Effect Size Calculator — computation & translation

This calculator computes and translates effect sizes for within t-tests (repeated measures) and between t-tests (independent groups) — with exact statistics for your own study. It shows three standardizations at once — d_z, d_rm, d_av — as well as three small-sample corrections and three CI methods. For a conceptual introduction with a guided example see the Effect Size tutorial.

A psychologist is investigating whether an 8-week mindfulness training improves well-being. Within: 40 participants, M_pre=45.8 (SD=8.4), M_post=52.4 (SD=9.6), r=.65. Convention: d = post − pre, d > 0 = increase. Between: 40 participants per group (waitlist control vs. training). Convention: d = intervention − control, d > 0 = intervention higher — parallel to within, so the same raw data yields the same sign in both modes.

dz — difference-score SD as denominator; usable directly for t-test power and CLES (Wuensch).
drm — d_z · √(2(1−r)) (Becker 1988): equals d_av under variance homogeneity, equals d_z at r=.5.
dav — average SD as denominator (Lakens 2013); no r in the denominator.

d_av is the most comparable to between designs. Since the pre-post correlation doesn't enter the denominator, d_av is — ceteris paribus — identical to Cohen's d from an independent-groups comparison. This allows a direct comparison across designs: a within-d_av of 0.5 means the same as a between-d_s of 0.5. d_z and d_rm, by contrast, depend on r and are design-specific.

j (Hedges) — 1 − 3/(4(n−1)−1); the most common.
nag (Nakagawa) — 1 − 3/(4(2n−2)−1); recommended for within designs.
Bon (Bonett) — √((n−2)/(n−1)); based on variance unbiasedness.

Bonett (2015) approx: z-based (Equations 8, 9, 16). Available for d_z, d_rm, d_av.
Rosenthal (1994) approx: t-based, only for d_rm — same SE as Bonett there, but crit_t instead of crit_z. No Rosenthal CI is defined in the original literature for d_z and d_av.
NCT (exact): noncentral t-distribution via direct numerical integration (Simpson's rule) of the definition T=(Z+ncp)/√(V/df); CDF inversion by bisection yields the ncp bounds. Accurate for arbitrary df, including non-integer ones (e.g. Welch df).

Whether variance homogeneity holds is a substantive judgment — the tool doesn't make it for you, but always shows both effect-size families:
A) Student's t — pooled SD, assumes equal population variances: d_s, g_s, with Bonett, Rosenthal, and NCT CIs.
B) Welch's t — Welch-Satterthwaite df, no homogeneity assumption (Delacre, Lakens & Leys 2017 recommend this as the default): dWelch (unweighted 1:1 average of the variances) and gWelch (Hedges correction with df_Welch), plus an alternative t-to-d conversion d = tWelch·√(1/n₁+1/n₂) (Borenstein et al. 2009) — identical to d_Welch at n₁=n₂, otherwise diverging. Both get an NCT CI by rescaling conf.limits.nct(tWelch, dfWelch) — the same trick used to get d_rm's CI from d_z's. For Welch, there is deliberately no closed-form approximate CI (Bonett-style) here — a reliable source for the variance formula under heteroscedasticity is lacking.

Upload a CSV file with two numeric columns. In within mode: column 1 = measurement 1 (pre), column 2 = measurement 2 (post). In between mode: column 1 = control, column 2 = intervention (different lengths allowed). The first row is treated as a header if it's non-numeric.

Bonett, D. G. (2015). Interval estimation of standardized mean differences in paired-samples designs. Journal of Educational and Behavioral Statistics, 40(3), 306–315.
Rosenthal, R. (1994). Parametric measures of effect size. In H. Cooper & L. V. Hedges (Eds.), The Handbook of Research Synthesis. Russell Sage Foundation.