Effect Sizes: Why Significance Isn't Enough and How to Report Cohen's d, η² and r
What an effect size is, why APA 7 requires it, which measure fits each test (d, η², r, V, R², odds ratio), how to get it in SPSS and how to interpret and report it.
Part of the series: Statistical Analysis for a Seminar Paper or Thesis: The Complete Guide
"A significant difference was found" doesn't say how big the difference is. With 2,000 participants a tiny half-point difference is significant; with 15, a large and important one may not be. The effect size answers the question significance can't: how much does it matter? That's why APA 7 requires it, and supervisors and graders notice when it's missing.
Which measure for which test
| Test | Effect size | small / medium / large |
|---|---|---|
| t-test | Cohen's d | 0.2 / 0.5 / 0.8 |
| ANOVA | η² (or partial η²) | 0.01 / 0.06 / 0.14 |
| Pearson / Spearman correlation | r itself | 0.1 / 0.3 / 0.5 |
| Chi-square | Cramér's V (Phi for 2×2) | 0.1 / 0.3 / 0.5 (df = 1) |
| Linear regression | R² (and Cohen's f²) | 0.02 / 0.13 / 0.26 (f²) |
| Logistic regression | odds ratio (Exp(B)) | depends on context |
| Mann-Whitney | r = Z / √N | 0.1 / 0.3 / 0.5 |
Cohen's thresholds are a rough guide, not a law. In some fields (educational interventions, for example) d = 0.3 is an impressive effect.
Getting it in SPSS
- Cohen's d: SPSS 27+ prints it in the t-test Effect Sizes table; older versions: mean difference divided by the pooled SD.
- η²: One-Way ANOVA's Effect Sizes table (recent versions); in GLM Univariate tick Estimates of effect size for partial η².
- Cramér's V: Crosstabs → Statistics → Phi and Cramer's V.
- R²: the regression's Model Summary table.
- r for Mann-Whitney: by hand - the output's Z divided by the square root of N.
Reporting it
The effect size goes right after p, in the same sentence:
"t(98) = 2.47, p = .015, d = 0.49" · "F(2, 147) = 11.42, p < .001, η² = .13" · "χ²(2, N = 180) = 9.84, p = .007, V = .23"
Add words when they help the reader: "...a medium-sized difference". In the discussion, the effect size is what lets you say whether a finding matters in practice.
Effect sizes for non-significant results
Report them too. A d = 0.45 that missed significance with 20 per group is an interesting finding: it suggests the sample was too small. That's exactly the link to sample size and power analysis, where the expected effect size decides how many participants you need.
Common mistakes
- Reporting only p - the most common mistake in student papers.
- Mixing up η² and partial η²: identical in a one-way ANOVA, not in a two-way. Say which you report.
- Not naming the measure - "0.49" alone means nothing.
- Calling r = .5 "a large effect" as if it proved causation.
FAQ
Will my supervisor really check? Yes - it's one of APA 7's most visible requirements.
Where does it fit? Steps 6-7 of 7, reading the output and writing the results: Statistical analysis for a seminar paper: the complete guide. Want someone to check your results chapter before you submit? Tell us.
Tell us what you need, and we'll come back with an expert in Statistical analysis and a quote.
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