2D ANOVA Assumptions

The 2D ANOVA VI makes the following assumptions:

• Assume that for each p, q, and r, is Normally distributed with mean 0 and variance .
• If a factor such as A is fixed, assume that the populations of measurements at each level of A are Normally distributed with mean and variance , and that all the populations at each of the levels have the same variance. In addition, assume that sum to zero. Analogous assumptions are made for B.
• If a factor such as A is random, assume that the effect of the level of A itself, , is a random variable Normally distributed with mean 0 and variance . Analogous assumptions are made for B.
• If all of the factors such as A and B associated with the effect of an interaction are fixed, assume that the populations of measurements at each level are Normally distributed with mean and variance . For any fixed p, sum to zero, when summing over all q. Similarly, for any fixed q, the means sum to zero, when summing over all p.
• If any of the factors such as A and B associated with the effect of an interaction are random, assume the effect is a random variable Normally distributed with mean 0 and variance . If A is fixed but B is random, then also assume that for any fixed q the means sum to zero, when summing over all p. Similarly, if B is fixed but A is random, assume that for any fixed p the means sum to zero, when summing over all q.
• Assume that all effects taken to be random variables are mutually independent.