## 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.

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