A p-value tells you whether a difference between two groups is likely to be real rather than random noise. It says nothing about how big that difference is. Effect size — most commonly Cohen's d — fills that gap by putting the size of a difference on a standardized, comparable scale. This guide explains how Cohen's d is calculated, why the standard deviation gets pooled, and when to reach for Hedges' g instead.

Cohen's d vs. the p-value

A p-value answers "could this difference have happened by chance?" — it's a statement about statistical significance, and it depends heavily on sample size. With a large enough sample, even a trivially small, practically meaningless difference can produce a tiny p-value. Cohen's d answers a different question: "how big is this difference, in a way that doesn't depend on how many people were in the study?" A d of 0.1 stays a d of 0.1 whether the study had 20 participants or 20,000. Reporting both together — statistical significance and effect size — gives a complete picture: is the effect real, and does it matter?

Why pool the standard deviation

Cohen's d standardizes the raw mean difference by dividing it by a standard deviation, so the result is expressed in "how many standard deviations apart" rather than in the original units (points, dollars, milliseconds). Because two independent groups can have different standard deviations, Cohen's d uses a pooled standard deviation — a weighted average of both groups' spread, where each group's contribution is weighted by its sample size (specifically, n − 1, its degrees of freedom). This assumes the two groups' underlying variability is reasonably similar; if one group's spread is dramatically larger than the other's, some researchers prefer Glass's delta, which divides by only the control group's standard deviation instead of a pooled figure.

When to use Hedges' g instead of d

Cohen's d has a known small-sample bias — it tends to slightly overestimate the true population effect size when the samples are small. Hedges' g applies a correction factor, always a little less than 1, that shrinks d toward zero to compensate. The correction is largest for small samples and shrinks toward zero as the combined sample size grows past roughly 50, at which point d and g are nearly identical. As a rule of thumb: report Hedges' g instead of, or alongside, Cohen's d whenever either group has fewer than about 20 observations, which is common in pilot studies and small clinical trials.