Effect Size Calculator Formula

Understand the math behind the effect size calculator. Each variable explained with a worked example.

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Formulas Used

Cohen's d

cohens_d = (mean1 - mean2) / pooled_sd

|d|

abs_d = abs((mean1 - mean2) / pooled_sd)

Pooled SD

pooled = pooled_sd

Raw Difference

raw_diff = mean1 - mean2

Variables

Variable	Description	Default
`mean1`	Group 1 Mean	78
`mean2`	Group 2 Mean	72
`s1`	Group 1 SD	10
`s2`	Group 2 SD	12
`pooled_sd`	Derived value`= sqrt((pow(s1, 2) + pow(s2, 2)) / 2)`	calculated

How It Works

How to Calculate Cohen's d

Formula

d = (Mean1 - Mean2) / Pooled SD

where Pooled SD = sqrt((s1^2 + s2^2) / 2)

Cohen's d expresses the difference between two means in standard deviation units. Guidelines: d < 0.2 = negligible, 0.2-0.5 = small, 0.5-0.8 = medium, > 0.8 = large. Effect size is independent of sample size, unlike the p-value.

Worked Example

Group 1: mean = 78, SD = 10. Group 2: mean = 72, SD = 12.

mean1 = 78mean2 = 72s1 = 10s2 = 12

01Pooled SD = sqrt((100 + 144) / 2) = sqrt(122) = 11.045
02d = (78 - 72) / 11.045 = 6 / 11.045 = 0.5432
03|d| = 0.5432 which is a medium effect size

Frequently Asked Questions

Why is effect size important?

Statistical significance (p-value) depends on sample size; with enough data, trivial differences become significant. Effect size measures practical significance independently of sample size.

What are typical benchmarks for Cohen's d?

Cohen proposed: 0.2 = small, 0.5 = medium, 0.8 = large. However, context matters. In clinical trials, a small effect may be clinically meaningful; in education, a medium effect might be unremarkable.

Are there other effect size measures?

Yes. Hedges' g corrects for small-sample bias. Glass' delta uses only one group's SD. For correlations, r itself is an effect size. For ANOVA, eta-squared or omega-squared are used.

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