Next section: Significance test

Rearranging the equation,

.

Therefore, to go from an estimate of to an estimate of σ², you multiply the estimate of by n. For this example n = 4, so the estimate of σ² is: MSB = (4)(1) = 4. In short,

where n is the number of subjects in each group and is the variance of the sample means.

The significance tests associated with analysis of variance are based on the ratio of MSB to MSE. If the ratio is large enough, then the null hypothesis that the population means are equal can be rejected. The next section discusses the distribution of MSB/MSE and how to conduct a significance test.

Next section: Significance test