Enter two sample sizes and standard deviations to compute the pooled variance as a weighted average, used for the equal-variance assumption before a two-sample t-test.
输入两组样本量 n₁、n₂ 与方差 s₁²、s₂²，求合并方差。
| Item | Formula / Note | Source / Standard |
|---|---|---|
| Pooled variance (two groups) | 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 |
| Pooled variance (k groups) | s_p^2 = sum(n_i - 1)s_i^2 / sum(n_i - 1) | NIST/SEMATECH e-Handbook of Statistical Methods §1.3.5.3 |
| Use in two-sample t-test | SE = s_p · sqrt(1/n1 + 1/n2) | Student (1908), The probable error of a mean, Biometrika 6(1) |
| Homogeneity assumption | Pooling is valid only under homogeneity of variance (Levene or Bartlett test) | Levene H. (1960); Bartlett MS (1937), Properties of sufficiency... |