Main Effects

Main Effects in Factorial Design

Factorial design is applicable whenever researchers wish to examine the influence of a particular factor among two or more factors in their study. This design is a method for controlling various factors of interest in just one experiment rather than repeating the same experiment for each of the factors or independent variables in the study. If there is no significant interaction between the factors and many factors are involved in the study, testing the main effects with a factorial design likely confers efficiency.

Plausibly, in factorial design, each factor may have more than one level. Hence, the significance of the main effect, which is the difference in the marginal means of one factor over the levels of other factors, can be examined. For instance, suppose an education researcher is interested in knowing how gender affects the ability of first-year college students to solve algebra problems. The first variable is gender, and the second variable is the level of difficulty of the algebra problems. The second variable has two levels of difficulty: difficult (proof of algebra theorems) and easy (solution of simple multiple-choice questions). In this example, the researcher uses and examines a 2 × 2 factorial design. The number “2” represents the number of levels that each factor has. If there are more than two factors, then the factorial design would be adjusted; for instance, the factorial design may look like 3 × 2 × 2 for three factors with 3 levels versus 2 levels and another 2-level factor. Therefore, a total of three main effects would have to be considered in the study.

In the previous example of 2 × 2 factorial design, however, both variables are thought to influence the ability of first-year college students to solve algebra problems. Hence, two main effects can be examined: (1) gender effects, while the level of difficulty effects is controlled and (2) level-of-difficulty effects, while gender effects are [Page 746]controlled. The hypothesis also can be stated in terms of whether first-year male and female college students differ in their ability to solve the more difficult algebra problems. The hypothesis can be answered by examining the simple main effects of gender or the simple main effects of the second variable (level of difficulty).

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