Enter two independent samples (means, standard deviations and sizes) to compute the t value and p value and test whether the two population means differ significantly.
| Item | Formula / Note | Source / Standard |
|---|---|---|
| Pooled-variance t statistic | t = (xbar1 - xbar2) / (s_p · sqrt(1/n1 + 1/n2)) | Student (1908), The probable error of a mean, Biometrika 6(1) |
| Pooled variance | s_p^2 = ((n1-1)s1^2 + (n2-1)s2^2) / (n1 + n2 - 2) | NIST/SEMATECH e-Handbook of Statistical Methods §1.3.5.3 |
| Welch correction | t = (xbar1 - xbar2)/sqrt(s1^2/n1 + s2^2/n2), df by Welch-Satterthwaite | Welch BL (1947), The generalization of Student's problem..., Biometrika 34 |
| Assumptions | Independent samples, near-normal populations, homogeneity of variance (Levene test) | NIST/SEMATECH e-Handbook of Statistical Methods §1.3.5.3 |