#### Analyses in the ONEWAYANOVA Statement

##### One-Degree-of-Freedom Contrast (TEST=CONTRAST)

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

##### Overall F Test (TEST=OVERALL)

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