Statistical Questions: How to Identify and Formulate Them

A statistical question is a question that can be answered by collecting data and where the answer is expected to vary. This distinction matters for students designing research projects, researchers reviewing literature, and professionals who need to interpret quantitative evidence. A question such as "What is the average height of maize plants in this field?" is not statistical because it seeks a single fixed value. A question such as "How much does maize plant height vary across different fertilizer treatments?" is statistical because it anticipates variation and requires data collection across multiple observations to answer. This article explains the defining characteristics of statistical questions, provides examples and non-examples, and offers a practical checklist and template for formulating questions that can be answered with data.

What Makes a Question Statistical

A statistical question has three defining features. First, it anticipates variability in the data that will be collected. Second, it requires data collection from multiple observations, subjects, or units. Third, the answer is expressed as a distribution, range, proportion, or model instead of a single deterministic value.

Consider the difference between a deterministic question and a statistical question. "Does this specific pig weigh 80 kilograms?" is deterministic because it has a single correct answer that can be verified by weighing that one animal. "What is the typical weaning weight of piglets in this herd?" is statistical because it requires weighing many piglets and the answer will involve a measure of central tendency such as the mean or median, along with a measure of variability such as the standard deviation or interquartile range. Descriptive statistics are the methods used to calculate, describe, and summarize collected research data in a logical and efficient way, and they include measures of central tendency and variability that directly answer statistical questions about a dataset [10].

The presence of variability is the core distinction. A statistical question acknowledges that individual observations differ from one another. The range, standard deviation, and interquartile range are three measures of variability that quantify how much individual recorded scores or observed values differ from one another [10]. When a question asks about a pattern, a relationship, a difference between groups, or a change over time, it is almost always statistical because these phenomena require data from many units to characterize.

Examples and Non-Examples of Statistical Questions

Understanding statistical questions is easier when comparing clear examples with clear non-examples. The following table provides a quick reference for distinguishing between the two categories.

The non-examples share a common feature: they can be answered with a single measurement, a single record, or a simple lookup. The examples share the feature of requiring multiple observations and expecting variation. A question about the mode of calving dates is a descriptive summary of existing data, but it is not a statistical question in the research sense because it does not involve collecting data to characterize variability or test a relationship.

The Role of Statistical Questions in Research Design

Statistical questions are the foundation of quantitative research because they determine the study design, the data collection methods, and the analysis plan. A poorly formulated question leads to ambiguous results, wasted resources, and conclusions that cannot be supported by the data. A well-formulated question aligns the research hypothesis with the statistical methods that will be used to test it.

Randomized controlled trials illustrate this connection between question and design. Randomized controlled trials are considered the highest level of evidence to establish causal associations in clinical research, and there are many RCT designs and features that can be selected to address a research hypothesis [6]. The design choices, including randomization methods, sample size, and statistical analysis, all flow from the specific question being asked. For example, a question about whether a new vaccine reduces disease incidence in a poultry flock requires a design that randomly assigns birds to treatment and control groups, specifies the outcome measure, and determines the sample size needed to detect a meaningful difference.

The estimand framework provides a structured way to define a treatment effect for a clinical question. The International Council for Harmonisation published the estimand framework in 2019, which proposes five attributes for an estimand: treatments, variables, target populations, population-level summaries, and intercurrent events [14]. Intercurrent events are events that occur after treatment initiation and affect the interpretation of the outcome. The framework also proposes strategies to handle these events, including the treatment policy strategy, the hypothetical strategy, the composite variable strategy, the while on treatment strategy, and the principal stratum strategy [14]. This framework forces researchers to be precise about what question they are actually answering, which is a discipline that applies to any statistical question, also those in pharmaceutical trials.

How to Identify a Statistical Question

Identifying whether a question is statistical requires a systematic assessment. The following checklist can be applied to any research question or to questions encountered in published literature.

Step 1: Determine Whether the Question Anticipates Variation

Ask whether the answer to the question is expected to differ across observations, subjects, time points, or conditions. If the question can be answered with a single value that does not depend on which units are measured, it is not statistical. If the answer would change depending on which animals, plants, samples, or patients are included, it is statistical.

Step 2: Determine Whether Data Collection Is Required

A statistical question requires data collection from multiple units. This could involve primary data collection such as weighing animals, taking soil samples, or administering surveys. It could also involve secondary data analysis using existing records, databases, or published datasets. If the question can be answered without collecting or accessing data from multiple units, it is not statistical.

Step 3: Determine Whether the Answer Will Be a Distribution or Summary

Statistical questions produce answers that are distributions, summary statistics, model estimates, or measures of association. Examples include the mean and standard deviation of weaning weights, the proportion of animals testing positive for a disease, the correlation between two variables, or the difference in outcomes between treatment groups. If the answer is a single number that does not require summarizing multiple observations, the question is not statistical.

Step 4: Determine Whether the Question Can Be Answered With Available Data

A statistical question must be answerable with data that can be collected or accessed. This requires considering the target population, the sampling frame, the measurement methods, and the resources available. A question that cannot be answered with available data may need to be revised or narrowed.

Step 5: Determine Whether the Question Is Specific Enough to Guide Analysis

A statistical question should specify the population, the variables, and the comparison or relationship of interest. Vague questions such as "Is this treatment effective?" are not specific enough to guide statistical analysis. A more specific question such as "Does treatment with antibiotic X reduce the 14-day mortality rate in calves with respiratory disease compared with standard care?" specifies the population, the intervention, the outcome, and the comparison.

A Template for Formulating Statistical Questions

The following template can be used to formulate statistical questions that are specific, answerable, and aligned with appropriate statistical methods.

Template Components

A well-formulated statistical question includes five components: the population, the variables, the comparison or relationship, the outcome measure, and the context or conditions.

The population is the group of units about which the question asks. Examples include all dairy cows in a specific herd, all soil samples from a particular field, or all patients with a specific condition in a defined region.

The variables are the characteristics that will be measured or observed. Variables can be categorical such as breed or treatment group, or continuous such as weight, temperature, or concentration.

The comparison or relationship is the specific contrast or association of interest. This could be a comparison between two or more groups, a relationship between two continuous variables, a change over time, or a prediction of an outcome from one or more predictors.

The outcome measure is the specific metric that will be used to answer the question. Examples include the mean difference between groups, the correlation coefficient, the odds ratio, or the prediction accuracy.

The context or conditions are the specific circumstances under which the question is asked. This includes the time period, the location, the management practices, or the environmental conditions.

Template Statement

Using these components, a statistical question can be formulated as follows:

"In [population], how does [variable of interest] compare between [group A] and [group B] with respect to [outcome measure], under [context or conditions]?"

Alternative formulations include:

"In [population], what is the relationship between [variable 1] and [variable 2], as measured by [outcome measure], under [context or conditions]?"

"In [population], how does [variable of interest] change over [time period], as measured by [outcome measure], under [context or conditions]?"

Examples Using the Template

Example 1: "In the dairy herd at this research station, how does the 305-day milk production compare between cows supplemented with a yeast culture and cows receiving a standard ration, as measured by the mean difference in kilograms of milk, during the 2024 lactation season?"

Example 2: "In feedlot steers, what is the relationship between days on feed and average daily gain, as measured by the correlation coefficient, under commercial feeding conditions in the Texas Panhandle?"

Example 3: "In broiler flocks raised on this farm, how does the mortality rate vary across different stocking densities, as measured by the proportion of birds dying before 35 days of age, during the summer months?"

Common Mistakes in Formulating Statistical Questions

Several recurring mistakes appear when students and researchers formulate statistical questions. Recognizing these patterns helps avoid them.

Asking a Question That Is Too Broad

A question such as "What is the effect of nutrition on animal health?" is too broad to be answered with data. It does not specify the population, the specific nutritional factor, the health outcome, or the comparison. Broad questions need to be narrowed to specific, measurable components before they can guide research.

Asking a Question That Is Too Narrow

A question such as "What is the weight of pig number 47?" is too narrow because it seeks a single value for a single unit. This type of question does not require statistical methods and cannot support generalizations about a larger population.

Confusing Descriptive Summaries With Statistical Questions

A question such as "What is the average daily gain of the 50 steers in this pen?" is a descriptive summary of existing data. It is not a statistical question in the research sense because it does not involve collecting data to characterize variability or test a relationship. However, descriptive statistics are essential for reporting the answers to basic questions about data, including who, what, why, when, where, and so what [10]. Descriptive summaries become statistical questions when they are used to make inferences about a larger population or to compare groups.

Asking Questions That Cannot Be Answered With the Available Data

A question that requires data that cannot be collected due to cost, time, or ethical constraints is not a practical statistical question. For example, a question about the lifetime productivity of dairy cows would require following animals for many years, which may not be feasible. The question may need to be revised to use a proxy outcome or a shorter time frame.

Asking Questions That Confuse Correlation With Causation

A statistical question about an association between two variables is different from a question about causation. Observational data can reveal associations, but causal conclusions require specific designs and assumptions. Mediation analysis addresses the question of the mechanisms by which an exposure causes an outcome, and it requires more confounders to be taken into account than the estimation of the overall effect size [7]. A question such as "Does obesity cause diabetes?" requires a different design and analysis than "Is obesity associated with diabetes?" Researchers must be clear about which type of question they are asking.

Statistical Questions Across Different Research Contexts

Statistical questions take different forms depending on the research context. Understanding these variations helps in identifying and formulating questions appropriate to each setting.

Descriptive Questions

Descriptive questions ask about the characteristics of a population or dataset. They are answered with measures of central tendency, variability, and frequency. Examples include questions about the average weight of animals in a herd, the distribution of soil nutrient levels across a field, or the proportion of patients with a specific symptom. Descriptive statistics are the specific methods used to calculate, describe, and summarize collected research data in a logical, meaningful, and efficient way [10].

Comparative Questions

Comparative questions ask about differences between groups. They are answered with tests of statistical significance, confidence intervals, and effect sizes. Examples include questions about whether one feed additive produces higher weight gain than another, whether a new diagnostic test detects disease more accurately than an existing test, or whether one surgical technique results in fewer complications than another. The design of randomized controlled trials offers many options for addressing comparative questions, and the choice of randomization method involves potential tradeoffs [6].

Relational Questions

Relational questions ask about associations between variables. They are answered with correlation coefficients, regression models, or measures of association. Examples include questions about the relationship between body condition score and milk production, the association between stocking density and mortality, or the correlation between two laboratory measurements. Repeated measures correlation is a statistical technique for determining the common within-individual association for paired measures assessed on two or more occasions for multiple individuals [11]. This approach is well-suited for research questions about the common linear association in paired repeated measures data [11].

Predictive Questions

Predictive questions ask about the probability of an outcome given certain predictors. They are answered with prediction models that estimate for an individual the probability that a condition or disease is already present or will occur in the future [9]. Prediction models in health care use predictors to estimate the probability that a condition is present, which is a diagnostic model, or will occur in the future, which is a prognostic model [9]. The PROBAST tool was developed to assess the risk of bias and applicability of prediction model studies, and it includes 20 signaling questions across 4 domains: participants, predictors, outcome, and analysis [9].

Mechanistic Questions

Mechanistic questions ask about the pathways by which an exposure causes an outcome. They are answered with mediation analysis or other causal inference methods. Mediation analysis expresses an overall exposure effect as a combination of an indirect and a direct effect [7]. For example, it might be of interest whether the increased risk of diabetes due to obesity is mediated by insulin resistance, and if so, how much of a direct effect remains [7]. Mediation analysis can reveal whether an exposure causes an outcome and also how it causes the outcome, but multiple assumptions must be satisfied that cannot easily be checked [7].

High-Dimensional Questions

High-dimensional questions involve datasets with a very large number of variables associated with each observation. Prominent examples in biomedical research include omics data with many measurements across the genome, proteome, or metabolome, as well as electronic health records data with large numbers of variables recorded for each patient [19]. The statistical analysis of such data requires knowledge and experience with complex methods adapted to the respective research questions [19]. In high-dimensional settings, traditional statistical methods may not be usable, and adequate analytic tools may still be lacking for some questions [19].

Time-Varying Questions

Time-varying questions ask about how associations or outcomes change across time. Time-varying effect modeling is a statistical approach that enables researchers to estimate dynamic associations between variables across time [18]. This approach can address innovative questions about processes that unfold across different levels of time, such as changes in associations across historical time, age-varying associations, and changes in outcomes relative to a specific event [18].

The Connection Between Statistical Questions and Sample Size

The formulation of a statistical question directly determines the sample size needed to answer it. Sample size calculations play an essential role in health research, yet published research often fails to report sample size selection [8]. For sample size estimation, researchers need to provide information regarding the statistical analysis to be applied, determine acceptable precision levels, decide on study power, specify the confidence level, and determine the magnitude of practical significance differences, which is the effect size [8].

A statistical question that specifies the population, the comparison, and the outcome measure provides the information needed to calculate an appropriate sample size. A vague question cannot guide sample size calculation because it does not specify the effect size of interest or the statistical analysis that will be applied. Research team members need to engage in an open and realistic dialog on the appropriateness of the calculated sample size for the research question, available data records, research timeline, and cost [8].

The following table illustrates how different statistical questions lead to different sample size considerations.

How to Evaluate Statistical Questions in Published Research

Readers of scientific literature need to evaluate whether the statistical questions in a study are well formulated and whether the analysis answers those questions. Several tools and frameworks support this evaluation.

Reporting Guidelines

Reporting guidelines provide checklists for what should be included in a research report. The EQUATOR Network is an international initiative that provides resources and guidelines for the reporting of health research [2]. These guidelines help readers assess whether the statistical questions, methods, and results are clearly reported.

Risk of Bias Assessment Tools

Risk of bias assessment tools help readers evaluate whether the design and analysis of a study are likely to produce unbiased answers to the statistical questions. PROBAST is a tool for assessing the risk of bias and applicability of prediction model studies, and it includes signaling questions across four domains: participants, predictors, outcome, and analysis [9]. This tool helps reviewers determine whether a prediction model study answers its stated question without bias.

Study Design Tools

Study design tools help researchers plan studies that can answer their statistical questions. The Experimental Design Assistant from the NC3Rs is a free online tool that helps researchers design rigorous and reproducible animal experiments [3]. This tool guides researchers through the process of specifying their statistical questions, designing the experiment, and planning the analysis.

Literature Search Tools

Literature search tools help researchers find published studies that address their statistical questions. The National Center for Biotechnology Information provides literature resources including PubMed, which is a database of biomedical literature [4][5]. These resources allow researchers to search for studies that have addressed similar questions and to evaluate the evidence base.

Common Failure Patterns in Statistical Question Formulation

Several failure patterns recur when statistical questions are poorly formulated. Recognizing these patterns helps researchers avoid them and helps readers identify weaknesses in published studies.

The Vague Question Pattern

The vague question pattern occurs when a question lacks specificity about the population, variables, comparison, or outcome. An example is "What is the effect of stress on animal performance?" This question cannot guide data collection or analysis because it does not specify what stress means, what performance means, which animals are included, or what comparison is being made.

The Single-Value Pattern

The single-value pattern occurs when a question seeks a single value instead of a distribution or relationship. An example is "What is the prevalence of mastitis in this herd?" If the question is answered by counting the number of cases in a specific herd at a specific time, it is a descriptive summary instead of a statistical question. However, if the question is "What is the prevalence of mastitis in dairy herds in this region, and how does it vary across herds?" it becomes statistical because it anticipates variation across herds.

The Data-Free Pattern

The data-free pattern occurs when a question is asked without considering whether data can be collected to answer it. An example is "Why do some cows develop ketosis and others do not?" This question is too broad and does not specify what data would be needed to answer it. A more specific question such as "Which factors measured at calving are associated with the development of ketosis in the first 30 days of lactation?" specifies the variables and the time frame.

The Correlation-Causation Confusion Pattern

The correlation-causation confusion pattern occurs when a question about association is treated as a question about causation. An example is "Does feeding moldy silage cause reduced milk production?" Answering this question requires a design that can support causal conclusions, such as a randomized controlled trial or a carefully designed observational study with appropriate adjustment for confounders. A question about whether moldy silage is associated with reduced milk production can be answered with observational data but cannot establish causation.

The Overreach Pattern

The overreach pattern occurs when a question asks for more than the data can support. An example is "What is the optimal stocking density for broiler chickens?" This question implies that a single optimal value exists, when the answer likely depends on many factors including the housing system, the season, the market weight, and the economic context. A more appropriate question might be "How does mortality and growth performance vary across stocking densities of 10, 12, and 14 birds per square meter?"

Practical Steps for Formulating Statistical Questions

The following practical steps guide the formulation of statistical questions that can be answered with data.

Step 1: Start With a Broad Area of Interest

Begin with a broad area of interest such as animal health, crop production, or patient outcomes. Write down what you want to know about this area without worrying about precision.

Step 2: Identify the Population

Specify the population about which you want to make claims. This could be all animals in a specific herd, all fields on a specific farm, or all patients with a specific condition. Be as specific as possible about the geographic area, the time period, and the characteristics of the population.

Step 3: Identify the Variables

Identify the variables that are relevant to your question. Distinguish between the outcome variable that you want to explain or predict and the predictor variables that might explain or predict it. Specify how each variable will be measured.

Step 4: Specify the Comparison or Relationship

Specify the comparison or relationship that interests you. Are you comparing two or more groups? Are you examining the relationship between two continuous variables? Are you predicting an outcome from several predictors? Are you examining change over time?

Step 5: Draft the Question Using the Template

Use the template to draft a specific statistical question. Review the question to ensure it includes the population, the variables, the comparison or relationship, the outcome measure, and the context.

Step 6: Test the Question Against the Checklist

Apply the checklist for identifying statistical questions. Confirm that the question anticipates variation, requires data collection, will produce a distribution or summary, can be answered with available data, and is specific enough to guide analysis.

Step 7: Revise Based on Feedback

Share the question with colleagues, mentors, or a statistician. Revise the question based on feedback about feasibility, clarity, and alignment with statistical methods.

Records and Documentation for Statistical Questions

Documenting the formulation of statistical questions is important for research transparency and reproducibility. The following records support the research process.

Research Protocol

A research protocol should include the statistical questions, the study design, the data collection methods, and the analysis plan. The protocol serves as a reference for the research team and can be reviewed by ethics committees, funding agencies, or regulatory bodies.

Data Management Plan

A data management plan should describe how data will be collected, stored, cleaned, and analyzed. The Research Data Framework from the National Institute of Standards and Technology provides a structure for describing the components of a data management plan [1]. This framework helps researchers document their data practices and ensures that data are available for verification and reuse.

Analysis Plan

An analysis plan should specify the statistical methods that will be used to answer each statistical question. The plan should include the primary analysis, sensitivity analyses, and any subgroup analyses. Pre-specifying the analysis plan reduces the risk of selective reporting and data dredging.

Analysis Code and Output

Analysis code and output should be preserved so that the analysis can be reproduced. This includes the software version, the code used for data cleaning and analysis, and the output files. Reproducible analysis supports the credibility of the research and allows others to verify the results.

Limitations of Statistical Questions

Statistical questions have limitations that researchers must acknowledge. A statistical question can only be answered within the constraints of the data that are collected. The quality of the answer depends on the quality of the data, the appropriateness of the study design, and the validity of the statistical methods.

Data Quality Limitations

Statistical questions cannot overcome poor data quality. If measurements are inaccurate, if samples are not representative of the population, or if data are missing in a systematic way, the answers to statistical questions will be biased. Researchers must invest in data quality controls, including standardized measurement protocols, calibration of instruments, and validation of data entry.

Design Limitations

Statistical questions cannot overcome design limitations. A cross-sectional study cannot answer questions about causation, and a study with a small sample size cannot detect small effects. Researchers must choose designs that are appropriate for their questions and must acknowledge the limitations of their designs when interpreting results.

Analysis Limitations

Statistical questions cannot overcome analysis limitations. Complex data require appropriate statistical methods, and the choice of methods involves assumptions that must be checked. In high-dimensional data settings, traditional statistical methods may not be usable, and adequate analytic tools may still be lacking for some questions [19].

Interpretation Limitations

Statistical questions produce answers that are estimates with uncertainty. A confidence interval can be calculated for virtually any variable or outcome measure in an experimental, quasi-experimental, or observational research study design [10]. Researchers must interpret their results with appropriate caution and must not overstate the precision or generalizability of their findings.

Professional Escalation Criteria

Researchers and practitioners should seek professional statistical advice in several situations. The following criteria indicate when consultation with a statistician or methodologist is warranted.

Complex Study Designs

Consult a statistician when the study design involves multiple groups, multiple time points, clustering, or adaptive elements. Randomized controlled trials have become increasingly diverse as new methods have been proposed to evaluate increasingly complex scientific hypotheses, and the choice of design involves tradeoffs that require statistical expertise [6].

High-Dimensional Data

Consult a statistician when the dataset has a very large number of variables associated with each observation. The statistical analysis of high-dimensional data requires knowledge and experience with complex methods, and traditional methods may not be appropriate [19].

Causal Questions

Consult a statistician when the question involves causation instead of association. Causal inference requires specific designs and assumptions, and the estimand framework provides a structured approach to defining treatment effects [14]. Bayesian approaches to causality treat causality statements as hypotheses about the world and compute the posterior distribution of the causal hypotheses given the data and background knowledge [13].

Prediction Model Development

Consult a statistician when developing or validating a prediction model. Prediction models require careful attention to the participants, predictors, outcome, and analysis, and tools such as PROBAST can help assess the risk of bias [9].

Sample Size Determination

Consult a statistician when determining the sample size for a study. Sample size calculations require information about the statistical analysis, acceptable precision levels, study power, confidence level, and effect size [8].

Mediation or Mechanism Questions

Consult a statistician when the question involves the mechanisms by which an exposure causes an outcome. Mediation analysis requires more confounders to be taken into account than the estimation of the overall effect size, and multiple assumptions must be satisfied that cannot easily be checked [7].

Frequently Asked Questions

What is the simplest definition of a statistical question?

A statistical question is a question that can be answered by collecting data and where the answer is expected to vary. The key feature is that the answer is not a single fixed value but a distribution, range, proportion, or relationship that emerges from multiple observations.

How can I tell if a question is statistical or not?

Apply three tests. First, does the question anticipate variation in the data? Second, does it require collecting data from multiple observations or units? Third, will the answer be expressed as a distribution, summary statistic, or model estimate? If the answer to all three is yes, the question is statistical.

Is "What is the average weight of these 10 pigs?" a statistical question?

No. This question seeks a single summary value from a specific set of 10 pigs. It is a descriptive summary of existing data instead of a statistical question. However, if the question were "What is the average weight of pigs in this herd, and how does it vary?" it would be statistical because it anticipates variation and requires sampling from a larger population.

Can a question about a single animal be a statistical question?

A question about a single animal is not statistical if it seeks a single value for that animal. However, a question about a single animal can be part of a statistical question if it is repeated over time or if it is compared with a population. For example, "How does this cow's milk production vary across her lactation?" is statistical because it involves repeated measurements that vary over time.

Why is it important to formulate a statistical question before collecting data?

The statistical question determines the study design, the data collection methods, the sample size, and the analysis plan. A poorly formulated question leads to ambiguous results and wasted resources. The estimand framework illustrates this by requiring researchers to define the treatment, variables, target population, population-level summary, and intercurrent events before conducting a trial [14].

What is the difference between a statistical question and a research hypothesis?

A statistical question is a question that can be answered with data. A research hypothesis is a specific, testable statement about the expected answer to a statistical question. For example, the statistical question "Does Diet A produce higher weight gain than Diet B?" can be paired with the research hypothesis "Diet A produces higher average daily weight gain than Diet B in broiler chickens."

How do I know if my statistical question can be answered with the data I have?

Review the data you have or can collect. Check whether the data include the population, variables, and time frame specified in your question. Check whether the sample size is adequate for the analysis you plan to conduct. If the data are insufficient, revise the question or plan additional data collection.

When should I consult a statistician about my statistical question?

Consult a statistician when your question involves complex study designs, high-dimensional data, causal inference, prediction models, sample size determination, or mediation analysis. Also consult a statistician when you are unsure whether your question can be answered with the data and methods available.

Related Articles

• Mammals That Lay Eggs: Surprising Examples
• Raven Sounds and Calls: What They Mean and How to Identify Them
• Inferential Statistical
• Inferential Statistical
• Inferential Statistical

References and Further Reading

• Research Data Framework. National Institute of Standards and Technology.
• EQUATOR Network. EQUATOR Network.
• Experimental Design Assistant. NC3Rs.
• NCBI Literature Resources. National Center for Biotechnology Information.
• PubMed. National Library of Medicine.
• Randomized Controlled Trials.. Chest, 2020.
• Mediation Analysis in Medical Research.. Deutsches Arzteblatt international, 2023.
• Sample size determination: A practical guide for health researchers.. Journal of general and family medicine, 2023.
• PROBAST: A Tool to Assess Risk of Bias and Applicability of Prediction Model Studies: Explanation and Elaboration.. Annals of internal medicine, 2019.
• Descriptive Statistics: Reporting the Answers to the 5 Basic Questions of Who, What, Why, When, Where, and a Sixth, So What?. Anesthesia and analgesia, 2017.
• Repeated Measures Correlation.. Frontiers in psychology, 2017.
• Multi-omics Data Integration.. Advances in experimental medicine and biology, 2026.
• Bayesian Causality.. The American statistician, 2020.
• Interpreting the Estimand Framework From a Causal Inference Perspective.. 2026.
• On the Application of Information Geometry to the Manifold Induced by the Parameters of the Mean Square Error of Probability Functions. 2026.
• Assessing the Accuracy and Readability of Generative Artificial Intelligence Responses for Esophageal and Gastric Cancer Patients.. 2026.
• Methodological concerns in the association between gut microbiota and sarcopenia: from cross-sectional associations to statistical fragility.. 2026.
• Time-Varying Effect Modeling to Address New Questions in Behavioral Research: Examples in Marijuana Use. Psychology of Addictive Behaviors, 2016.
• Statistical analysis of high-dimensional biomedical data: a gentle introduction to analytical goals, common approaches and challenges. BMC Medicine, 2023.
• Statistical evaluation of panel repeatability in Check-All-That-Apply questions. 2016.
• Primer of biostatistics : statistical software program version 6.0. 1981.
• MT model space: Statistical versus compositional versus example-based machine translation. Machine Translation, 2005.
• Ten questions concerning statistical data analysis in human-centric buildings research: A focus on thermal comfort investigations. Building and Environment, 2024.
• Literature Review and Example: Quality of University Services using Servperf and Statistical Techniques to Reduce Variables in Latent Variables. International Journal of Engineering Trends and Technology, 2023.
• Examples of pitfalls in statistical analysis - 1. Summarizing your data before statistical analysis. Japanese Journal of Anesthesiology, 1996.

This article is educational and does not replace institutional policy, professional advice, or applicable safety and regulatory requirements.