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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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Research works printed but not linked: 1
- 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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“Cohen’s d is a measure of effect size that quantifies the standardized difference between two means, in this case, human and model performance (Sullivan & Feinn, 2012).”
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“P -values indicate whether a difference exists, but they do not describe the difference in the effect size [9].”
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“Sullivan and Feinn (2012) stated that both the size of the effect and the p -value need to be reported this is because the p -value can tell whether there is an effect, but it cannot tell how big the effect is.”
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“…intervention effectiveness: • Pre-Post Intervention Analysis: Paired t-tests or Wilcoxon signed-rank tests were commonly used to compare outcome measures before and after physical activity interventions, with effect sizes calculated to determine clinical significance (Sullivan & Feinn, 2012).”
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“%) was mainly due to scheduling changes and non-confirmed appointments by mothers who had initially expressed their availability for the trial.”
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“Broader distributional shifts (severity between 0.5 and 0.8, since this signals a medium to large effect where the joint feature-target relationship is meaningfully distorted [48]) that involve shifts in the relationship of multiple features with the model’s target variable trigger partial…”
InfluentialRangarajan, P., & Boyle, J. (2025) · arXiv (Cornell University) · doi:10.48550/arxiv.2510.15889
“Effect size calculations indicate large effect sizes (Cohen’s d > 0.8) for framework improvements in six of eight evaluated scenarios, with medium effect sizes observed in the remaining two scenarios [19].”
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“…the number of variables entered for regression analyses resulted in imprecise estimates with large con fi dence intervals (Wooldridge, 2012), the sample size obtained had suf fi cient power to detect medium to large effect sizes for all the outcomes in sensitivity analyses (Sullivan & Feinn, 2012).”
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“The effectiveness of the intervention will be further determined with the calculation of effect sizes expressed in Cohen’s d as insignificant (0; 0.19), small (0.2; 0.49), moderate (0.5; 0.79) and large (> 0.8) 69 with their respective 95% CI.”
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“Based on conventional benchmarks, η p ² values of .01, .06, and .14 and Cohen’s d values of .2, .5, and .8 were interpreted as small, medium, and large effects, respectively (Richardson, 2011; Sullivan & Feinn, 2012).”
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“Since 0.6 is a medium effect size as per Cohen’s d (Sullivan & Feinn, 2012), it shows that the median of post-intervention scores is reasonably greater than that of the pre-intervention scores.”
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“…effect size of a variable in a group A with respect to a reference group B , defined as: The review of the various effect size indices captured in Sullivan and Feinn (2012) stipulates that the magnitude of the odds ratio ranges between small when evaluated to 1 : 5, medium , when evaluated to 2,…”
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“Considering the large sample size included in this analysis and the difference in sample size between the 2 groups, t -tests were conducted to assess the statistical differences in means, and Cohen’s d statistic was calculated to quantify the effect sizes [31, 32].”
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“This is generally considered to be the minimum standard for a medium or moderate difference that would be meaningful and visible to the naked eye of a careful observer (Sullivan & Feinn, 2012).”
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“Conclusions were derived from the magnitude of the effect sizes based on the between-group difference of the within-group change in outcomes of interest, and surrounding 95% CI, rather than the p-values [47 , 48 ].”
Hermosaningtyas, A. A., Kroma, A., Gornowicz‐Porowska, J., Urbańska, M., Budzianowska, A., & Kikowska, M. A. (2025) · Applied Sciences · doi:10.3390/app15158625
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“Because statistical tests can yield significant p values for small differences in large samples that are not clinically important, we used standardized mean difference (SMD) to measure the effect size between groups [11].”
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“Regarding maximizing differences, a threshold of 1.5 SD units is consistent with a very large effect size (Cohen, 1988), and that difference translates, on average, to participants drawn from nonoverlapping distributions of more than 71% (Sullivan & Feinn, 2012).”
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“Cohen’s d is a specific type of effect size index with values categorized by Cohen as small (d = 0.2), medium (d = 0.5), and large (d ≥ 0.8), asserting that a medium effect size of 0.5 is perceptible to a careful observer without the aid of instrumentation (Sullivan & Feinn, 2012).”
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“The sample had power to find an effect (Ellis 2010; Fisher 1935; Lakens 2024; Norman 2010; Smith 2024; Social Sciences Statistics and Stangroom 2024; Sullivan and Feinn 2012; Van Voorhis and Morgan 2007), that is, per cell n s > = 12 exceeded the number of dependent variables.”
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“According to standard interpretations (Sullivan and Feinn 2012), this represents a “small” effect size.”
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“In addition, the Cohen's d was calculated for the comparison of parametric data and interpreted as follows; 0.00 < 0.20 as very small, 0.20 < 0.50 as small, 0.50 < 0.80 as medium and ≥ 0.80 as large [34].”
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“No se realizaron análisis de prueba de hipótesis para la normalidad, ya que como la muestra fue grande, los p valores del análisis tienden a ser estadísticamente significativos llevando a que se cometa un error de tipo I (Sullivan & Feinn, 2012).”
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“First, the overall sample size is small, particularly for males, which can impact the robustness of the findings and their association with effect size [73].”
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“Therefore, a big data research typically includes the ASD (Birkeland et al., 2017; Huang et al., 2023; Sullivan and Feinn, 2012), a statistical metric used to assess the differences between two cohorts that is not influenced by sample size, unlike the P value.”
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“Moreover, it is highly dependent on sample size [21].”
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“According to Cohen, “a medium effect of 5 is visible to the naked eye of a careful observer” (Fritz et al., 2012; Ho et al., 2019; Sullivan & Feinn, 2012). data has a normal distribution for the control group but not for the intervention group.”
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“Previous studies reported that Student's t‑tests are suitable when sample size is small and effect size is large (39,40). in addition, bone fracture healing scores were analyzed using a Kruskal‑Wallis test followed by dunn's post hoc analysis.”
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“However, the limitations of p ‐values have been widely discussed [4, 5], as they only indicate statistical significance without addressing the clinical importance of the findings.”
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“Cohen ’ s d test was used to investigate the effect size of 6MWT parameters (20).”
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“To examine overlaps of patterns of psychedelic use, we computed percentages and Pearson´s correlations (identical to Phi for bivariate measures) for which r > ± 0.2 indicates small effects, r > ± 0.5 medium effects, and r > ± 0.8 large effects 53 .”
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“…Pearson’s correlations (which is equivalent to Phi) to examine the strength of associations between the indicators of whether or not individuals self-report knowledge concerning a neurotechnology, whereby r > ± 0.2 indicate small effects, r > ± 0.5 medium effects, and r > ± 0.8 large effects 73 .”
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“Each classifier was ranked on a three-level scale as follows for Cohen’s d: small (d = 0.2), medium (d = 0.5), and large (d ≥ 0.8) [55] and Cliff’s delta: small ( δ : 0.11–0.27), medium ( δ : 0.28–0.42) and large ( δ > 0.43) [56].”
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“The effect size of approximately 0.34–0.39 in our two exploratory analyses would be classified as small–moderate, providing evidence of a practical and non-negligible difference in perceived empathy between the male GC and female GC scenarios (Hojat & Xu, 2004 ; Sullivan & Feinn, 2012).”
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“35 The signi fi cance level was set as p 0.05.”
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“The ob tained Cohen’s d value suggests a meaningful differ ence between the scores, and even though it is lower than in most validation studies, it is still at a satisfac tory level, as d > 0.8 is considered a large effect size [10, 20–22].”
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“Cohen's d was calculated to estimate treatment effect sizes (Sullivan and Feinn 2012), and statistical significance was set at p < 0.05, two‐tailed.”
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“With a small effect size of 0.14 [20–22], power 80% and significance level of 0.05% a sample size of 350 was deemed adequate.”
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“16 We assumed a medium effect size ( d = 0.5), so as not to overestimate participants ’ learning at the end of training, and an alpha level of .05 and a power 1 − β of 0.8, since these are the most conventionally accepted values in most fi elds 17 – 19.”
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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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