For each hypothesis, the VI computes number f that is used to calculate the associated sig probability. For example, for the hypothesis (A), that (p = 0 for all the levels p), (fixed A), the VI computes
then
where
is an F distribution with degrees of freedom a 1 and abc(L 1). You can then use the probabilities sigA, sigB, sigC, sigAB,..., sig ABC to determine when you should reject the associated hypotheses (A), (B), (C), (AB),..., (ABC).
How do you know when to reject the null hypothesis? For each hypothesis, you choose a level of significance. This level of significance is how likely you want it to be that you mistakenly reject the hypothesis (a common choice is 0.05). Compare your chosen level of significance with the associated sig probability output. If the sig probability is less than your chosen level of significance, you should reject the null hypothesis.
If, for instance, A is a random effect, your level of significance is 0.05, and sigA = 0.03, you must reject the hypothesis that and conclude that factor A has an effect on the experimental observations.
With some models there are no appropriate tests for certain hypotheses. If such is the case, the output parameters directly involved with the testing of these hypotheses are 1.0.