Hello Liz:
The F-test for factor C (subject) random effect requires repetitions of the
experiment. This means that there must be more than one sample per cell
(i.e., n > 1).
A "cell" refers to a particular combination of factor levels (A, B, and C).
From Table 4 of the 3dANOVA3 documentation, we see that calculation of F(C)
requires estimation of MSE. However, from Table 2, we see that estimation
of MSE requires n > 1. Hence, if there is only one sample per cell (n = 1),
then it is not possible to test for factor C effect.
To put this in English: In order to determine if there is a subject effect,
it is necessary to compare the subject-to-subject variation (MSC) with the pure
measurement error (MSE). But MSE can be estimated only if we have repetitions
of the entire experiment.
Usually, the factor C (subject) random effect is not of inherent interest.
Doug Ward
