Effect Size in Statistics: Interpreting the Magnitude of Findings

Effect size is a quantitative measure of the magnitude of a phenomenon, used to answer a specific research question. It tells you how large a difference or how strong an association actually is, independent of whether the result is statistically significant. For students, researchers, and life-science professionals, understanding effect size is essential because a p-value alone cannot tell you whether a finding matters in practical terms. This article explains what effect size is, how to calculate common measures, how to interpret them in different contexts, and why reporting effect size alongside confidence intervals improves the quality of scientific communication.

Why Effect Size Matters Beyond the P-Value

Null hypothesis significance testing has long been the dominant statistical approach in biology and many other fields. However, this approach has serious limitations. Most importantly, it does not provide two crucial pieces of information: the magnitude of an effect of interest and the precision of the estimate of that magnitude. Researchers should be interested in biological or practical importance, which can be assessed using the magnitude of an effect, but not its statistical significance alone. Presenting measures of the magnitude of effects and their confidence intervals in all biological journals would allow researchers to assess relationships within data more effectively than using p-values alone, regardless of statistical significance. Routine presentation of effect sizes would also encourage researchers to view their results in the context of previous research and facilitate the incorporation of results into future meta-analyses, which has become a standard method of quantitative review in biology. Two dimensionless classes of effect size statistics are particularly useful: d statistics for standardized mean differences and r statistics for correlation coefficients, because these can be calculated from almost all study designs and their calculations are essential for meta-analysis. Unstandardized effect size statistics such as mean differences and regression coefficients are no less important, but standardized measures allow comparison across studies. The Publication Manual of the American Psychological Association has called for the reporting of effect sizes and their confidence intervals. Estimates of effect size are useful for determining the practical or theoretical importance of an effect, the relative contributions of factors, and the power of an analysis. A survey of articles published in 2009 and 2010 in the Journal of Experimental Psychology: General found that effect sizes were reported for fewer than half of the analyses, and no article reported a confidence interval for an effect size. The most often reported analysis was analysis of variance, and almost half of these reports were not accompanied by effect sizes. Partial eta squared was the most commonly reported effect size estimate for analysis of variance. For t tests, two-thirds of the articles did not report an associated effect size estimate, with Cohen's d being the most often reported. Drawing conclusions based on the statistical result of a dichotomous p-value instead of a spectrum can mislead researchers into concluding that there is no difference between two groups or two treatments. In addition to the p-value, the utilization of effect size, defined as the magnitude of difference between studied groups, may help obtain a better global understanding of the statement "no effect." Although statistical significance does not mean clinical significance, learning to adequately interpret data allows researchers to disclose transparent results and conclusions while warding off their own bias. Without appropriate interpretation, researchers may be blinded from the truth.

Defining Effect Size

Effect size is defined as a quantitative reflection of the magnitude of some phenomenon that is used for the purpose of addressing a question of interest. This definition is purposely more inclusive than many existing definitions and is unique with regard to linking effect size to a question of interest. There is confusion in the literature on the definition of effect size, and the term is used inconsistently. Three facets of effect size are dimension, measure or index, and value. Ten corollaries follow from this definition, and ideal qualities of effect sizes have been reviewed. Accompanying an effect size with an interval estimate that acknowledges the uncertainty with which the population value of the effect size has been estimated is important. Effect size quantifies the magnitude of the difference or the strength of the association between variables. In clinical research, it is important to calculate and report the effect size and the confidence interval because it is needed for sample size calculation, meaningful interpretation of results, and meta-analyses. There are many different effect size measures that can be organized into two families or groups: the d family and the r family. The d family includes measures that quantify the differences between groups. The r family includes measures that quantify the strength of the association. Effect sizes that are presented in the same units as the characteristic being measured and compared are known as nonstandardized or simple effect sizes. Nonstandardized effect sizes have the advantage of being more informative, easier to interpret, and easier to evaluate in the light of clinical significance or practical relevance. Standardized effect sizes are unit-less and are helpful for combining and comparing effects of different outcome measures or across different studies, such as in meta-analysis. The choice of the correct effect size measure depends on the research question, study design, targeted audience, and the statistical assumptions being made. For a complete and meaningful interpretation of results from a clinical research study, the investigator should make clear the type of effect size being reported, its magnitude and direction, the degree of uncertainty of the effect size estimate as presented by the confidence intervals, and whether the results are compatible with a clinically meaningful effect.

At a Glance: Common Effect Size Measures

The table below summarizes the most common effect size measures, what they quantify, their typical interpretation benchmarks, and when to use them. These benchmarks are general guidelines and should be replaced with field-specific estimates when those are available.

Researchers typically use Cohen's guidelines of Pearson's r = .10, .30, and .50, and Cohen's d = 0.20, 0.50, and 0.80 to interpret observed effect sizes as small, medium, or large, respectively. However, these guidelines were not based on quantitative estimates and are only recommended if field-specific estimates are unknown. A study investigating the distribution of effect sizes in gerontology found that effect sizes of Pearson's r = .12, .20, and .32 for individual differences research and Hedges' g = 0.16, 0.38, and 0.76 for group differences research were interpreted as small, medium, and large effects in that field. Cohen's guidelines appeared to overestimate effect sizes in gerontology. Researchers in that field were encouraged to use Pearson's r = .10, .20, and .30, and Cohen's d or Hedges' g = 0.15, 0.40, and 0.75 to interpret small, medium, and large effects, and to recruit larger samples. This example illustrates why field-specific benchmarks are preferable to generic guidelines.

Cohen's d: Measuring Standardized Mean Differences

Cohen's d is one of the most widely used effect size measures for comparing two group means. It expresses the difference between two means in terms of standard deviation units. A Cohen's d of 0.50 means the two group means differ by half a standard deviation. This standardization allows comparison of effects across studies that use different measurement scales. Cohen's d consistently exhibited low bias, high precision, and accurate coverage across a wide range of scenarios in a simulation study comparing effect sizes for skewed psychological data. The same study found that other mean-based indices derived from d, such as the Common Language Effect Size and the parametric overlap coefficient, showed substantial bias and low coverage, particularly under skewness and heteroscedasticity. Effect-size indices derived from d are not interchangeable, and high empirical correlations do not guarantee the same precision. Cohen's d remains the most robust estimator of a location difference, whereas the non-parametric Overlapping Index provides a more complete view of the entire distribution. Researchers should select effect sizes based on their statistical properties and interpret effects in light of the full distribution instead of through mean-based conventions alone.

Calculating Cohen's d

To calculate Cohen's d, subtract the mean of one group from the mean of the other group and divide by the pooled standard deviation. The pooled standard deviation is a weighted average of the two group standard deviations, giving more weight to the group with the larger sample size. For example, in a study comparing dental age estimation methods, the Nolla method overestimated chronological age by a mean of 0.59 years with a Cohen's dz of 0.52, while the Demirjian method overestimated by 1.09 years with a Cohen's dz of 0.89. The dz notation indicates a repeated measures design where the same participants are measured under both conditions. In that study, both dental methods systematically overestimated chronological age, and the effect sizes indicated moderate to large discrepancies. Sex differences in dental age discrepancies were small, with Cohen's d values of 0.14 or less, indicating that the overestimation was similar for males and females.

Interpreting Cohen's d

The conventional benchmarks for Cohen's d are 0.20 for small, 0.50 for medium, and 0.80 for large effects. These values are widely taught and used, but they are not universal. Field-specific estimates should be used when available. In gerontology, for example, Hedges' g values of 0.16, 0.38, and 0.76 were found to represent small, medium, and large effects, which are lower than Cohen's original benchmarks. This finding suggests that Cohen's guidelines may overestimate effect sizes in some fields. When interpreting Cohen's d, consider the context of the research question, the measurement instrument, and the practical implications of the observed difference. A small effect size in one context may be practically important if the outcome is serious or difficult to change.

Pearson's r: Measuring Strength of Association

Pearson's r is a measure of the strength and direction of the linear association between two continuous variables. It ranges from -1 to +1, where 0 indicates no linear association, and values closer to -1 or +1 indicate stronger associations. The sign indicates the direction of the association, with positive values indicating that higher values of one variable are associated with higher values of the other, and negative values indicating the opposite. Pearson's r is the most commonly used effect size for correlational research and is also used in meta-analysis to combine correlation coefficients across studies. The conventional benchmarks for Pearson's r are .10 for small, .30 for medium, and .50 for large effects. As with Cohen's d, these benchmarks should be replaced with field-specific estimates when available. In gerontology, Pearson's r values of .12, .20, and .32 were found to represent small, medium, and large effects for individual differences research, which are lower than the conventional benchmarks.

Squared Correlation as Variance Explained

The square of Pearson's r, known as the coefficient of determination, represents the proportion of variance in one variable that is explained by the other variable. A Pearson's r of .30 corresponds to an r squared of .09, meaning that 9 percent of the variance is shared between the two variables. This interpretation is useful for understanding the practical importance of an association. However, it is important to remember that correlation does not imply causation, and the proportion of variance explained is a descriptive statistic that does not indicate whether the relationship is causal. In a study of premature infants, BMI and BMI-for-age z-scores were positively correlated with dental age discrepancies with rho values of 0.27 to 0.31 and with cervical vertebral maturation stage with rho values of 0.35 to 0.36, indicating small-to-moderate associations. These correlations suggest that anthropometric context is relevant when interpreting dental age estimates, but they do not establish a causal relationship.

Odds Ratio and Other Measures for Binary Outcomes

When the outcome of interest is binary, such as the presence or absence of a disease, the odds ratio is a common effect size measure. The odds ratio compares the odds of an event occurring in one group to the odds of it occurring in another group. An odds ratio of 1 indicates no difference between groups, an odds ratio greater than 1 indicates higher odds in the first group, and an odds ratio less than 1 indicates lower odds. Odds ratios are widely used in epidemiology and clinical research because they can be calculated from case-control studies and logistic regression models. The interpretation of odds ratios requires care because they are not the same as risk ratios, especially when the outcome is common. For rare outcomes, the odds ratio approximates the risk ratio, but for common outcomes, the two measures diverge. When reporting odds ratios, it is important to include the confidence interval to convey the precision of the estimate. In a study comparing two syphilis testing algorithms, overall agreement between the algorithms was high at 96.3 percent with a Cohen's kappa of 0.709, but the wide confidence interval of Cohen's kappa suggested statistical uncertainty, likely related to the limited number of discordant cases. Three of 82 ECLIA-reactive samples with reactive RPR but nonreactive TPHA results did not fulfill the serological criteria of the ECDC testing sequence at the time of evaluation, and follow-up serological findings in two of these cases were considered compatible with recent or early active syphilis. This example illustrates how effect size measures such as Cohen's kappa can quantify agreement and how confidence intervals convey uncertainty.

Effect Size in Regression Models

Linear regression analysis is a well-known statistical technique that serves as a basis for understanding the relationships between variables. Its simplicity and interpretability make it a preferred choice in healthcare research, as it enables researchers and practitioners to model and predict outcomes effectively. The primary objective of linear regression is to fit a linear equation to observed data, allowing one to predict and interpret the effects of predictor variables. A simple linear regression involves a single independent variable, whereas multiple linear regression includes multiple predictors. A linear-regression model is used to identify the general underlying pattern connecting independent and dependent variables, prove the relationship between these variables, and predict the dependent variables for a specified value of the independent variables. In regression analysis, effect sizes can be reported as unstandardized regression coefficients, which express the change in the dependent variable for a one-unit change in the independent variable, or standardized regression coefficients, which express the change in standard deviation units. The coefficient of determination, R squared, represents the proportion of variance in the dependent variable explained by the independent variables. For multilevel models, effect size reporting is crucial for interpretation of applied research results and for conducting meta-analysis. Appropriate effect size measures for multilevel models include the intraclass correlation coefficient for random effects and standardized regression coefficients or f squared for fixed effects. Complexities associated with reporting R squared as an effect size measure in multilevel models have been explored, along with appropriate effect size measures for more complex models including the three-level model and the random slopes model.

Practical Workflow for Calculating and Reporting Effect Size

The following steps provide a practical workflow for incorporating effect size into research practice. These steps apply to students, researchers, and life-science professionals who are designing studies, analyzing data, or writing reports.

Step 1: Determine the Appropriate Effect Size Measure

Identify the family of effect size that matches your research question. If you are comparing group means, use a d family measure such as Cohen's d or Hedges' g. If you are examining the strength of association between variables, use an r family measure such as Pearson's r or Spearman's rho. If your outcome is binary, consider the odds ratio or risk ratio. The choice depends on the research question, study design, targeted audience, and the statistical assumptions being made. For mediation models, specific effect size measures have been developed for communicating indirect effects. For multilevel models, the intraclass correlation coefficient is appropriate for random effects, and standardized regression coefficients or f squared are appropriate for fixed effects.

Step 2: Calculate the Effect Size and Its Confidence Interval

Calculate the effect size using the appropriate formula for your chosen measure. For Cohen's d, divide the difference between group means by the pooled standard deviation. For Pearson's r, calculate the correlation coefficient using standard statistical software. For odds ratios, calculate the ratio of odds between groups. After calculating the effect size, calculate its confidence interval. The confidence interval conveys the precision of the estimate and allows readers to assess the range of plausible values. No article in a survey of psychology journals reported a confidence interval for an effect size, indicating that this practice is not yet routine. Reporting confidence intervals alongside effect sizes is strongly recommended because it acknowledges the uncertainty with which the population value of the effect size has been estimated.

Step 3: Interpret the Effect Size in Context

Interpret the effect size using appropriate benchmarks. If field-specific estimates are available, use those instead of generic guidelines. Consider the practical or clinical significance of the effect size in the context of your research question. A statistically significant result with a small effect size may not be practically important, while a non-significant result with a moderate effect size may warrant further investigation with a larger sample. The combined use of an effect size and its confidence interval enables one to assess the relationships within data more effectively than the use of p-values, regardless of statistical significance.

Step 4: Report the Effect Size Transparently

When writing your report or manuscript, include the effect size, its confidence interval, and a clear statement of what the effect size means in the context of your study. Make clear the type of effect size being reported, its magnitude and direction, the degree of uncertainty of the effect size estimate as presented by the confidence intervals, and whether the results are compatible with a clinically meaningful effect. This transparency allows readers to evaluate the practical importance of your findings and facilitates the incorporation of your results into future meta-analyses.

Software Tools for Effect Size Calculation

Several software tools are available to assist with effect size calculation and conversion. The R package metaConvert automatically calculates and flexibly converts multiple effect size measures. It applies more than 120 formulas to convert any relevant input data into Cohen's d, Hedges' g, mean difference, odds ratio, risk ratio, incidence rate ratio, correlation coefficient, Fisher's r-to-z transformed correlation coefficient, variability ratio, coefficient of variation ratio, or number needed to treat. Researchers unfamiliar with R can use this software through a browser-based graphical interface. This suite helps researchers in the life sciences and other disciplines estimate and convert effect sizes more easily and accurately. The Experimental Design Assistant from the NC3Rs is another tool that can help researchers design experiments with appropriate sample sizes and statistical power. The Research Data Framework from the National Institute of Standards and Technology provides guidance on data management practices that support reproducible research. The EQUATOR Network provides reporting guidelines for health research that include recommendations for reporting effect sizes. These tools support the practical implementation of effect size reporting in research.

Records and Measurements for Effect Size Reporting

Maintaining clear records of effect size calculations is essential for reproducible research. For each analysis, record the following information: the type of effect size measure used, the formula or software function used to calculate it, the raw data or summary statistics used as inputs, the calculated effect size value, the confidence interval, and the interpretation benchmarks used. This documentation allows other researchers to verify your calculations and to convert your effect sizes to other measures if needed for meta-analysis. When reporting effect sizes in publications, include enough detail about the calculation method that readers can reproduce the calculation from the reported summary statistics. For example, when reporting Cohen's d, report the means, standard deviations, and sample sizes for each group, or report the pooled standard deviation used in the calculation. When reporting Pearson's r, report the sample size and the correlation coefficient. When reporting odds ratios, report the contingency table or the odds in each group.

Common Failure Patterns in Effect Size Reporting

Several common failure patterns occur in effect size reporting. One pattern is omitting effect sizes entirely. A survey of articles published in 2009 and 2010 in the Journal of Experimental Psychology: General found that effect sizes were reported for fewer than half of the analyses, and no article reported a confidence interval for an effect size. For t tests, two-thirds of the articles did not report an associated effect size estimate. This omission prevents readers from assessing the practical importance of findings and hinders meta-analysis. Another pattern is using inappropriate benchmarks. Generic guidelines such as Cohen's benchmarks may not be appropriate for all fields. In gerontology, Cohen's guidelines appeared to overestimate effect sizes, and field-specific benchmarks were lower. Using inappropriate benchmarks can lead to misinterpretation of the practical importance of findings. A third pattern is reporting effect sizes without confidence intervals. The confidence interval conveys the precision of the estimate, and without it, readers cannot assess the range of plausible values. A fourth pattern is using effect size measures that are not appropriate for the data. For example, mean-based effect sizes such as Cohen's d may perform poorly when data are highly skewed or when variances are unequal. A simulation study found that the Common Language Effect Size and the parametric overlap coefficient showed substantial bias and low coverage under skewness and heteroscedasticity, while Cohen's d remained robust. A fifth pattern is interpreting effect sizes without considering the full distribution of the data. The non-parametric Overlapping Index provides a more complete view of the entire distribution and may be more appropriate when distributions differ in shape as well as location.

Limitations of Effect Size Measures

Effect size measures have several limitations that researchers should understand. Standardized effect sizes such as Cohen's d and Pearson's r are unit-less, which allows comparison across studies but can obscure the practical meaning of the effect. Nonstandardized effect sizes such as mean differences and regression coefficients are more informative and easier to interpret in the light of clinical significance or practical relevance, but they cannot be compared across studies that use different measurement scales. The choice between standardized and nonstandardized effect sizes depends on the research question and the intended audience. Another limitation is that effect size measures are estimates, and like all estimates, they are subject to sampling variability. The confidence interval conveys the precision of the estimate, but many researchers fail to report it. A third limitation is that effect size benchmarks are arbitrary and context-dependent. The conventional benchmarks for Cohen's d and Pearson's r were not based on quantitative estimates and are only recommended if field-specific estimates are unknown. Researchers should use field-specific benchmarks when available. A fourth limitation is that effect size measures may not capture all aspects of an effect. For example, mean-based effect sizes focus on location differences and may miss differences in distribution shape or variance. The non-parametric Overlapping Index focuses on the entire distributional differences and may provide a more complete view. A fifth limitation is that effect size measures are only as good as the data and study design. Poor study design, measurement error, and confounding can bias effect size estimates just as they can bias any other statistical estimate.

Field-Specific Effect Size Benchmarks

The choice of interpretation benchmarks should be guided by field-specific knowledge. Cohen's guidelines of Pearson's r = .10, .30, and .50, and Cohen's d = 0.20, 0.50, and 0.80 are widely used, but they were not based on quantitative estimates and are only recommended if field-specific estimates are unknown. A study in gerontology extracted effect sizes from meta-analyses published in 10 top-ranked gerontology journals and calculated the 25th, 50th, and 75th percentile ranks for Pearson's r and Cohen's d or Hedges' g values as indicators of small, medium, and large effects. The resulting benchmarks were lower than Cohen's guidelines, suggesting that Cohen's guidelines overestimate effect sizes in gerontology. Researchers in gerontology were encouraged to use Pearson's r = .10, .20, and .30, and Cohen's d or Hedges' g = 0.15, 0.40, and 0.75 to interpret small, medium, and large effects, and to recruit larger samples. This example demonstrates the importance of developing and using field-specific benchmarks. Novel effect size interpretation guidelines have also been developed for rehabilitation research, indicating that this field has recognized the need for context-appropriate benchmarks. When field-specific benchmarks are not available, researchers should use the generic guidelines with caution and acknowledge their limitations.

Effect Size in Meta-Analysis

Effect size measures are essential for meta-analysis, which combines data from multiple research articles to produce a quantitative summary of evidence. Meta-analysis requires that individual studies report effect sizes in a common metric or that effect sizes can be converted to a common metric. The R package metaConvert facilitates this process by automatically calculating and flexibly converting multiple effect size measures. It applies more than 120 formulas to convert any relevant input data into Cohen's d, Hedges' g, mean difference, odds ratio, risk ratio, incidence rate ratio, correlation coefficient, Fisher's r-to-z transformed correlation coefficient, variability ratio, coefficient of variation ratio, or number needed to treat. This flexibility is important because different studies may report different effect size measures, and conversion is often necessary to combine them. Routine presentation of effect sizes in primary research facilitates the incorporation of results into future meta-analysis, which has been increasingly used as the standard method of quantitative review in biology. When effect sizes are not reported in primary studies, meta-analysts may need to calculate them from summary statistics or contact study authors for additional data. This additional effort can be avoided if researchers report effect sizes and their confidence intervals in their publications.

Effect Size and Sample Size Planning

Effect size is a key input for sample size calculations and power analysis. A priori power analysis requires an estimate of the expected effect size to determine the sample size needed to detect that effect with a specified level of power. In a randomized controlled trial of telemedicine-based family care for premature infants, sample size was determined by a priori power analysis with alpha of 0.05 and power of 0.80 based on expected effect sizes from prior telemedicine intervention studies. The study enrolled 186 premature infants, with 93 in each group. This example illustrates how effect size estimates from previous research inform sample size planning. When effect size estimates are not available from previous research, researchers may need to conduct pilot studies or use conservative estimates based on the smallest effect of practical interest. The choice of effect size for sample size planning should be justified and reported in the methods section of research articles. Using an effect size that is too large will result in an underpowered study, while using an effect size that is too small will result in an unnecessarily large study that may be impractical or unethical.

Effect Size in Diagnostic and Agreement Studies

Effect size measures are also used in diagnostic and agreement studies to quantify the level of agreement between different measurement methods or observers. Cohen's kappa is a common measure of agreement for categorical outcomes that accounts for agreement occurring by chance. In a study comparing antemortem computed tomography findings with autopsy findings in head injury cases, agreement between CT scan and autopsy findings was assessed using percentage agreement, Cohen's kappa coefficient, and McNemar's test. Substantial agreement was observed for skull fractures, extradural hemorrhages, intraventricular hemorrhage, and cerebellar herniation, whereas lower agreement was observed for scalp injuries, subarachnoid hemorrhage, and brain lacerations. The study concluded that antemortem CT scan demonstrated good concordance with autopsy for skull fractures and major intracranial hemorrhages and proved to be a valuable adjunct in the evaluation of fatal head injury cases. However, a CT scan could not completely replace conventional medicolegal autopsy. In another study comparing two syphilis testing algorithms, overall agreement between the algorithms was high at 96.3 percent with a Cohen's kappa of 0.709, but the wide confidence interval of Cohen's kappa suggested statistical uncertainty. These examples illustrate how effect size measures such as Cohen's kappa quantify agreement and how confidence intervals convey the precision of agreement estimates.

Effect Size in Experimental Design

Effect size considerations should inform experimental design from the earliest stages. The Experimental Design Assistant from the NC3Rs is a tool that helps researchers design experiments with appropriate sample sizes and statistical power. The Research Data Framework from the National Institute of Standards and Technology provides guidance on data management practices that support reproducible research. The EQUATOR Network provides reporting guidelines for health research that include recommendations for reporting effect sizes. These resources support the integration of effect size considerations into the research workflow. When designing an experiment, researchers should consider the smallest effect size that would be practically or clinically meaningful, the expected variability in the outcome measure, and the sample size needed to detect that effect with adequate power. These considerations should be documented in the study protocol and reported in the methods section of the resulting publication.

Professional Escalation Criteria

Researchers who encounter difficulties with effect size calculation or interpretation should seek guidance from appropriate sources. If you are unsure which effect size measure is appropriate for your research question, consult a statistician or a methods expert in your field. If you are conducting a meta-analysis and need to convert effect sizes across studies, consider using the metaConvert software suite or consult a systematic review methods expert. If you are preparing a manuscript for publication and are unsure about the reporting requirements for effect sizes, consult the journal's instructions to authors and relevant reporting guidelines from the EQUATOR Network. If you are a student or trainee, seek guidance from your supervisor or course instructor. If you are a life-science professional applying effect size concepts in practice, consider continuing education opportunities in statistics and research methods. The National Center for Biotechnology Information provides literature resources that can help you stay current with methodological developments in effect size estimation and interpretation.

Frequently Asked Questions

What is the difference between statistical significance and effect size?

Statistical significance indicates whether an observed effect is unlikely to have occurred by chance, typically assessed using a p-value. Effect size indicates the magnitude of the effect, independent of sample size. A result can be statistically significant with a very small effect size if the sample is large enough, and a result can be non-significant with a large effect size if the sample is too small. Statistical significance does not mean clinical or practical significance. Drawing conclusions based on the statistical result of a dichotomous p-value instead of a spectrum can mislead researchers into concluding that there is no difference between two groups or two treatments. In addition to the p-value, the utilization of effect size may help obtain a better global understanding of the statement "no effect."

How do I choose between Cohen's d and Pearson's r?

Choose Cohen's d when you are comparing the means of two groups on a continuous outcome. Choose Pearson's r when you are examining the strength and direction of the linear association between two continuous variables. The d family includes measures that quantify the differences between groups, while the r family includes measures that quantify the strength of the association. The choice of the correct effect size measure depends on the research question, study design, targeted audience, and the statistical assumptions being made.

What is a good effect size?

There is no universal answer to this question. The interpretation of effect size depends on the research context, the field of study, and the practical implications of the finding. Generic guidelines such as Cohen's benchmarks for small, medium, and large effects are widely used, but they were not based on quantitative estimates and are only recommended if field-specific estimates are unknown. Field-specific benchmarks should be used when available. In gerontology, for example, field-specific benchmarks were lower than Cohen's guidelines, suggesting that Cohen's guidelines overestimate effect sizes in that field.

Why should I report confidence intervals for effect sizes?

Confidence intervals convey the precision of the effect size estimate and acknowledge the uncertainty with which the population value of the effect size has been estimated. Without a confidence interval, readers cannot assess the range of plausible values for the effect size. The combined use of an effect size and its confidence interval enables one to assess the relationships within data more effectively than the use of p-values, regardless of statistical significance. For a complete and meaningful interpretation of results, the investigator should make clear the type of effect size being reported, its magnitude and direction, and the degree of uncertainty of the effect size estimate as presented by the confidence intervals.

Can I convert one effect size measure to another?

Yes, many effect size measures can be converted to other measures using established formulas. The R package metaConvert automatically calculates and flexibly converts multiple effect size measures, applying more than 120 formulas to convert any relevant input data into Cohen's d, Hedges' g, mean difference, odds ratio, risk ratio, incidence rate ratio, correlation coefficient, Fisher's r-to-z transformed correlation coefficient, variability ratio, coefficient of variation ratio, or number needed to treat. This conversion is often necessary for meta-analysis, which requires that individual studies report effect sizes in a common metric.

What should I do if my data are not normally distributed?

If your data are not normally distributed, consider whether mean-based effect sizes such as Cohen's d are appropriate. A simulation study found that Cohen's d consistently exhibited low bias, high precision, and accurate coverage across all scenarios, including skewed data, whereas other mean-based indices showed substantial bias and low coverage under skewness and heteroscedasticity. The non-parametric Overlapping Index remained unbiased under shape differences and variance heterogeneity but performed less reliably when the populations truly overlapped. Researchers should select effect sizes based on their statistical properties and interpret effects in light of the full distribution instead of through mean-based conventions alone.

How is effect size used in sample size calculations?

Effect size is a key input for sample size calculations and power analysis. A priori power analysis requires an estimate of the expected effect size to determine the sample size needed to detect that effect with a specified level of power. In a randomized controlled trial, sample size was determined by a priori power analysis with alpha of 0.05 and power of 0.80 based on expected effect sizes from prior studies. When effect size estimates are not available from previous research, researchers may need to conduct pilot studies or use conservative estimates based on the smallest effect of practical interest.

What is the difference between standardized and unstandardized effect sizes?

Standardized effect sizes such as Cohen's d and Pearson's r are unit-less and allow comparison across studies that use different measurement scales. Nonstandardized effect sizes such as mean differences and regression coefficients are presented in the same units as the characteristic being measured and have the advantage of being more informative, easier to interpret, and easier to evaluate in the light of clinical significance or practical relevance. Standardized effect sizes are helpful for combining and comparing effects of different outcome measures or across different studies, such as in meta-analysis. The choice between standardized and nonstandardized effect sizes depends on the research question and the intended audience.

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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.
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• A Simple Guide to Effect Size Measures.. JAMA otolaryngology-- head & neck surgery, 2023.
• Effect size, confidence interval and statistical significance: a practical guide for biologists.. Biological reviews of the Cambridge Philosophical Society, 2007.
• Effect Size Guidelines, Sample Size Calculations, and Statistical Power in Gerontology.. Innovation in aging, 2019.
• The effect of display size on ultrasound interpretation.. The American journal of emergency medicine, 2022.
• Application and interpretation of linear-regression analysis.. Medical hypothesis, discovery & innovation ophthalmology journal, 2024.
• On effect size.. Psychological methods, 2012.
• Editorial Commentary: The Power of Interpretation: Utilizing the P Value as a Spectrum, in Addition to Effect Size, Will Lead to Accurate Presentation of Results.. Arthroscopy : the journal of arthroscopic & related surgery : official publication of the Arthroscopy Association of North America and the International Arthroscopy Association, 2022.
• Comparison of CDC and ECDC reverse sequence algorithms for syphilis diagnosis: clinical implications of discordant serological results.. 2026.
• Discrepancies and associations among chronological age, dental age, and cervical vertebral maturation in growing orthodontic patients: A cross-sectional study in a Spanish orthodontic clinical sample.. 2026.
• Comparative Study of Antemortem Computed Tomography (CT) Findings With Autopsy Findings in Head Injury Cases.. 2026.
• Not normal: a simulation study comparing effect sizes for skewed psychological data.. 2026.
• The influence of family care guidance for premature infants based on a telemedicine model on their neurodevelopmental assessment indicators.. 2026.
• Effect size measures for mediation models: quantitative strategies for communicating indirect effects.. Psychological methods, 2011.
• metaConvert: an automatic suite for estimation of 11 different effect size measures and flexible conversion across them. Research Synthesis Methods, 2025.
• Effect size measures for multilevel models: definition, interpretation, and TIMSS example. Large-scale Assessments in Education, 2018.
• Eta Squared and Partial Eta Squared as Measures of Effect Size in Educational Research.. 2011.
• Use of Effect Size Measures along with p-Value in Scientific Publications. Borneo Epidemiology Journal, 2021.
• Novel Effect Size Interpretation Guidelines and an Evaluation of Statistical Power in Rehabilitation Research. Archives of Physical Medicine and Rehabilitation, 2020.
• A test of two interpretations of the apparent size effects in a distorted room. Journal of Experimental Psychology, 1962.

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