Therefore,

.

(Click here for the formula for unequal sample sizes.) The example data from the section on testing of linear combinations of means are reproduced here.

The means af the Aspirin, Tylenol, and Placebo conditions are 4, 3, and 2 respectively. The sample variances are 1.334, 1.334, and 0.666, The MSE is the mean of the three sample variances and is therefore:Aspirin Tylenol Placebo 3 2 2 5 2 1 3 4 3 5 4 2

(1.334 + 1.334 + 0.666)/3 = 1.111.

Estimating σ² using the sample means is slightly more complicated than using the sample variances. The first step is to use the sample means to estimate the variance of the sampling distribution of the mean (). In an experiment there are "a" means. The variance of these "a" means is used as the estimate of