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Using Effect Size—or Why the P Value Is Not Enough
Open accessAbstract
These statements about the importance of effect sizes were made by two of the most influential statistician-researchers of the past half-century. Yet many submissions to Journal of Graduate Medical Education omit mention of the effect size in quantitative studies while prominently displaying the P value. In this paper, we target readers with little or no statistical background in order to encourage you to improve your comprehension of the relevance of effect size for planning, analyzing, reporting, and understanding education research studies.In medical education research studies that compare different educational interventions, effect size is the magnitude of the difference between groups. The absolute effect size is the difference between the average, or mean, outcomes in two different intervention groups. For example, if an educational intervention resulted in the improvement of subjects' examination scores by an average total of 15 of 50 questions as compared to that of another intervention, the absolute effect size is 15 questions or 3 grade levels (30%) better on the examination. Absolute effect size does not take into account the variability in scores, in that not every subject achieved the average outcome.In another example, residents' self-assessed confidence in performing a procedure improved an average of 0.4 point on a Likert-type scale ranging from 1 to 5, after simulation training. While the absolute effect size in the first example appears clear, the effect size in the second example is less apparent. Is a 0.4 change a lot or trivial? Accounting for variability in the measured improvement may aid in interpreting the magnitude of the change in the second example.Thus, effect size can refer to the raw difference between group means, or absolute effect size, as well as standardized measures of effect, which are calculated to transform the effect to an easily understood scale. Absolute effect size is useful when the variables under study have intrinsic meaning (eg, number of hours of sleep). Calculated indices of effect size are useful when the measurements have no intrinsic meaning, such as numbers on a Likert scale; when studies have used different scales so no direct comparison is possible; or when effect size is examined in the context of variability in the population under study.Calculated effect sizes can also quantitatively compare results from different studies and thus are commonly used in meta-analyses.The effect size is the main finding of a quantitative study. While a P value can inform the reader whether an effect exists, the P value will not reveal the size of the effect. In reporting and interpreting studies, both the substantive significance (effect size) and statistical significance (P value) are essential results to be reported.For this reason, effect sizes should be reported in a paper's Abstract and Results sections. In fact, an estimate of the effect size is often needed before starting the research endeavor, in order to calculate the number of subjects likely to be required to avoid a Type II, or β, error, which is the probability of concluding there is no effect when one actually exists. In other words, you must determine what number of subjects in the study will be sufficient to ensure (to a particular degree of certainty) that the study has acceptable power to support the null hypothesis. That is, if no difference is found between the groups, then this is a true finding.Statistical significance is the probability that the observed difference between two groups is due to chance. If the P value is larger than the alpha level chosen (eg, .05), any observed difference is assumed to be explained by sampling variability. With a sufficiently large sample, a statistical test will almost always demonstrate a significant difference, unless there is no effect whatsoever, that is, when the effect size is exactly zero; yet very small differences, even if significant, are often meaningless. Thus, reporting only the significant P value for an analysis is not adequate for readers to fully understand the results.For example, if a sample size is 10 000, a significant P value is likely to be found even when the difference in outcomes between groups is negligible and may not justify an expensive or time-consuming intervention over another. The level of significance by itself does not predict effect size. Unlike significance tests, effect size is independent of sample size. Statistical significance, on the other hand, depends upon both sample size and effect size. For this reason, P values are considered to be confounded because of their dependence on sample size. Sometimes a statistically significant result means only that a huge sample size was used.3A commonly cited example of this problem is the Physicians Health Study of aspirin to prevent myocardial infarction (MI).4 In more than 22 000 subjects over an average of 5 years, aspirin was associated with a reduction in MI (although not in o
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“Concerning effect size, the r-value was 0.34.This would be counted as medium effect size (Sullivan & Feinn, 2012).”
From Teaching and Learning Science Using YouTube Videos and Discovery Learning in Primary School (2020) · cites this paper as Sullivan & Feinn, 2012
Experimental — accuracy not yet measuredIn the citing paper
“effect sizes, however, are independent of sample size (Sullivan and Feinn, 2012).”
From A chatbot-delivered intervention for optimizing social media use and reducing perceived isolation among rural-living LGBTQ+ youth: Development, acceptability, usability, satisfaction, and utility (2023) · cites this paper as Sullivan and Feinn, 2012
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- Coe R. It's the effect size, stupid: what “effect size” is and why it is important. Paper presented at the 2002 Annual Conference of the British Educational Research Association, University of Exeter, Exeter, Devon, England, September 12–14, 2002. http://www.leeds.ac.uk/educol/documents/00002182.htm. Accessed March 23, 2012.
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“Effect sizes are independent of the sample size and are statistically categorized as small (0.20–0.49), medium (0.50– 0.79), or large (>0.80) [27].”
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“Cohen’s d values were interpreted according to conventional thresholds, with values of 0.2 indicating a small effect, 0.5 a medium effect, and 0.8 or greater a large effect (Sullivan and Feinn, 2012).”
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“Effect sizes were classified as follows: small (~ 0.2), medium (~ 0.5), and large (> 0.8) [37].”
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“In addition to p -values, Cohen’s d was used to quantify effect size and assess the practical relevance of observed differences (Sullivan & Feinn, 2012).”
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“This distinction is crucial as large sample sizes can yield statistical significance even for trivially small differences [34].”
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“Cohen’s criteria were adopted for interpretation: values of approximately 0.20 were considered small effects, 0.50 moderate, and ≥ 0.80 large for d ; similarly, h values of 0.20, 0.50, and 0.80 indicated small, medium, and large effects, respectively [53].”
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“Given that both groups comprised equal sample sizes ( n = 1000), differences in latent distributions were quantified using Cohen’s d effect size [43,44]: where d i denotes the effect size in the i th latent dimension; µ 1,i and µ 2,i are the group means; and s 1,i and s 2,i are the corresponding…”
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“Physiological aging leads to reduced organ function, diminished reserves, and disrupted homeostasis, contributing to the frailty syndrome (FS) [1].”
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“Cohen ' s d indicates observed differences; it does not suggest remedial actions or define appropriate compensation [1].”
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“According to Sullivan and Feinn (2012), a p-value can indicate whether or not an effect exists.”
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“By avoiding within-group tests and presenting effect sizes (ηp²), we adhere to best practices for small, randomized trials (Sullivan & Feinn, 2012; Lakens, 2013).”
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“To determine ICC, between-cluster variance, within-cluster variance, and residual variance are required [14, 15].”
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“Cohen (1988) classified effect sizes as small (d = 0.2), medium (d = 0.5), and large (d ≥ 0.8) (Sullivan and Feinn, 2012).”
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“Interpretation of effect sizes was done using d = 0.2 as small, d = 0.5 moderate, and d = 0.8 large effect (Lakens 2013; Sullivan and Feinn 2012).”
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“Referring to the thresholds commonly used in clinical and psychological research: an intervention effect is considered small if the effect size is 0.2, moderate if it is 0.5, and large if it is equal to or greater than 0.8 [23].”
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“In the absence of appropriate previous literature to help us determine a more precise effect size for the primary analyses, we powered to detect a very small effect size (d = 0.1) [23].”
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“Statistical significance was set at p 0.05 [31, 32].”
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“To assess the relative influence of a predictor construct, the effect size is assessed apart from the p value presentation (Sullivan and Feinn 2012).”
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“Effect sizes were calculated using Cohen's d , where values of 0.2, 0.5, and 0.8 indicated small, moderate, and large differences between group means, respectively (Sullivan and Feinn 2012).”
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“Cohen classified effect sizes as small ( d = 0.2), medium ( d = 0.5), and large ( d ≥ 0.8) [41].”
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“This can be seen when evaluating the effect size using standardized regression coefficients (β) and variance explained (R²) (Parno et al. 2020 ; Sullivan and Feinn 2012).”
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“However, we acknowledge that these thresholds are arbitrary and context-dependent [38].”
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“The Cohen’s d effect size (ES) was calculated to measure the difference between the means of two groups and classified as follows: 0.20 for small effects, 0.50 for moderate effects, 0.80 for large effects, and 1.30 for very large effects 37 .”
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“SMD was used to measure the magnitude of difference between the groups rather than the p -value because of their insensitivity to sample size [16].”
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“Clinical signifi - cance in both conditions was assessed by evaluating effect sizes (Sullivan & Feinn, 2012), which were calculated by (1) performing Wilcoxon signed-ranked tests for nonparametric comparisons of related samples, and (2) dividing z scores by the square root of observations (Field,…”
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“In neurolinguistics, where effect sizes vary substantially across paradigms and populations, confidence intervals around effect estimates provide important information for evaluating both theoretical implications and practical significance (Sullivan & Feinn, 2012).”
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“Given attunement scores range from 1 to 8, these effects may be practically meaningful despite limited statistical significance (Schäfer & Schwarz, 2019; Sullivan & Feinn, 2012).”
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“67,68 Given the strong evidence supporting the MFIS ’ s ability to detect changes following program participation, 69,70 and its emerging psychometric properties in PD, 71 future RCTs evaluating the program in people with PD should consider incorporating the MFIS to better capture the program ’ s…”
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“…statistical significance (Shreffler & huecker, 2023). thus, very large surveys often detect statistically significant but trivial differences (Sullivan & Feinn, 2012). this underscores the need to focus on effect-size estimates (with confidence intervals) rather than p-values alone. the…”
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“Retaining study participants was challenging, implicating statistical power and risk of type II errors [55, 56].”
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“Due to the small sample size of the current study ( N = 36) and the potential impact of sample size on tests of significance, effect sizes may be more representative of treatment effects (Sullivan & Feinn, 2012) and therefore, were the focus of interpretation.”
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Influential
Metadata
- Authors
- Sullivan, G. M., & Feinn, R.
- Affiliations
- University of Connecticut (US)
- Corresponding author
- Sullivan, Gail M.
- Venue
- Journal of Graduate Medical Education
- Published
- 2012-09
- Volume
- 4
- Issue
- 3
- Pages
- 279-282
- ISSN
- 1949-8349 (ISSN-L)
- 1949-8357
- PMC
- PMC3444174
- OpenAlex
- W2107026277
- Cited by
- 5,553
- References
- 6
- Citations by year
- 2026: 607 · 2025: 877 · 2024: 759 · 2023: 547 · 2022: 574 · 2021: 499 · 2020: 416 · 2019: 419 · 2018: 320 · 2017: 222 · 2016: 215 · 2015: 83 · 2014: 9 · 2013: 4 · 2012: 2
- FWCI
- 35.75
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Journal of Graduate Medical Education (publishedVersion)
- Europe PMC (PubMed Central) (publishedVersion)
- PubMed Central (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Meta-analysis and systematic reviews
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
- Social Sciences › Education › Educational Research and Methods
- Keywords
- effect size, p-values, statistical significance, substantive significance, standardized mean difference, medical education research, educational intervention, meta-analysis, simulation-based training, resident confidence, test scores, interpretation of study results, graduate medical education, reporting guidelines
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