description, release date, funding agency, geographic coverage, subject terms, topical archive, curation level, single principal investigator (PI), institutional PI, the total number of PIs, total variables in data files, question text availability, study variable indexing, level of restriction, total unique users downloading study data files and codebooks, total unique users downloading data only, and total unique papers citing data through November 2021. Studies map to the papers and curation logs table through ICPSR study numbers as “STUDY”. However, not every study in this table will have records in the papers and curation logs tables.

Papers (“ICPSR_PAPERS”): 94,755 publications collected from 2000-08-11 to 2021-11-16 in the ICPSR Bibliography and enriched with metadata from the Dimensions database with variables for paper number, identifier, title, authors, publication venue, item type, publication date, input date, ICPSR series numbers used in the paper, ICPSR study numbers used in the paper, the Dimension identifier, and the Dimensions link to the publication’s full text. Papers map to the studies table through ICPSR study numbers in the “STUDY_NUMS” field. Each record represents a single publication, and because a researcher can use multiple datasets when creating a publication, each record may list multiple studies or series.

Curation logs (“ICPSR_CURATION_LOGS”): 649 curation logs for 563 ICPSR studies (although most studies in the subset had one curation log, some studies were associated with multiple logs, with a maximum of 10) curated between February 2017 and December 2019 with variables for study number, action labels assigned to work description sentences using a classifier trained on ICPSR curation logs, hours of work associated with a single log entry, and total hours of work logged for the curation ticket. Curation logs map to the study and paper tables through ICPSR study numbers as “STUDY”. Each record represents a single logged action, and future users may wish to aggregate actions to the study level before joining tables.

figure 2

Entity-relation diagram.

Technical Validation

We report on the reliability of the dataset’s metadata in the following subsections. To support future reuse of the dataset, curation services provided through ICPSR improved data quality by checking for missing values, adding variable labels, and creating a codebook.

All 10,605 studies available through ICPSR have a DOI and a full-text description summarizing what the study is about, the purpose of the study, the main topics covered, and the questions the PIs attempted to answer when they conducted the study. Personal names (i.e., principal investigators) and organizational names (i.e., funding agencies) are standardized against an authority list maintained by ICPSR; geographic names and subject terms are also standardized and hierarchically indexed in the ICPSR Thesaurus 34 . Many of ICPSR’s studies (63%) are in a series and are distributed through the ICPSR General Archive (56%), a non-topical archive that accepts any social or behavioral science data. While study data have been available through ICPSR since 1962, the earliest digital release date recorded for a study was 1984-03-18, when ICPSR’s database was first employed, and the most recent date is 2021-10-28 when the dataset was collected.

Curation level information was recorded starting in 2017 and is available for 1,125 studies (11%); approximately 80% of studies with assigned curation levels received curation services, equally distributed between Levels 1 (least intensive), 2 (moderately intensive), and 3 (most intensive) (Fig.  3 ). Detailed descriptions of ICPSR’s curation levels are available online 35 . Additional metadata are available for a subset of 421 studies (4%), including information about whether the study has a single PI, an institutional PI, the total number of PIs involved, total variables recorded is available for online analysis, has searchable question text, has variables that are indexed for search, contains one or more restricted files, and whether the study is completely restricted. We provided additional metadata for this subset of ICPSR studies because they were released within the past five years and detailed curation and usage information were available for them. Usage statistics including total downloads and data file downloads are available for this subset of studies as well; citation statistics are available for 8,030 studies (76%). Most ICPSR studies have fewer than 500 users, as indicated by total downloads, or citations (Fig.  4 ).

figure 3

ICPSR study curation levels.

figure 4

ICPSR study usage.

A subset of 43,102 publications (45%) available in the ICPSR Bibliography had a DOI. Author metadata were entered as free text, meaning that variations may exist and require additional normalization and pre-processing prior to analysis. While author information is standardized for each publication, individual names may appear in different sort orders (e.g., “Earls, Felton J.” and “Stephen W. Raudenbush”). Most of the items in the ICPSR Bibliography as of 2021-11-16 were journal articles (59%), reports (14%), conference presentations (9%), or theses (8%) (Fig.  5 ). The number of publications collected in the Bibliography has increased each decade since the inception of ICPSR in 1962 (Fig.  6 ). Most ICPSR studies (76%) have one or more citations in a publication.

figure 5

ICPSR Bibliography citation types.

figure 6

ICPSR citations by decade.

Usage Notes

The dataset consists of three tables that can be joined using the “STUDY” key as shown in Fig.  2 . The “ICPSR_PAPERS” table contains one row per paper with one or more cited studies in the “STUDY_NUMS” column. We manipulated and analyzed the tables as CSV files with the Pandas library 36 in Python and the Tidyverse packages 37 in R.

The present MICA dataset can be used independently to study the relationship between curation decisions and data reuse. Evidence of reuse for specific studies is available in several forms: usage information, including downloads and citation counts; and citation contexts within papers that cite data. Analysis may also be performed on the citation network formed between datasets and papers that use them. Finally, curation actions can be associated with properties of studies and usage histories.

This dataset has several limitations of which users should be aware. First, Jira tickets can only be used to represent the intensiveness of curation for activities undertaken since 2017, when ICPSR started using both Curation Levels and Jira. Studies published before 2017 were all curated, but documentation of the extent of that curation was not standardized and therefore could not be included in these analyses. Second, the measure of publications relies upon the authors’ clarity of data citation and the ICPSR Bibliography staff’s ability to discover citations with varying formality and clarity. Thus, there is always a chance that some secondary-data-citing publications have been left out of the bibliography. Finally, there may be some cases in which a paper in the ICSPSR bibliography did not actually obtain data from ICPSR. For example, PIs have often written about or even distributed their data prior to their archival in ICSPR. Therefore, those publications would not have cited ICPSR but they are still collected in the Bibliography as being directly related to the data that were eventually deposited at ICPSR.

In summary, the MICA dataset contains relationships between two main types of entities – papers and studies – which can be mined. The tables in the MICA dataset have supported network analysis (community structure and clique detection) 30 ; natural language processing (NER for dataset reference detection) 32 ; visualizing citation networks (to search for datasets) 38 ; and regression analysis (on curation decisions and data downloads) 29 . The data are currently being used to develop research metrics and recommendation systems for research data. Given that DOIs are provided for ICPSR studies and articles in the ICPSR Bibliography, the MICA dataset can also be used with other bibliometric databases, including DataCite, Crossref, OpenAlex, and related indexes. Subscription-based services, such as Dimensions AI, are also compatible with the MICA dataset. In some cases, these services provide abstracts or full text for papers from which data citation contexts can be extracted for semantic content analysis.

Code availability

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We thank the ICPSR Bibliography staff, the ICPSR Data Curation Unit, and the ICPSR Data Stewardship Committee for their support of this research. This material is based upon work supported by the National Science Foundation under grant 1930645. This project was made possible in part by the Institute of Museum and Library Services LG-37-19-0134-19.

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L.H. and A.T. conceptualized the study design, D.B., E.M., and S.L. prepared the data, S.L., L.F., and L.H. analyzed the data, and D.B. validated the data. All authors reviewed and edited the manuscript.

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Hemphill, L., Thomer, A., Lafia, S. et al. A dataset for measuring the impact of research data and their curation. Sci Data 11 , 442 (2024). https://doi.org/10.1038/s41597-024-03303-2

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This article is a practical introduction to statistical analysis for students and researchers. We’ll walk you through the steps using two research examples. The first investigates a potential cause-and-effect relationship, while the second investigates a potential correlation between variables.

Table of contents

Step 1: write your hypotheses and plan your research design, step 2: collect data from a sample, step 3: summarise your data with descriptive statistics, step 4: test hypotheses or make estimates with inferential statistics, step 5: interpret your results, frequently asked questions about statistics.

To collect valid data for statistical analysis, you first need to specify your hypotheses and plan out your research design.

Writing statistical hypotheses

The goal of research is often to investigate a relationship between variables within a population . You start with a prediction, and use statistical analysis to test that prediction.

A statistical hypothesis is a formal way of writing a prediction about a population. Every research prediction is rephrased into null and alternative hypotheses that can be tested using sample data.

While the null hypothesis always predicts no effect or no relationship between variables, the alternative hypothesis states your research prediction of an effect or relationship.

  • Null hypothesis: A 5-minute meditation exercise will have no effect on math test scores in teenagers.
  • Alternative hypothesis: A 5-minute meditation exercise will improve math test scores in teenagers.
  • Null hypothesis: Parental income and GPA have no relationship with each other in college students.
  • Alternative hypothesis: Parental income and GPA are positively correlated in college students.

Planning your research design

A research design is your overall strategy for data collection and analysis. It determines the statistical tests you can use to test your hypothesis later on.

First, decide whether your research will use a descriptive, correlational, or experimental design. Experiments directly influence variables, whereas descriptive and correlational studies only measure variables.

  • In an experimental design , you can assess a cause-and-effect relationship (e.g., the effect of meditation on test scores) using statistical tests of comparison or regression.
  • In a correlational design , you can explore relationships between variables (e.g., parental income and GPA) without any assumption of causality using correlation coefficients and significance tests.
  • In a descriptive design , you can study the characteristics of a population or phenomenon (e.g., the prevalence of anxiety in U.S. college students) using statistical tests to draw inferences from sample data.

Your research design also concerns whether you’ll compare participants at the group level or individual level, or both.

  • In a between-subjects design , you compare the group-level outcomes of participants who have been exposed to different treatments (e.g., those who performed a meditation exercise vs those who didn’t).
  • In a within-subjects design , you compare repeated measures from participants who have participated in all treatments of a study (e.g., scores from before and after performing a meditation exercise).
  • In a mixed (factorial) design , one variable is altered between subjects and another is altered within subjects (e.g., pretest and posttest scores from participants who either did or didn’t do a meditation exercise).
  • Experimental
  • Correlational

First, you’ll take baseline test scores from participants. Then, your participants will undergo a 5-minute meditation exercise. Finally, you’ll record participants’ scores from a second math test.

In this experiment, the independent variable is the 5-minute meditation exercise, and the dependent variable is the math test score from before and after the intervention. Example: Correlational research design In a correlational study, you test whether there is a relationship between parental income and GPA in graduating college students. To collect your data, you will ask participants to fill in a survey and self-report their parents’ incomes and their own GPA.

Measuring variables

When planning a research design, you should operationalise your variables and decide exactly how you will measure them.

For statistical analysis, it’s important to consider the level of measurement of your variables, which tells you what kind of data they contain:

  • Categorical data represents groupings. These may be nominal (e.g., gender) or ordinal (e.g. level of language ability).
  • Quantitative data represents amounts. These may be on an interval scale (e.g. test score) or a ratio scale (e.g. age).

Many variables can be measured at different levels of precision. For example, age data can be quantitative (8 years old) or categorical (young). If a variable is coded numerically (e.g., level of agreement from 1–5), it doesn’t automatically mean that it’s quantitative instead of categorical.

Identifying the measurement level is important for choosing appropriate statistics and hypothesis tests. For example, you can calculate a mean score with quantitative data, but not with categorical data.

In a research study, along with measures of your variables of interest, you’ll often collect data on relevant participant characteristics.

Population vs sample

In most cases, it’s too difficult or expensive to collect data from every member of the population you’re interested in studying. Instead, you’ll collect data from a sample.

Statistical analysis allows you to apply your findings beyond your own sample as long as you use appropriate sampling procedures . You should aim for a sample that is representative of the population.

Sampling for statistical analysis

There are two main approaches to selecting a sample.

  • Probability sampling: every member of the population has a chance of being selected for the study through random selection.
  • Non-probability sampling: some members of the population are more likely than others to be selected for the study because of criteria such as convenience or voluntary self-selection.

In theory, for highly generalisable findings, you should use a probability sampling method. Random selection reduces sampling bias and ensures that data from your sample is actually typical of the population. Parametric tests can be used to make strong statistical inferences when data are collected using probability sampling.

But in practice, it’s rarely possible to gather the ideal sample. While non-probability samples are more likely to be biased, they are much easier to recruit and collect data from. Non-parametric tests are more appropriate for non-probability samples, but they result in weaker inferences about the population.

If you want to use parametric tests for non-probability samples, you have to make the case that:

  • your sample is representative of the population you’re generalising your findings to.
  • your sample lacks systematic bias.

Keep in mind that external validity means that you can only generalise your conclusions to others who share the characteristics of your sample. For instance, results from Western, Educated, Industrialised, Rich and Democratic samples (e.g., college students in the US) aren’t automatically applicable to all non-WEIRD populations.

If you apply parametric tests to data from non-probability samples, be sure to elaborate on the limitations of how far your results can be generalised in your discussion section .

Create an appropriate sampling procedure

Based on the resources available for your research, decide on how you’ll recruit participants.

  • Will you have resources to advertise your study widely, including outside of your university setting?
  • Will you have the means to recruit a diverse sample that represents a broad population?
  • Do you have time to contact and follow up with members of hard-to-reach groups?

Your participants are self-selected by their schools. Although you’re using a non-probability sample, you aim for a diverse and representative sample. Example: Sampling (correlational study) Your main population of interest is male college students in the US. Using social media advertising, you recruit senior-year male college students from a smaller subpopulation: seven universities in the Boston area.

Calculate sufficient sample size

Before recruiting participants, decide on your sample size either by looking at other studies in your field or using statistics. A sample that’s too small may be unrepresentative of the sample, while a sample that’s too large will be more costly than necessary.

There are many sample size calculators online. Different formulas are used depending on whether you have subgroups or how rigorous your study should be (e.g., in clinical research). As a rule of thumb, a minimum of 30 units or more per subgroup is necessary.

To use these calculators, you have to understand and input these key components:

  • Significance level (alpha): the risk of rejecting a true null hypothesis that you are willing to take, usually set at 5%.
  • Statistical power : the probability of your study detecting an effect of a certain size if there is one, usually 80% or higher.
  • Expected effect size : a standardised indication of how large the expected result of your study will be, usually based on other similar studies.
  • Population standard deviation: an estimate of the population parameter based on a previous study or a pilot study of your own.

Once you’ve collected all of your data, you can inspect them and calculate descriptive statistics that summarise them.

Inspect your data

There are various ways to inspect your data, including the following:

  • Organising data from each variable in frequency distribution tables .
  • Displaying data from a key variable in a bar chart to view the distribution of responses.
  • Visualising the relationship between two variables using a scatter plot .

By visualising your data in tables and graphs, you can assess whether your data follow a skewed or normal distribution and whether there are any outliers or missing data.

A normal distribution means that your data are symmetrically distributed around a center where most values lie, with the values tapering off at the tail ends.

Mean, median, mode, and standard deviation in a normal distribution

In contrast, a skewed distribution is asymmetric and has more values on one end than the other. The shape of the distribution is important to keep in mind because only some descriptive statistics should be used with skewed distributions.

Extreme outliers can also produce misleading statistics, so you may need a systematic approach to dealing with these values.

Calculate measures of central tendency

Measures of central tendency describe where most of the values in a data set lie. Three main measures of central tendency are often reported:

  • Mode : the most popular response or value in the data set.
  • Median : the value in the exact middle of the data set when ordered from low to high.
  • Mean : the sum of all values divided by the number of values.

However, depending on the shape of the distribution and level of measurement, only one or two of these measures may be appropriate. For example, many demographic characteristics can only be described using the mode or proportions, while a variable like reaction time may not have a mode at all.

Calculate measures of variability

Measures of variability tell you how spread out the values in a data set are. Four main measures of variability are often reported:

  • Range : the highest value minus the lowest value of the data set.
  • Interquartile range : the range of the middle half of the data set.
  • Standard deviation : the average distance between each value in your data set and the mean.
  • Variance : the square of the standard deviation.

Once again, the shape of the distribution and level of measurement should guide your choice of variability statistics. The interquartile range is the best measure for skewed distributions, while standard deviation and variance provide the best information for normal distributions.

Using your table, you should check whether the units of the descriptive statistics are comparable for pretest and posttest scores. For example, are the variance levels similar across the groups? Are there any extreme values? If there are, you may need to identify and remove extreme outliers in your data set or transform your data before performing a statistical test.

From this table, we can see that the mean score increased after the meditation exercise, and the variances of the two scores are comparable. Next, we can perform a statistical test to find out if this improvement in test scores is statistically significant in the population. Example: Descriptive statistics (correlational study) After collecting data from 653 students, you tabulate descriptive statistics for annual parental income and GPA.

It’s important to check whether you have a broad range of data points. If you don’t, your data may be skewed towards some groups more than others (e.g., high academic achievers), and only limited inferences can be made about a relationship.

A number that describes a sample is called a statistic , while a number describing a population is called a parameter . Using inferential statistics , you can make conclusions about population parameters based on sample statistics.

Researchers often use two main methods (simultaneously) to make inferences in statistics.

  • Estimation: calculating population parameters based on sample statistics.
  • Hypothesis testing: a formal process for testing research predictions about the population using samples.

You can make two types of estimates of population parameters from sample statistics:

  • A point estimate : a value that represents your best guess of the exact parameter.
  • An interval estimate : a range of values that represent your best guess of where the parameter lies.

If your aim is to infer and report population characteristics from sample data, it’s best to use both point and interval estimates in your paper.

You can consider a sample statistic a point estimate for the population parameter when you have a representative sample (e.g., in a wide public opinion poll, the proportion of a sample that supports the current government is taken as the population proportion of government supporters).

There’s always error involved in estimation, so you should also provide a confidence interval as an interval estimate to show the variability around a point estimate.

A confidence interval uses the standard error and the z score from the standard normal distribution to convey where you’d generally expect to find the population parameter most of the time.

Hypothesis testing

Using data from a sample, you can test hypotheses about relationships between variables in the population. Hypothesis testing starts with the assumption that the null hypothesis is true in the population, and you use statistical tests to assess whether the null hypothesis can be rejected or not.

Statistical tests determine where your sample data would lie on an expected distribution of sample data if the null hypothesis were true. These tests give two main outputs:

  • A test statistic tells you how much your data differs from the null hypothesis of the test.
  • A p value tells you the likelihood of obtaining your results if the null hypothesis is actually true in the population.

Statistical tests come in three main varieties:

  • Comparison tests assess group differences in outcomes.
  • Regression tests assess cause-and-effect relationships between variables.
  • Correlation tests assess relationships between variables without assuming causation.

Your choice of statistical test depends on your research questions, research design, sampling method, and data characteristics.

Parametric tests

Parametric tests make powerful inferences about the population based on sample data. But to use them, some assumptions must be met, and only some types of variables can be used. If your data violate these assumptions, you can perform appropriate data transformations or use alternative non-parametric tests instead.

A regression models the extent to which changes in a predictor variable results in changes in outcome variable(s).

  • A simple linear regression includes one predictor variable and one outcome variable.
  • A multiple linear regression includes two or more predictor variables and one outcome variable.

Comparison tests usually compare the means of groups. These may be the means of different groups within a sample (e.g., a treatment and control group), the means of one sample group taken at different times (e.g., pretest and posttest scores), or a sample mean and a population mean.

  • A t test is for exactly 1 or 2 groups when the sample is small (30 or less).
  • A z test is for exactly 1 or 2 groups when the sample is large.
  • An ANOVA is for 3 or more groups.

The z and t tests have subtypes based on the number and types of samples and the hypotheses:

  • If you have only one sample that you want to compare to a population mean, use a one-sample test .
  • If you have paired measurements (within-subjects design), use a dependent (paired) samples test .
  • If you have completely separate measurements from two unmatched groups (between-subjects design), use an independent (unpaired) samples test .
  • If you expect a difference between groups in a specific direction, use a one-tailed test .
  • If you don’t have any expectations for the direction of a difference between groups, use a two-tailed test .

The only parametric correlation test is Pearson’s r . The correlation coefficient ( r ) tells you the strength of a linear relationship between two quantitative variables.

However, to test whether the correlation in the sample is strong enough to be important in the population, you also need to perform a significance test of the correlation coefficient, usually a t test, to obtain a p value. This test uses your sample size to calculate how much the correlation coefficient differs from zero in the population.

You use a dependent-samples, one-tailed t test to assess whether the meditation exercise significantly improved math test scores. The test gives you:

  • a t value (test statistic) of 3.00
  • a p value of 0.0028

Although Pearson’s r is a test statistic, it doesn’t tell you anything about how significant the correlation is in the population. You also need to test whether this sample correlation coefficient is large enough to demonstrate a correlation in the population.

A t test can also determine how significantly a correlation coefficient differs from zero based on sample size. Since you expect a positive correlation between parental income and GPA, you use a one-sample, one-tailed t test. The t test gives you:

  • a t value of 3.08
  • a p value of 0.001

The final step of statistical analysis is interpreting your results.

Statistical significance

In hypothesis testing, statistical significance is the main criterion for forming conclusions. You compare your p value to a set significance level (usually 0.05) to decide whether your results are statistically significant or non-significant.

Statistically significant results are considered unlikely to have arisen solely due to chance. There is only a very low chance of such a result occurring if the null hypothesis is true in the population.

This means that you believe the meditation intervention, rather than random factors, directly caused the increase in test scores. Example: Interpret your results (correlational study) You compare your p value of 0.001 to your significance threshold of 0.05. With a p value under this threshold, you can reject the null hypothesis. This indicates a statistically significant correlation between parental income and GPA in male college students.

Note that correlation doesn’t always mean causation, because there are often many underlying factors contributing to a complex variable like GPA. Even if one variable is related to another, this may be because of a third variable influencing both of them, or indirect links between the two variables.

Effect size

A statistically significant result doesn’t necessarily mean that there are important real life applications or clinical outcomes for a finding.

In contrast, the effect size indicates the practical significance of your results. It’s important to report effect sizes along with your inferential statistics for a complete picture of your results. You should also report interval estimates of effect sizes if you’re writing an APA style paper .

With a Cohen’s d of 0.72, there’s medium to high practical significance to your finding that the meditation exercise improved test scores. Example: Effect size (correlational study) To determine the effect size of the correlation coefficient, you compare your Pearson’s r value to Cohen’s effect size criteria.

Decision errors

Type I and Type II errors are mistakes made in research conclusions. A Type I error means rejecting the null hypothesis when it’s actually true, while a Type II error means failing to reject the null hypothesis when it’s false.

You can aim to minimise the risk of these errors by selecting an optimal significance level and ensuring high power . However, there’s a trade-off between the two errors, so a fine balance is necessary.

Frequentist versus Bayesian statistics

Traditionally, frequentist statistics emphasises null hypothesis significance testing and always starts with the assumption of a true null hypothesis.

However, Bayesian statistics has grown in popularity as an alternative approach in the last few decades. In this approach, you use previous research to continually update your hypotheses based on your expectations and observations.

Bayes factor compares the relative strength of evidence for the null versus the alternative hypothesis rather than making a conclusion about rejecting the null hypothesis or not.

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.

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

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

Statistical analysis is the main method for analyzing quantitative research data . It uses probabilities and models to test predictions about a population from sample data.

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Reporting statistical methods and outcome of statistical analyses in research articles

  • Published: 15 June 2020
  • Volume 72 , pages 481–485, ( 2020 )

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  • Mariusz Cichoń 1  

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Statistical methods constitute a powerful tool in modern life sciences. This tool is primarily used to disentangle whether the observed differences, relationships or congruencies are meaningful or may just occur by chance. Thus, statistical inference is an unavoidable part of scientific work. The knowledge of statistics is usually quite limited among researchers representing the field of life sciences, particularly when it comes to constraints imposed on the use of statistical tools and possible interpretations. A common mistake is that researchers take for granted the ability to perform a valid statistical analysis. However, at the stage of data analysis, it may turn out that the gathered data cannot be analysed with any known statistical tools or that there are critical flaws in the interpretation of the results due to violations of basic assumptions of statistical methods. A common mistake made by authors is to thoughtlessly copy the choice of the statistical tests from other authors analysing similar data. This strategy, although sometimes correct, may lead to an incorrect choice of statistical tools and incorrect interpretations. Here, I aim to give some advice on how to choose suitable statistical methods and how to present the results of statistical analyses.

Important limits in the use of statistics

Statistical tools face a number of constraints. Constraints should already be considered at the stage of planning the research, as mistakes made at this stage may make statistical analyses impossible. Therefore, careful planning of sampling is critical for future success in data analyses. The most important is ensuring that the general population is sampled randomly and independently, and that the experimental design corresponds to the aims of the research. Planning a control group/groups is of particular importance. Without a suitable control group, any further inference may not be possible. Parametric tests are stronger (it is easier to reject a null hypothesis), so they should always be preferred, but such methods can be used only when the data are drawn from a general population with normal distribution. For methods based on analysis of variance (ANOVA), residuals should come from a general population with normal distribution, and in this case there is an additional important assumption of homogeneity of variance. Inferences made from analyses violating these assumptions may be incorrect.

Statistical inference

Statistical inference is asymmetrical. Scientific discovery is based on rejecting null hypotheses, so interpreting non-significant results should be taken with special care. We never know for sure why we fail to reject the null hypothesis. It may indeed be true, but it is also possible that our sample size was too small or variance too large to capture the differences or relationships. We also may fail just by chance. Assuming a significance level of p = 0.05 means that we run the risk of rejecting a null hypothesis in 5% of such analyses. Thus, interpretation of non-significant results should always be accompanied by the so-called power analysis, which shows the strength of our inference.

Experimental design and data analyses

The experimental design is a critical part of study planning. The design must correspond to the aims of the study presented in the Introduction section. In turn, the statistical methods must be suited to the experimental design so that the data analyses will enable the questions stated in the Introduction to be answered. In general, simple experimental designs allow the use of simple methods like t-tests, simple correlations, etc., while more complicated designs (multifactor designs) require more advanced methods (see, Fig. 1 ). Data coming from more advanced designs usually cannot be analysed with simple methods. Therefore, multifactor designs cannot be followed by a simple t-test or even with one-way ANOVA, as factors may not act independently, and in such a case the interpretation of the results of one-way ANOVA may be incorrect. Here, it is particularly important that one may be interested in a concerted action of factors (interaction) or an action of a given factor while controlling for other factors (independent action of a factor). But even with one factor design with more than two levels, one cannot use just a simple t-test with multiple comparisons between groups. In such a case, one-way ANOVA should be performed followed by a post hoc test. The post hoc test can be done only if ANOVA rejects the null hypothesis. There is no point in using the post hoc test if the factors have only two levels (groups). In this case, the differences are already clear after ANOVA.

figure 1

Test selection chart

Description of statistical methods in the Materials and methods section

It is in the author’s interest to provide the reader with all necessary information to judge whether the statistical tools used in the paper are the most suitable to answer the scientific question and are suited to the data structure. In the Materials and methods section, the experimental design must be described in detail, so that the reader may easily understand how the study was performed and later why such specific statistical methods were chosen. It must be clear whether the study is planned to test the relationships or differences between groups. Here, the reader should already understand the data structure, what the dependent variable is, what the factors are, and should be able to determine, even without being directly informed, whether the factors are categorical or continuous, and whether they are fixed or random. The sample size used in the analysis should be clearly stated. Sometimes sample sizes used in analyses are smaller than the original. This can happen for various reasons, for example if one fails to perform some measurements, and in such a case, the authors must clearly explain why the original sample size differs from the one used in the analyses. There must be a very good reason to omit existing data points from the analyses. Removing the so-called outliers should be an exception rather than the rule.

A description of the statistical methods should come at the end of the Materials and methods section. Here, we start by introducing the statistical techniques used to test predictions formulated in the Introduction. We describe in detail the structure of the statistical model (defining the dependent variable, the independent variables—factors, interactions if present, character of the factors—fixed or random). The variables should be defined as categorical or continuous. In the case of more advanced models, information on the methods of effects estimation or degrees of freedom should be provided. Unless there are good reasons, interactions should always be tested, even if the study is not aimed at testing an interaction. If the interaction is not the main aim of the study, non-significant interactions should be dropped from the model and new analyses without interactions should be carried out and such results reported. If the interaction appears to be significant, one cannot remove it from the model even if the interaction is not the main aim of the study. In such a case, only the interaction can be interpreted, while the interpretation of the main effects is not allowed. The author should clearly describe how the interactions will be dealt with. One may also consider using a model selection procedure which should also be clearly described.

The authors should reassure the reader that the assumptions of the selected statistical technique are fully met. It must be described how the normality of data distribution and homogeneity of variance was checked and whether these assumptions have been met. When performing data transformation, one needs to explain how it was done and whether the transformation helped to fulfil the assumptions of the parametric tests. If these assumptions are not fulfilled, one may apply non-parametric tests. It must be clearly stated why non-parametric tests are performed. Post hoc tests can be performed only when the ANOVA/Kruskal–Wallis test shows significant effects. These tests are valid for the main effects only when the interaction is not included in the model. These tests are also applicable for significant interactions. There are a number of different post hoc tests, so the selected test must be introduced in the materials and methods section.

The significance level is often mentioned in the materials and methods section. There is common consensus among researchers in life sciences for a significance level set at p = 0.05, so it is not strictly necessary to report this conventional level unless the authors always give the I type error (p-value) throughout the paper. If the author sets the significance level at a lower value, which could be the case, for example, in medical sciences, the reader must be informed about the use of a more conservative level. If the significance level is not reported, the reader will assume p = 0.05. In general, it does not matter which statistical software was used for the analyses. However, the outcome may differ slightly between different software, even if exactly the same model is set. Thus, it may be a good practice to report the name of the software at the end of the subsection describing the statistical methods. If the original code of the model analysed is provided, it would be sensible to inform the reader of the specific software and version that was used.

Presentation of the outcome in the Results section

Only the data and the analyses needed to test the hypotheses and predictions stated in the Introduction and those important for discussion should be placed in the Results section. All other outcome might be provided as supplementary materials. Some descriptive statistics are often reported in the Results section, such as means, standard errors (SE), standard deviation (SD), confidence interval (CI). It is of critical importance that these estimates can only be provided if the described data are drawn from a general population with normal distribution; otherwise median values with quartiles should be provided. A common mistake is to provide the results of non-parametric tests with parametric estimates. If one cannot assume normal distribution, providing arithmetic mean with standard deviation is misleading, as they are estimates of normal distribution. I recommend using confidence intervals instead of SE or SD, as confidence intervals are more informative (non-overlapping intervals suggest the existence of potential differences).

Descriptive statistics can be calculated from raw data (measured values) or presented as estimates from the calculated models (values corrected for independent effects of other factors in the model). The issue whether estimates from models or statistics calculated from the raw data provided throughout the paper should be clearly stated in the Materials and methods section. It is not necessary to report the descriptive statistics in the text if it is already reported in the tables or can be easily determined from the graphs.

The Results section is a narrative text which tells the reader about all the findings and guides them to refer to tables and figures if present. Each table and figure should be referenced in the text at least once. It is in the author’s interest to provide the reader the outcome of the statistical tests in such a way that the correctness of the reported values can be assessed. The value of the appropriate statistics (e.g. F, t, H, U, z, r) must always be provided, along with the sample size (N; non-parametric tests) or degrees of freedom (df; parametric tests) and I type error (p-value). The p-value is an important information, as it tells the reader about confidence related to rejecting the null hypothesis. Thus one needs to provide an exact value of I type error. A common mistake is to provide information as an inequality (p < 0.05). There is an important difference for interpretation if p = 0.049 or p = 0.001.

The outcome of simple tests (comparing two groups, testing relationship between two variables) can easily be reported in the text, but in case of multivariate models, one may rather report the outcome in the form of a table in which all factors with their possible interactions are listed with their estimates, statistics and p-values. The results of post hoc tests, if performed, may be reported in the main text, but if one reports differences between many groups or an interaction, then presenting such results in the form of a table or graph could be more informative.

The main results are often presented graphically, particularly when the effects appear to be significant. The graphs should be constructed so that they correspond to the analyses. If the main interest of the study is in an interaction, then it should be depicted in the graph. One should not present interaction in the graph if it appeared to be non-significant. When presenting differences, the mean or median value should be visualised as a dot, circle or some other symbol with some measure of variability (quartiles if a non-parametric test was performed, and SD, SE or preferably confidence intervals in the case of parametric tests) as whiskers below and above the midpoint. The midpoints should not be linked with a line unless an interaction is presented or, more generally, if the line has some biological/logical meaning in the experimental design. Some authors present differences as bar graphs. When using bar graphs, the Y -axis must start from a zero value. If a bar graph is used to show differences between groups, some measure of variability (SD, SE, CI) must also be provided, as whiskers, for example. Graphs may present the outcome of post hoc tests in the form of letters placed above the midpoint or whiskers, with the same letter indicating lack of differences and different letters signalling pairwise differences. The significant differences can also be denoted as asterisks or, preferably, p-values placed above the horizontal line linking the groups. All this must be explained in the figure caption. Relationships should be presented in the form of a scatterplot. This could be accompanied by a regression line, but only if the relationship is statistically significant. The regression line is necessary if one is interested in describing a functional relationship between two variables. If one is interested in correlation between variables, the regression line is not necessary, but could be placed in order to visualise the relationship. In this case, it must be explained in the figure caption. If regression is of interest, then providing an equation of this regression is necessary in the figure caption. Remember that graphs serve to represent the analyses performed, so if the analyses were carried out on the transformed data, the graphs should also present transformed data. In general, the tables and figure captions must be self-explanatory, so that the reader is able to understand the table/figure content without reading the main text. The table caption should be written in such a way that it is possible to understand the statistical analysis from which the results are presented.

Guidelines for the Materials and methods section:

Provide detailed description of the experimental design so that the statistical techniques will be understandable for the reader.

Make sure that factors and groups within factors are clearly introduced.

Describe all statistical techniques applied in the study and provide justification for each test (both parametric and non-parametric methods).

If parametric tests are used, describe how the normality of data distribution and homogeneity of variance (in the case of analysis of variance) was checked and state clearly that these important assumptions for parametric tests are met.

Give a rationale for using non-parametric tests.

If data transformation was applied, provide details of how this transformation was performed and state clearly that this helped to achieve normal distribution/homogeneity of variance.

In the case of multivariate analyses, describe the statistical model in detail and explain what you did with interactions.

If post hoc tests are used, clearly state which tests you use.

Specify the type of software and its version if you think it is important.

Guidelines for presentation of the outcome of statistical analyses in the Results section:

Make sure you report appropriate descriptive statistics—means, standard errors (SE), standard deviation (SD), confidence intervals (CI), etc. in case of parametric tests or median values with quartiles in case of non-parametric tests.

Provide appropriate statistics for your test (t value for t-test, F for ANOVA, H for Kruskal–Wallis test, U for Mann–Whitney test, χ 2 for chi square test, or r for correlation) along with the sample size (non-parametric tests) or degrees of freedom (df; parametric tests).

t 23  = 3.45 (the number in the subscript denotes degree of freedom, meaning the sample size of the first group minus 1 plus the sample size of the second group minus 1 for the test with independent groups, or number of pairs in paired t-test minus 1).

F 1,23  = 6.04 (first number in the subscript denotes degrees of freedom for explained variance—number of groups within factor minus 1, second number denotes degree of freedom for unexplained variance—residual variance). F-statistics should be provided separately for all factors and interactions (only if interactions are present in the model).

H = 13.8, N 1  = 15, N 2  = 18, N 3  = 12 (N 1, N 2, N 3 are sample sizes for groups compared).

U = 50, N 1  = 20, N 2  = 19 for Mann–Whitney test (N 1 and N 2 are sample sizes for groups).

χ 2  = 3.14 df = 1 (here meaning e.g. 2 × 2 contingency table).

r = 0.78, N = 32 or df = 30 (df = N − 2).

Provide exact p-values (e.g. p = 0.03), rather than standard inequality (p ≤ 0.05)

If the results of statistical analysis are presented in the form of a table, make sure the statistical model is accurately described so that the reader will understand the context of the table without referring to the text. Please ensure that the table is cited in the text.

The figure caption should include all information necessary to understand what is seen in the figure. Describe what is denoted by a bar, symbols, whiskers (mean/median, SD, SE, CI/quartiles). If you present transformed data, inform the reader about the transformation you applied. If you present the results of a post hoc test on the graph, please note what test was used and how you denote the significant differences. If you present a regression line on the scatter plot, give information as to whether you provide the line to visualise the relationship or you are indeed interested in regression, and in the latter case, give the equation for this regression line.

Further reading in statistics:

Sokal and Rolf. 2011. Biometry. Freeman.

Zar. 2010. Biostatistical analyses. Prentice Hall.

McDonald, J.H. 2014. Handbook of biological statistics. Sparky House Publishing, Baltimore, Maryland.

Quinn and Keough. 2002. Experimental design and data analysis for biologists. Cambridge University Press.

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Cichoń, M. Reporting statistical methods and outcome of statistical analyses in research articles. Pharmacol. Rep 72 , 481–485 (2020). https://doi.org/10.1007/s43440-020-00110-5

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DOI : https://doi.org/10.1007/s43440-020-00110-5

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Century of statistical ecology reviewed

Crunching numbers isn't exactly how Neil Gilbert, a postdoctoral researcher at Michigan State University, envisioned a career in ecology.

"I think it's a little funny that I'm doing this statistical ecology work because I was always OK at math, but never particularly enjoyed it," he explained. "As an undergrad, I thought, I'll be an ecologist -- that means that I can be outside, looking at birds, that sort of thing."

As it turns out," he chuckled, "ecology is a very quantitative discipline."

Now, working in the Zipkin Quantitative Ecology lab, Gilbert is the lead author on a new article in a special collection of the journal Ecology that reviews the past century of statistical ecology .

Statistical ecology, or the study of ecological systems using mathematical equations, probability and empirical data, has grown over the last century. As increasingly large datasets and complex questions took center stage in ecological research, new tools and approaches were needed to properly address them.

To better understand how statistical ecology changed over the last century, Gilbert and his fellow authors examined a selection of 36 highly cited papers on statistical ecology -- all published in Ecology since its inception in 1920.

The team's paper examines work on statistical models across a range of ecological scales from individuals to populations, communities, ecosystems and beyond. The team also reviewed publications providing practical guidance on applying models. Gilbert noted that because, "many practicing ecologists lack extensive quantitative training," such publications are key to shaping studies.

Ecology is an advantageous place for such papers, because it is one of, "the first internationally important journals in the field. It has played an outsized role in publishing important work," said lab leader Elise Zipkin, a Red Cedar Distinguished Associate Professor in the Department of Integrative Biology.

"It has a reputation of publishing some of the most influential papers on the development and application of analytical techniques from the very beginning of modern ecological research."

The team found a persistent evolution of models and concepts in the field, especially over the past few decades, driven by refinements in techniques and exponential increases in computational power.

"Statistical ecology has exploded in the last 20 to 30 years because of advances in both data availability and the continued improvement of high-performance computing clusters," Gilbert explained.

Included among the 36 reviewed papers were a landmark 1945 study by Lee R. Dice on predicting the co-occurrence of species in space -- Ecology's most highly cited paper of all time -- and an influential 2002 paper led by Darryl MacKenzie on occupancy models. Ecologists use these models to identify the range and distribution of species in an environment.

Mackenzie's work on species detection and sampling, "played an outsized role in the study of species distributions," says Zipkin. MacKenzie's paper, which was cited more than 5,400 times, spawned various software packages that are now widely used by ecologists, she explained.

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  • Neil A. Gilbert, Bruna R. Amaral, Olivia M. Smith, Peter J. Williams, Sydney Ceyzyk, Samuel Ayebare, Kayla L. Davis, Wendy Leuenberger, Jeffrey W. Doser, Elise F. Zipkin. A century of statistical Ecology . Ecology , 2024; DOI: 10.1002/ecy.4283

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James Buenfil Wins Best Student Paper Competition for the 2024 Statistical Methods in Imaging Conference

research paper for statistical analysis

We are proud to announce that Statistics Ph.D. student James Buenfil has won the Theory and Methods student paper competition for the Statistical Methods in Imaging Conference, to be held May 29-31, 2024, at the JW Marriott Indianapolis, for his work "Asymmetric Canonical Correlation Analysis of Riemannian and High-Dimensional Data."  

Student paper competition winners will present their work at the conference on May 29th. Congratulations James! 

Social Security

Research, statistics & policy analysis, social security bulletin, vol.  84, no.  2.

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This special issue of the Social Security Bulletin features an article of exceptional scope and depth covering recent mortality patterns in the U.S. population by cause, race, ethnicity, sex, and age.

Differences in mortality rates by race and ethnicity affect the distribution of outcomes of Social Security program participation. This article summarizes and compares recent trends in cause-specific mortality by sex and age group among four major racial and ethnic groups in the U.S. population. Causes of death are examined both at the level of broad categories, such as neoplasms, and of specific subcategories, such as lung cancers.

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Experimental R&D Value Added Statistics for the U.S. and States Now Available

Research and development activity accounted for 2.3 percent of the U.S. economy in 2021, according to new experimental statistics released today by the Bureau of Economic Analysis. R&D as a share of each state’s gross domestic product, or GDP, ranged from 0.3 percent in Louisiana and Wyoming to 6.3 percent in New Mexico, home to federally funded Los Alamos National Laboratory and Sandia National Laboratories.


These statistics are part of a new Research and Development Satellite Account  BEA is developing in partnership with the National Center for Science and Engineering Statistics of the National Science Foundation . The statistics complement BEA’s national data on R&D investment  and provide BEA’s first state-by-state numbers on R&D.

The new statistics, covering 2017 to 2021, provide information on the contribution of R&D to GDP (known as R&D value added), compensation, and employment for the nation, all 50 states, and the District of Columbia. In the state statistics, R&D is attributed to the state where the R&D is performed.

Some highlights from the newly released statistics:

R&D activity is highly concentrated in the United States. The top ten R&D-producing states account for 70 percent of U.S. R&D value added. California alone accounts for almost a third of U.S. R&D. Other top R&D-producing states include Washington, Massachusetts, Texas, and New York.


Treating R&D as a sector allows for comparisons with other industries and sectors of the U.S. economy. For instance, R&D’s share of U.S. value added in 2021 is similar to hospitals (2.4 percent) and food services and drinking places (2.2 percent).

Comparison of R and D with Other Sectors

Eighty-five percent of R&D value added is generated by the business sector, followed by government, and nonprofit institutions serving households.

Within the business sector, the professional, scientific, and technical services industry accounts for 40 percent of business R&D value added.    Information (15 percent), chemical manufacturing (12 percent), and computer and electronic product manufacturing (11 percent) also account for sizable shares.


Visit the R&D Satellite Account on BEA’s website for the full set of experimental statistics and accompanying information. To help refine the methodology and presentation of these statistics, BEA is seeking your feedback. Please submit comments to  [email protected] .


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