Effect Size Calculator

In short An effect size says how BIG a difference is, which is the question a p-value cannot answer. The two samples loaded above give Cohen's d = 2.1918 — the difference between the means expressed in pooled standard deviations — which also comes out as a correlation of 0.7387 and an η² of 0.5457. In plain terms, 98.6% of the first group scores above the AVERAGE of the second. Hedges' g of 2.0723 is the same figure corrected for small-sample bias, and it is always slightly smaller; with 14 degrees of freedom the correction is 5.45%, and it matters below about twenty per group. The reason to report one at all is that a p-value shrinks as you collect more data while an effect size does not. Two studies can share a p-value and disagree completely about whether the effect is worth acting on, and a very large sample will return p < 0.001 for a difference nobody could notice. The 0.2 / 0.5 / 0.8 landmarks are Cohen's own rough guide, and he explicitly warned against them being treated as thresholds — what counts as large depends entirely on the field and the cost of acting. A d of 0.2 from a cheap intervention across a population can matter far more than a d of 1.0 from an expensive one.