Two Estimates of Variance (2 of 5)

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Therefore, if MSB is sufficiently larger than MSE, the null hypothesis can be rejected. If MSB is not sufficiently larger than MSE then the null hypothesis cannot be rejected. How much larger is "sufficiently" larger? That is determined by the statistical analysis explained in a later section.

How σ² is Estimated by MSE
The estimation of σ² by MSE in the analysis of variance is exactly the same as the estimation of σ² by MSE in the construction of confidence intervals on a linear combination of means and in the testing of linear combinations of means. It is very similar to the estimation of σ² by MSE in the construction of confidence intervals on the difference between means and in the testing of differences between means. The only difference is that there are "a" groups instead of two groups.

For simplicity, assume that the sample sizes in each of the "a" samples are equal. The variance (σ²) is estimated by s² in each of the samples. The average of these "a" estimates of σ² is then used as an overall estimate of σ².