Cohen's d Effect Size Calculator

Cohen’s d Effect Size

Cohen’s d measures the standardized difference between two group means. While a p-value tells you if an effect is statistically significant, Cohen’s d tells you how large that effect actually is.
Statistical significance does not imply practical importance, and the gap between the two widens as samples grow: with 10,000 people per group, a difference far too small to matter to anybody will still come back with p below 0.001.

Formula:

d = (M₁ − M₂) / Pooled SD

Pooled SD = √[ ((n₁−1)SD₁² + (n₂−1)SD₂²) / (n₁+n₂−2) ]

If sample sizes are equal, the pooled SD simplifies to: Pooled SD = √[ (SD₁² + SD₂²) / 2 ]

Interpreting Cohen’s d (Jacob Cohen, 1988):

Cohen’s own warning about that table. He offered those cutoffs reluctantly, for fields with no prior results to compare against, and they have been treated as law ever since. A d of 0.3 in a field where every published effect sits near 0.1 is large. A d of 0.5 for a drug competing against one that already delivers 0.9 is a step backwards. Compare against your own literature before you reach for the labels.

A more concrete reading: overlap. Convert d into the proportion of Group 2 that the average member of Group 1 scores above, which is Φ(d). A d of 0.5 puts the average Group 1 member at the 69th percentile of Group 2. A d of 0.2 puts them at the 58th, barely off the middle. The calculator reports this figure, and it is usually more persuasive to a non-statistical reader than the d itself.

Sign of d:

The sign indicates direction: positive d means Group 1 has a higher mean. Typically report the absolute value and state direction separately.

Alternative: Hedges’ g

For small samples (n < 20), Hedges’ g applies a correction factor: g = d × (1 − 3/(4(n₁+n₂)−9)) This calculator reports both d and g.

Relationship to statistical power:

Larger effect sizes require smaller samples to detect reliably. A power analysis uses Cohen’s d (along with α and desired power) to determine minimum sample size. That is the practical reason to report an effect size at all: it is what lets the next researcher work out how many participants they need.

Context matters:

In medicine, even a small d can be clinically important if the outcome is serious. In education research, a d of 0.4 is considered a threshold for meaningful impact (Hattie’s findings). Always interpret Cohen’s d in the context of the field and the outcome being measured.