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 — especially with large sample sizes.

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):

| |d| | Effect Size | Practical meaning | |—|—|—| | 0.2 | Small | Noticeable but small real-world impact | | 0.5 | Medium | Visible and meaningful difference | | 0.8 | Large | Obvious and practically significant | | 1.2+ | Very large | Rare — strong intervention effect |

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. This is why reporting effect sizes matters — it enables future researchers to plan their studies properly.

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.