Factorial Design

Factorial designs are a form of true experiment, where multiple factors (the researcher-controlled independent variables) are manipulated or allowed to vary, and they provide researchers two main advantages. First, they allow researchers to examine the main effects of two or more individual independent variables simultaneously. Second, they allow researchers to detect interactions among variables. An interaction is when the effects of one variable vary according to [Page 262]the levels of another variable. Such interactions can only be detected when the variables are examined in combination.

When using a factorial design, the independent variable is referred to as a factor and the different values of a factor are referred to as levels. For example, a researcher might examine the effect of the factor, medication dosage, of different levels (Factor 1 with three levels: low, medium, or high) for two different types of psychotherapy (Factor 2 with two levels: Type 1 and Type 2). Because this is a form of true experiment, it requires that subjects or respondents be randomly assigned to each of the conditions.

In the literature, factorial designs are reported according to the number of variables and the number of levels in the variables. The example described in the previous paragraph is a 3 × 2 factorial design, which indicates that there are two factors, where Factor 1 has three levels and Factor 2 has two levels. The total number of groups (or cells or conditions) in the design is the product of the number of levels. For a 3 × 2 design this is six groups. In general, an mxn design has mn groups, so a 5 × 6 design requires 30 groups.

To make the explanation more concrete, let us consider, in detail, the simplest type of factorial design: a 2 × 2 design with equal numbers of people randomly assigned to each of the four groups. Suppose the researcher is testing the effect of two different forms of psychotherapy (Type 1 and Type 2) and medication dosage (low or medium) on level of symptom improvement (the dependent variable) measured on a scale of 1 (showing no improvement) to 20 (showing a great deal of improvement). Thus, there are four groups in this design to which subjects are randomly assigned: (1) Type 1 psychotherapy and low medication dosage; (2) Type 1 psychotherapy and medium medication dosage; (3) Type 2 psychotherapy and low medication dosage; and (4) Type 2 psychotherapy and medium medication dosage. The clearest way to examine the data for main effects is to put the group means in a table (see Table 1). The row and column marginals are used to examine for main effects of each of the independent variables. To examine the main effect of medication dosage on symptom improvement, the table is read across and the means are compared in the low dose row versus the medium dose row. These data show a main effect of dose with patients receiving the medium level showing greater symptom improvement compared with the low dose medication group (10 vs. 15). To examine the main effect of type of psychotherapy on symptom improvement, the table is read down by column, comparing the overall means for the two groups receiving Psychotherapy 1 versus the two groups receiving Psychotherapy 2 (15 vs. 10). The data show that patients receiving Psychotherapy 1 showed greater symptom improvement compared with patients receiving Psychotherapy 2.

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