Factorial ANOVA

In designed experiments, a factorial ANOVA is an ANOVA design where all possible combinations of the factors (i.e., levels of independent variables) are represented in the experiment. If many factors are studied or the number of levels is high for the factors, this type of design will result in a large number of experimental conditions (i.e., a very large design). For, example, a design with only three factors but with 5 levels per factor, would result in 125 experimental groups (5 x 5 x 5).