Which effect size should you report for each test?

Most journals now require one. Here is the mapping.

The mapping

| Test | Effect size | |---|---| | Independent t-test | Cohen's d, or Hedges' g for small samples | | Paired t-test | Cohen's d for paired data | | One-way ANOVA | Eta squared (η²) or omega squared (ω²) | | Factorial ANOVA | Partial eta squared (ηp²) | | Repeated-measures ANOVA | Partial eta squared | | Mann-Whitney U | r, calculated as z / √N | | Wilcoxon signed-rank | r, same formula | | Kruskal-Wallis | Epsilon squared or eta squared based on H | | Chi-square (2x2) | Odds ratio, risk ratio, or phi | | Chi-square (larger) | Cramér's V | | Correlation | r itself, or r² for variance explained | | Linear regression | R², plus standardised coefficients | | Logistic regression | Odds ratios with confidence intervals |

The benchmarks, and why to be careful with them

Cohen's conventions (d of .2 small, .5 medium, .8 large; r of .1, .3, .5) are useful only as a rough orientation. Cohen proposed them reluctantly and for a specific literature.

What counts as large depends entirely on your field. A d of .2 for a cheap public-health intervention across a population can matter enormously. A d of .8 in a tightly controlled in vitro assay may be unremarkable.

Interpret against comparable studies in your own area, not against a table.

Report the confidence interval

An effect size without an interval is an estimate presented as a fact. d = 0.62, 95% CI [0.11, 1.13] tells your reader the effect is probably positive and possibly small, which is honest. d = 0.62 alone does not.

Omega squared over eta squared

Eta squared is biased upward, particularly with small samples. Omega squared corrects for this and is the better choice where your software provides it.

In Plotara

Effect sizes are reported with every test, alongside confidence intervals, and included in the Methods text and the Python export.