14.67 Between-subjects estimate This exercise motivates the formula for the between-subjects estimate of the variance in one-way ANOVA. Suppose each population mean equals m (that is, H0 is true) and each sample size equals n. Then the sampling distribution of each yi has mean m and variance s2>n, and the sample mean of the yi values is the overall sample mean, 5y6.

a. Treating the g sample means as g observations having sample mean y, explain why Σ1yi - y22> 1g - 12 estimates the variance s2>n of the distribution of the 5yi6 values.

b. Using part

a, explain why the between-groups estimate

Σn1yi - y22> 1g - 12 estimates s2. (For the unequal sample size case, the formula replaces n by ni. )