The hypotheses are
where is the number of groups, are the contrast coefficients, and is the null contrast value.
The test is the usual 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 is the number of groups.
The test is the usual overall 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