Simple Main Effect

Table 1 presents hypothetical data from a factorial design. Observations in each cell are averaged to produce a cell mean. Averaging over all levels of one factor produces means for the overall main effect of the other factor. For example, the six values observed with Drug 1 have a mean of 8.0 averaged over both dosage levels. Similarly, the six values from Drug 2 have a mean of 3.0. The difference between 8.0 and 3.0 is the overall main effect of the drug factor.

The two drugs could be compared separately for each dosage level. The difference between Drug 1 and Drug 2 in the 10 mg condition is 3.0 (= 7.0 − 4.0). This difference is an example of a simple main effect. That is, we can define a simple main effect as a difference in the value of a dependent variable found between two levels of one factor when another factor is held constant. The difference between the two drugs in the 20 mg condition is 7.0 (= 9.0 − 2.0).

Simple main effects can also be defined for the other factor. The difference between the two dosage levels for Drug 1 is 2.0 (= 9.0 − 7.0). Similarly, the difference between the two dosage levels for Drug 2 is 2.0 (= 4.0 − 2.0).

Simple main effects are often tested after finding a significant interaction in a factorial design. However, this practice can be misleading. For example, Berrin-Wasserman, Winnick, and Borod reported a 2 × 2 design with a significant interaction and no significant simple main effects. A more complex problem is illustrated by Friedman, Putnam, Ritter, Hamberger, and Berman, who reported a 3 × 4 factorial design with a significant interaction in which testing simple main effects led to an incorrect interpretation of the reason for the significant interaction.