A p-value tells you whether an effect is likely to be different from zero; an effect size tells you how big it is. APA 7 recommends reporting effect sizes for primary results (APA, 2020), and examiners increasingly expect you to interpret them, not just list them. This guide explains the effect sizes you are most likely to meet in a thesis, gives the commonly used benchmarks with their sources, and explains when those benchmarks should not be used.
Why effect sizes matter
Statistical significance depends heavily on sample size. With 2,000 participants, a tiny difference that nobody would notice in practice can be highly significant; with 15 participants, a substantial difference may not reach significance. Effect sizes are largely independent of sample size, so they let readers judge the practical importance of a result and compare it with other studies (Sullivan & Feinn, 2012). They are also the basis of power analysis and meta-analysis.
Two families of effect size
- The d family expresses differences between means in standard deviation units, for example Cohen’s d and Hedges’ g.
- The r family expresses the strength of association or the proportion of variance explained, for example Pearson’s r, eta squared (η²), partial eta squared (ηp²), omega squared (ω²), R² in regression, and Cramér’s V for categorical data.
Cohen’s d and Hedges’ g
Cohen’s d is the difference between two means divided by a standard deviation, usually the pooled standard deviation of the two groups. A d of 0.50 means the group means are half a standard deviation apart. Hedges’ g applies a small correction that reduces the slight upward bias of d in small samples; with more than about 20 participants per group the two are almost identical (Lakens, 2013). Use the Cohen’s d calculator to compute d, g and a confidence interval from means and SDs.
| Cohen’s d | Cohen (1988) label |
|---|---|
| 0.20 | Small |
| 0.50 | Medium |
| 0.80 | Large |
For paired designs, the most common version is dz (mean difference divided by the SD of the differences). It can be considerably larger than d for the same data, so always say which version you report (Lakens, 2013).
Correlation coefficients (r)
Pearson’s r and Spearman’s ρ are themselves effect sizes. Cohen (1988) proposed .10, .30 and .50 as small, medium and large. The squared correlation, r², gives the proportion of shared variance. The non-parametric effect size r for the Mann-Whitney U and Wilcoxon tests, calculated as |z| / √N, is usually interpreted with the same benchmarks (Fritz et al., 2012).
Eta squared, partial eta squared and omega squared
These measure the proportion of variance in the dependent variable associated with an effect in ANOVA.
- Eta squared (η²) = SSeffect / SStotal.
- Partial eta squared (ηp²) = SSeffect / (SSeffect + SSerror). This is what SPSS reports. In one-way between-groups ANOVA it equals η², but in factorial and repeated measures designs it is larger and not comparable across designs (Richardson, 2011).
- Omega squared (ω²) is a less biased estimate of the population value and is recommended for small samples (Lakens, 2013).
| η² / ω² | Cohen (1988) label |
|---|---|
| .01 | Small |
| .06 | Medium |
| .14 | Large |
These benchmarks are often applied to partial eta squared as well, but strictly they were proposed for the proportion of total variance. Use them cautiously for ηp² from complex designs.
R² in regression
R² is the proportion of variance in the outcome explained by all predictors together. Cohen (1988) expressed regression effect sizes as f² = R² / (1 − R²), with .02, .15 and .35 as small, medium and large; these correspond to R² of roughly .02, .13 and .26. Report adjusted R² as well when you have several predictors. See the linear regression calculator.
Effect sizes for categorical data
For the chi-square test of independence, the usual effect size is Cramér’s V (equal to phi, φ, for 2 × 2 tables). Its interpretation depends on the size of the table: Cohen’s (1988) benchmarks for the related index w are .10, .30 and .50, which apply directly to V only when the smaller dimension of the table is 2. For larger tables the thresholds for V are lower. The chi-square calculator reports Cramér’s V. Odds ratios and risk ratios are common alternatives in health research.
Agreement and reliability coefficients
Cohen’s kappa for inter-rater agreement is usually interpreted with the labels of Landis and Koch (1977): .41–.60 moderate, .61–.80 substantial and .81–1.00 almost perfect. Cronbach’s alpha is a reliability coefficient rather than an effect size; see Cronbach’s alpha interpretation.
Summary table
| Effect size | Used with | Small | Medium | Large |
|---|---|---|---|---|
| Cohen’s d / Hedges’ g | t tests | 0.20 | 0.50 | 0.80 |
| r (Pearson, Spearman, or |z|/√N) | Correlation; Mann-Whitney, Wilcoxon | .10 | .30 | .50 |
| η² / ω² | ANOVA | .01 | .06 | .14 |
| f² | Regression | .02 | .15 | .35 |
| w (≈ Cramér’s V when min(rows, cols) = 2) | Chi-square | .10 | .30 | .50 |
Source for all benchmarks in this table: Cohen (1988).
Benchmarks are a last resort
Cohen himself presented these values as conventions for situations with no better information, and he warned against applying them mechanically (Cohen, 1988). An effect described as ‘small’ can be very important. For example, a cheap intervention that slightly improves exam pass rates across a whole country may matter a great deal. A ‘large’ effect in a tiny, biased sample may mean little. Whenever possible:
- Compare your effect size with those reported in similar studies or meta-analyses in your field.
- Consider the practical meaning in the original units, for example ‘students in the intervention group scored on average 5.3 marks higher’.
- Report a confidence interval for the effect size so readers can see its precision.
- Remember that some authors propose different thresholds for practical significance. Ferguson (2009), for example, suggests d ≈ 0.41 or r ≈ .20 as a recommended minimum effect size representing a practically significant effect in social science data.
Converting between d and r
For two groups of equal size, r = d / √(d² + 4), and d = 2r / √(1 − r²). So d = 0.50 corresponds to r ≈ .24, and r = .30 corresponds to d ≈ 0.63 (Fritz et al., 2012). Conversions are useful when comparing your result with studies that reported a different measure.
Reporting effect sizes in APA style
Report the effect size right after the test statistic and p-value, and describe it in words in the discussion:
Students who received feedback scored higher than those who did not, t(98) = 3.12, p = .002, d = 0.62, 95% CI [0.22, 1.02], a medium-to-large effect.
Teaching method had a significant effect on exam scores, F(2, 57) = 8.10, p < .001, η² = .22, indicating that teaching method was associated with 22% of the variance in scores.
Use a leading zero for d (which can exceed 1) but not for r, η², R² or V, which cannot (APA, 2020). Greek symbols such as η and ω are not italicised.
Roman Urdu mein khulasa
Effect size batata hai ke farq ya rishta kitna bara hai, jabke p-value sirf ye batati hai ke woh zero se mukhtalif hai ya nahi. Cohen (1988) ke mutabiq d = 0.20 chhota, 0.50 darmiyana aur 0.80 bara; r = .10, .30, .50; aur η² = .01, .06, .14. Lekin ye sirf rough rules hain, is liye apne field ki pichli studies se bhi compare karein. SPSS partial η² deta hai, to report karte waqt sahi naam likhein. APA 7 har main result ke saath effect size maangta hai, behtar hai confidence interval ke saath.
Frequently asked questions
What is a good effect size?
There is no universal ‘good’ value. Cohen’s (1988) conventions (d = 0.2, 0.5, 0.8; r = .1, .3, .5; η² = .01, .06, .14) are rough guides. Compare with similar studies whenever possible.
What is the difference between eta squared and partial eta squared?
Eta squared divides the effect’s sum of squares by the total; partial eta squared divides it by the effect plus error only. They are equal in one-way ANOVA but differ in factorial and repeated measures designs.
Should I report Cohen’s d or Hedges’ g?
Hedges’ g corrects a small bias in d and is preferred for small samples. With larger samples they are nearly identical. State which one you report.
Which effect size goes with a Mann-Whitney U test?
r = |z| / √N is commonly reported, interpreted with the same .10/.30/.50 benchmarks as correlations.
Do I need effect sizes if my result is not significant?
Yes. Reporting effect sizes and confidence intervals for non-significant results shows what effects remain plausible and helps future meta-analyses.
Related calculators
- Cohen’s d Effect Size Calculator
- One-Way ANOVA Calculator with Tukey HSD
- Chi-Square Test of Independence Calculator
- Test chooser: which statistical test should I use?
References
- American Psychological Association. (2020). Publication manual of the American Psychological Association (7th ed.). https://doi.org/10.1037/0000165-000
- Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum Associates.
- Ferguson, C. J. (2009). An effect size primer: A guide for clinicians and researchers. Professional Psychology: Research and Practice, 40(5), 532–538. https://doi.org/10.1037/a0015808
- Fritz, C. O., Morris, P. E., & Richler, J. J. (2012). Effect size estimates: Current use, calculations, and interpretation. Journal of Experimental Psychology: General, 141(1), 2–18. https://doi.org/10.1037/a0024338
- Lakens, D. (2013). Calculating and reporting effect sizes to facilitate cumulative science: A practical primer for t-tests and ANOVAs. Frontiers in Psychology, 4, 863. https://doi.org/10.3389/fpsyg.2013.00863
- Landis, J. R., & Koch, G. G. (1977). The measurement of observer agreement for categorical data. Biometrics, 33(1), 159–174. https://doi.org/10.2307/2529310
- Richardson, J. T. E. (2011). Eta squared and partial eta squared as measures of effect size in educational research. Educational Research Review, 6(2), 135–147. https://doi.org/10.1016/j.edurev.2010.12.001
- Sullivan, G. M., & Feinn, R. (2012). Using effect size—or why the P value is not enough. Journal of Graduate Medical Education, 4(3), 279–282. https://doi.org/10.4300/JGME-D-12-00156.1
Written and maintained by the ScholarCalc team. Last reviewed: November 2026.