Standardized mean difference calculator

What this computes

The standardized mean difference (SMD) expresses the gap between two arms in units of pooled standard deviation, so a continuous outcome measured on different scales across studies can be pooled in a meta-analysis. This calculator takes the summary statistics you read off a paper (mean, standard deviation and sample size for each arm) and returns the SMD as Hedges g, the small-sample-corrected estimator, alongside its 95% confidence interval and the raw mean difference in the outcome's native units.

The formula

Cohen's d is the mean difference divided by the pooled within-groups SD; Hedges g multiplies d by the correction factor J, which removes the upward bias d carries in small samples.

MD        = m₁ − m₂
s_pooled  = √[ ((n₁−1)·sd₁² + (n₂−1)·sd₂²) / (n₁+n₂−2) ]
d         = MD / s_pooled
J         = 1 − 3 / (4·(n₁+n₂−2) − 1)
g         = J · d
Var(g)    = (n₁+n₂)/(n₁·n₂) + g² / (2·(n₁+n₂))
95% CI    = g ± 1.96·√Var(g)

These are the estimator and variance of Cochrane Handbook §6.5.1.2 and Hedges & Olkin (1985). The correction is negligible above roughly 40 total participants and matters most for small trials, where it pulls the estimate toward zero.

When it is valid

Use the SMD when the two arms measure the same construct on different instruments or scales, both arms report a mean and an SD, and the outcome is roughly continuous. Interpret the sign against your own coding of arm 1 versus arm 2. The tool does not assume which direction is beneficial.

When it is not

The SMD assumes a single pooled SD describes both arms. When the arm SDs differ by more than about twofold, that assumption is strained. The tool flags this inline. Do not standardize when the outcome is genuinely on one shared scale (report the raw mean difference instead), when the SDs you have are of change scores mixed with endpoint scores across studies, or when a group is smaller than two participants. If a paper reports SEs, confidence intervals or IQRs rather than SDs, recover the SD first, then bring it here.