
TwoWay ANOVA Balanced designs
Another point about twoway ANOVA is related to the number of subjects in each cell of the design. If the between groups IV has equal numbers of subjects in each of its levels, then you have a balanced design. With a balanced design, each of the two IVs and the interaction are independent of each other. Each IV can be significant or nonsignificant and the interaction can be significant or non significant without any influence or effect from one or the other effects. Ray, in particular (pp. 200207), describes all the possible outcomes of a 2 X 2 experiment, giving all the outcomes depending on what is significant or not.
When there are different numbers in the levels of the between groups IV, however, this independence starts to disappear. The results for one IV or and/or the interaction will depend somewhat on what happened on the other IV. Therefore as much as possible you should try to keep the numbers of subjects in each level of the IV as close as possible to each other. I have not seen any textbook 'rule of thumb' regarding how disparate the cell numbers have to be before the results become invalid. On my experience, though, the rule of thumb I would give, is that if the largest cell number was greater than three times the smallest cell number, the results would start to become too invalid to interpret.
