KIMRA

Research toolsEffect size

Cohen's d effect size

Computes the standardised mean difference between two independent groups, with Hedges' correction for small samples and a confidence interval.

Group 1
Group 2

Results

Cohen's d
1.00095% CI 0.463 to 1.537
Hedges' g (small-sample corrected)
0.987
Pooled standard deviation
2.0000
Conventional magnitude
Large (|d| ≥ 0.8)
Interval excludes zero
Yes

Cohen's thresholds are conventions, not findings. Whether an effect matters depends on the outcome and the field, not on the number alone.

When to use it

  • Reporting the magnitude of a difference in a unit-free way.
  • Preparing an effect size for inclusion in a meta-analysis.
  • Comparing findings measured on different scales or instruments.

Formula

  s_pooled = √( ( (n₁−1)s₁²  +  (n₂−1)s₂² ) / ( n₁ + n₂ − 2 ) )

  d  =  ( M₁ − M₂ ) / s_pooled

Hedges' correction for small-sample bias:

  g  =  d × ( 1  −  3 / ( 4(n₁ + n₂) − 9 ) )

Confidence interval:

  SE(d) = √( (n₁ + n₂)/(n₁n₂)  +  d² / (2(n₁ + n₂)) )
  CI    = d  ±  z · SE(d)

Worked example

Two groups of 30, with means of 10 and 8 and a standard deviation of 2 in each.

Group 1
M = 10, SD = 2, n = 30
Group 2
M = 8, SD = 2, n = 30

Pooled SD 2.00. Cohen's d = 1.00 (0.46 to 1.54). Hedges' g = 0.99.

The groups differ by a full pooled standard deviation. The interval excludes zero, and Hedges' correction barely moves the estimate because the samples are not small.