Testing the 2D ANOVA Hypotheses

For each hypothesis, the VI computes a number f that is used to calculate the associated sig probability. For example, for the hypothesis (A), that for all the levels p, (fixed A), the VI computes

then

where

is an F distribution with degrees of freedom a – 1 and (a – 1)(b – 1). You can then use the probabilities sigA, sigB, and sigAB to determine when you should reject the associated hypotheses (A), (B), and (AB).

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.

For example, if A is a random effect, your chosen level of significance is 0.05, and the output sigA is 0.03, then you must reject the hypothesis and conclude that factor A has an effect on the experimental observations.