The hypotheses are
where G is the number of groups, are the contrast coefficients, and is the null contrast value.
The test is the usual F test for a contrast in one-way ANOVA. It assumes normal data with common group variances and requires and .
O’Brien and Muller (1993, Section 8.2.3.2) give the exact power as
where
The hypotheses are
where G is the number of groups.
The test is the usual overall F test for equality of means in one-way ANOVA. It assumes normal data with common group variances and requires and .
O’Brien and Muller (1993, Section 8.2.3.1) give the exact power as
where the noncentrality is
and