Table 2.

Factorial design scheme, with 2 factors and 2 levels of each factor

	A absent	A present
B absent	A−, B−	A+, B−
B present	A−, B+	A+, B+

−, factor absent; +, factor present. With balanced randomization to each of the 4 groups, half of all subjects receive treatment A and half receive treatment B. This orthogonal configuration of A and B provides sample size efficiency for estimating the main effects of both A and B as long as A and B effects are at least additive. Finding synergistic combinations is a primary interest to optimize treatment benefit. Should the A and B combination show synergy (positive interaction), then the conclusion is that the effect of A depends on the level of B and vice versa. Thus, the A and B main effects become somewhat moot, in that A+B treatment effect is greater than the sum of the main effects.