Effect Size Calculator
Cohen's d from two groups' summaries — how many standard deviations apart the means sit — with Hedges' small-sample correction beside it and the convention bands named as conventions.
Effect Size Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- Two-group summaries with a pooled SD — no paired-design d or Glass's delta
- Normal-theory conventions; skewed data deserve a robust alternative (out of scope)
In short: Group 1: n = 40, mean 72, s = 9. Group 2: n = 45, mean 68, s = 8. The pooled standard deviation is √((39×81 + 44×64)/83) = 8.484571, so Cohen's d = (72−68)/8.484571 = 0.471444 — the means sit 0.47 SD apart. Hedges' correction J = 1 − 3/(4×83−1) = 0.990937 trims it to g = 0.467171, the small-sample-honest version. By the conventional bands this reads SMALL — 0.471444 sits a hair under the 0.5 medium line, which is exactly why the bands are printed as conventions rather than grades. Translated to the correlation scale: r ≈ 0.229434. A real, visible effect that no p-value alone would size.
Formula
d = (m₁−m₂)/sₚ · sₚ = √(((n₁−1)s₁²+(n₂−1)s₂²)/(n₁+n₂−2)) · g = d·(1 − 3/(4df−1)) · r = d/√(d²+4)
The pooled SD weights each group's variance by its degrees of freedom — the honest middle when sizes differ. Hedges' J shrinks d by a factor that matters most below ~50 total n, because d estimated from small samples runs hot. The bands (0.2, 0.5, 0.8) are Cohen's conventions for behavioural research, not boundaries of nature.
Worked Example
- Enter each group's n, mean and SD — summaries, not raw lists.
- Read d: the mean gap measured in pooled SDs.
- Quote Hedges' g when the groups are small; quote the band with the words “convention” attached.
- Use the r translation when your audience thinks in correlations.
Defaults: d = 0.471444, sₚ = 8.484571, J = 0.990937, g = 0.467171, r = 0.229434 — the small band, a hair under 0.5. Drive the gap to 8 points: d = 0.942888, large by the same conventions.
Strengths & Limits Of This Model
Where this engine is strong
- Hedges' correction printed beside d with its J factor shown
- Bands named as conventions, direction printed explicitly
Where it stops
- No confidence interval on d
- No correction for unequal variances (Glass's delta)
Practical Use Cases
Research synthesis
comparable effect sizes across studies
Product experiments
how big, not just how sure
Teaching
significance vs size, separated cleanly
Methodology & Editorial Standards
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Effect Size Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
Why do I need an effect size if I already have a p-value?
Because they answer different questions: the p-value mixes size with sample — a trivial gap turns significant at huge n, and a huge gap stays non-significant at tiny n. d strips the sample size back out and states the separation in shared units. The pair is honest; either one alone is a sales pitch.
Why pool the two SDs instead of averaging them?
The pooled SD weights each group by its degrees of freedom, so a group of 40 counts more than a group of 5 — the honest denominator for a shared yardstick. With equal n it reduces to the root-mean-square of the two SDs; with unequal n the plain average quietly lets the small group punch above its evidence.
When does Hedges' correction matter?
J = 1 − 3/(4df−1) is nearly 1 at large samples (0.997 at df = 250) but visibly below 1 when the groups are small — at df = 18 it trims about 4%. d estimated from small samples runs systematically hot, and g is the debiased version. Under roughly 50 total subjects, quote g; above it, the two agree to noise.
The bands call 0.471444 “small.” Is a small effect unimportant?
No — and the word is Cohen's, not nature's. A small effect on a high-volume process can be enormous in dollars; a large effect on a rare event can be a rounding error. The bands are a shared vocabulary for behavioural research, which is why the card names them as conventions and lets your context price the consequence.
Why translate d into r?
Different audiences store intuition in different currencies. r = d/√(d²+4) puts the same separation on the correlation scale, where “shared variance” readers live. At the defaults, r ≈ 0.229434 sounds small until you square it — about 5% common variance, which is the same fact wearing honest clothes.
What if both SDs are zero?
Then there is no yardstick: the pooled SD is 0 and d divides by zero. Two groups of identical values have no measurable spread, so “how many SDs apart” has no answer. The page refuses by name rather than print a limit that would flatter any difference.
Negative d — is that a problem?
Only of ordering: a negative sign means group 2's mean is the higher one. The convention bands key on magnitude; the card prints the direction explicitly so nobody infers importance from a minus sign.
Does this page test whether the difference is significant?
No — deliberately. Significance is the hypothesis-test pages' question; this page sizes the effect the test would be run ON. The honest workflow runs both: size it here, test it there, and quote them as the separate sentences they are.