Effect Size Interpretation Guide
Conventional thresholds for the most commonly reported effect size measures. These benchmarks (primarily from Cohen, 1988) are starting points — always interpret effect sizes in the context of your field and research question.
Interpretation Thresholds
| Measure | Used With | Small | Medium | Large |
|---|---|---|---|---|
| Cohen's d | t-tests | 0.20 | 0.50 | 0.80 |
| Hedges' g | t-tests (small samples) | 0.20 | 0.50 | 0.80 |
| η² (eta-squared) | ANOVA | .01 | .06 | .14 |
| Partial η² (partial eta-squared) | Factorial ANOVA | .01 | .06 | .14 |
| Pearson r | Correlation | .10 | .30 | .50 |
| R² | Regression | .02 | .13 | .26 |
| Cramér's V | Chi-square | .10 | .30 | .50 |
| Odds Ratio (OR) | Logistic regression | 1.5 | 2.5 | 4.3 |
Formulas
Cohen's d
$$d = \frac{\bar{X}_1 - \bar{X}_2}{s_p}$$
where \(s_p\) is the pooled standard deviation. Use for independent-samples t-tests with roughly equal group sizes.
Hedges' g
$$g = d \times \left(1 - \frac{3}{4(n_1 + n_2) - 9}\right)$$
Bias-corrected version of Cohen's d. Preferred when either group has n < 20.
Eta-squared (η²)
$$\eta^2 = \frac{SS_{\text{between}}}{SS_{\text{total}}}$$
Proportion of total variance explained by the IV. Tends to overestimate in small samples.
Partial η²
$$\eta_p^2 = \frac{SS_{\text{effect}}}{SS_{\text{effect}} + SS_{\text{error}}}$$
Proportion of variance explained after removing other effects. Standard output in SPSS for factorial ANOVA.
Pearson r
$$r = \frac{\sum (X_i - \bar{X})(Y_i - \bar{Y})}{\sqrt{\sum (X_i - \bar{X})^2 \sum (Y_i - \bar{Y})^2}}$$
Ranges from −1 to +1. Pearson r is both a test statistic and an effect size measure.
R²
$$R^2 = 1 - \frac{SS_{\text{residual}}}{SS_{\text{total}}}$$
Proportion of variance in the DV explained by all predictors. Use adjusted R² when comparing models.
Cramér's V
$$V = \sqrt{\frac{\chi^2}{N \cdot (k - 1)}}$$
where \(k\) = min(rows, columns). Ranges from 0 to 1. Use with chi-square test of independence.
Odds Ratio (OR)
$$OR = \frac{p_1 / (1 - p_1)}{p_2 / (1 - p_2)}$$
OR = 1 means no effect. OR > 1 means higher odds in group 1. Always report with a 95% CI.
Important Caveats
- Cohen's benchmarks are guidelines, not rules. A "small" effect in clinical psychology may be life-changing; a "large" effect in education may be routine.
- Always interpret in context. Compare your effect sizes to those found in similar published studies in your field.
- Confidence intervals matter. A point estimate of d = 0.50 with a CI of [0.05, 0.95] is far less informative than d = 0.50, 95% CI [0.40, 0.60].
- η² vs. partial η²: SPSS reports partial η² by default. They are equal in one-way designs but can differ substantially in factorial designs.
- Odds ratios are symmetric around 1, not 0. An OR of 0.5 and an OR of 2.0 represent the same strength of association in opposite directions.