Analyses in the ONEWAYANOVA Statement

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

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

     

Overall F Test (TEST=OVERALL)

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