Quick answer: An effect size is a number that says how big a difference or relationship is, in units that transcend your sample — Cohen’s d for group differences, r for relationships, η² for ANOVA, odds ratios for categorical outcomes. p-values only rule out chance; effect sizes carry the science. A study can be “highly significant” with a trivial effect (huge n) or “non-significant” with a meaningful one (small n) — the effect size is what makes results comparable across studies and meta-analyses possible. The p-value partnership is explained in the p-value explainer.
The four families and their benchmarks
| Family | Statistic | Small / medium / large |
|---|---|---|
| Group difference (standardized) | Cohen’s d, Hedges’ g | 0.2 / 0.5 / 0.8 |
| Relationship strength | Pearson r | 0.1 / 0.3 / 0.5 |
| Variance explained (ANOVA) | η², partial η² | 0.01 / 0.06 / 0.14 |
| Categorical association | φ (phi), Cramér’s V, odds ratio | 0.1 / 0.3 / 0.5 (φ/V) |
Benchmarks are conventions, not laws — d = 0.45 for a cheap educational intervention can be consequential at scale, while d = 0.6 for an expensive drug with side effects may disappoint. Worked conversions keep them honest: two groups of means 72.1 and 66.4 with pooled SD ≈ 7.2 give d = 5.7/7.2 ≈ 0.78 — a medium-to-large effect, matching what our jamovi t-test walkthrough reports. Hedges’ g is the small-sample-corrected cousin; prefer it under n ≈ 20 per group.
Why effect size decides study value
- Planning: the expected effect size is the main input of a power analysis — the calculation is walked through in the power guide.
- Interpretation: a significant p with η² = 0.01 explains 1% of variance — statistically real, practically negligible; only the effect size reveals that.
- Meta-analysis: d, r and log-odds-ratios are the currencies studies are pooled in; no effect size, no synthesis.
- Reporting standards: APA requires effect sizes and CIs alongside p-values; their intervals are the honest-uncertainty view covered in the confidence intervals guide.
Every tool in our tutorials computes them: jamovi offers d, η² and φ as tick-boxes (the chi-square guide shows φ in action), R Commander prints them through its means and ANOVA dialogs, and the categorical reasoning behind φ/V is in the hypothesis testing guide. For one-to-one coaching on choosing, computing and defending effect sizes, Ampersand Academy teaches statistics one-to-one.
Frequently asked questions
What is an effect size in statistics?
A standardized measure of how large a difference or relationship is – Cohen d for group gaps, r for correlations, eta-squared for ANOVA, phi or odds ratios for categorical data. Unlike p-values, effect sizes do not shrink as samples grow.
Why is the p-value not enough?
Because p mixes effect size with sample size. A trivial difference becomes significant with enough data, and a meaningful one can miss significance with too little – only the effect size separates those cases.
What is a large effect size for Cohen’s d?
By convention 0.2 is small, 0.5 medium and 0.8 large – a d of 0.8 means the group means differ by 0.8 standard deviations. Context matters: even small effects can matter at scale or in cheap interventions.
What is the difference between eta-squared and partial eta-squared?
Eta-squared is the share of total variance a factor explains in the whole model; partial eta-squared isolates the factor against error variance alone, which is why partial values run larger in factorial designs.
Can an effect size be negative?
Yes for signed measures like d and r – the sign just encodes direction, for example group B scoring higher than group A. Magnitudes like eta-squared and Cramer’s V are always positive.