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Within-Group and Between-Group Variance
For two groups:
$$\sigma^2=\frac{n_1\sigma_1^2+n_2\sigma_2^2}{n_1+n_2}+\frac{n_1n_2}{(n_1+n_2)^2}(\bar{x}_1-\bar{x}_2)^2$$
Usage
- Useful when the individual group variances and means are known.
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Within-Group and Between-Group Variance
For two groups:
$$\sigma^2=\frac{n_1\sigma_1^2+n_2\sigma_2^2}{n_1+n_2}+\frac{n_1n_2}{(n_1+n_2)^2}(\bar{x}_1-\bar{x}_2)^2$$
Usage
- Useful when the individual group variances and means are known.
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