Error Terms in F Tests |
Random-effects ANOVAs are distinguished from fixed-effects ANOVAs by which error mean squares are used as the denominator for F tests. Under a fixed-effects model, there is only one true error term in the model, and the corresponding mean square is used as the denominator for all tests. This is how the usual analysis is computed in PROC ANOVA, for example. However, in a random-effects model for a nested experiment, mean squares are compared sequentially. The correct denominator in the test for the first factor is the mean square due to the second factor; the correct denominator in the test for the second factor is the mean square due to the third factor; and so on. Only the mean square due to the last factor, the one at the bottom of the nesting order, should be compared to the error mean square.