Cohen's d effect size & Pooled Standard Deviation formula

Statistical significance (p-value) vs practical significance (Cohen's d)

Cohen’s d expresses a mean difference in pooled-standard-deviation units. Unlike a test statistic, it does not multiply by the square root of sample size, but its estimate and precision still depend on the samples; unequal sizes also affect the pooled variance weighting.

This version uses sample standard deviations and weights each variance by n-1. It assumes independent groups and a common-variance interpretation. It is not a paired-sample effect-size formula. The sign depends on which group is subtracted.

The familiar 0.2, 0.5 and 0.8 thresholds are rough conventions, not universal measures of practical importance. Domain context and uncertainty matter. Small samples can bias d; no Hedges correction or confidence interval is calculated here.

Pooled Standard Deviation and Cohen's d formulas

Uses degrees-of-freedom weighting (C2 - 1) and (F2 - 1) so unequal group sizes (e.g., n1 = 30 vs n2 = 15) weight variances accurately.

=IF(OR(COUNT(A2:F2)<>6,C2<2,F2<2,MOD(C2,1)<>0,MOD(F2,1)<>0,B2<0,E2<0),"Invalid group statistics",IF(B2^2+E2^2=0,"Undefined zero dispersion",ROUND((A2 - D2) / SQRT(((C2 - 1) * (B2 ^ 2) + (F2 - 1) * (E2 ^ 2)) / (C2 + F2 - 2)), 4)))

Inspect the pooled standard deviation

Returns the pooled standard deviation only; it does not classify the effect size.

=IF(OR(COUNT(A2:F2)<>6,C2<2,F2<2,MOD(C2,1)<>0,MOD(F2,1)<>0,B2<0,E2<0),"Invalid group statistics",ROUND(SQRT(((C2 - 1) * (B2 ^ 2) + (F2 - 1) * (E2 ^ 2)) / (C2 + F2 - 2)), 4))

Further reading

• Microsoft Support — STDEV.S function
• Microsoft Support — SQRT function
• NIST — Degrees-of-freedom pooling