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.
Table of Contents
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.
Official documentation
For the full reference behind this guide, read the NIST/SEMATECH e-Handbook page on measures of scale. It is the source the details above are drawn from, and the first place to check when an option or attribute name changes.
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.
Last updated on · Written by Dinesh Kumar R
