factorial designs Flashcards
essentials of factorial designs
Factorial designs examine the effects of more than one independent variable. Factorial designs are identified with a notation system that identifies the number of independent variables, the number of levels of each independent variable, and the total number of conditions in the study. For example, a 2 × 3 (“2 by 3”) factorial design has two independent variables, the first with two levels and the second with three levels, and six different conditions (2 times 3).
outcomes - main effects and interactions
The overall influence of an independent variable in a factorial study is called a main effect. There are two possible main effects in a 2 × 3 design, one for the factor with two levels and one for the factor with three levels. The main advantage of a factorial design over studies with a single independent variable is that factorials allow the discovery of interactions between the factors. In an interaction, the influence of one independent variable differs for the levels of the other independent variable. The outcomes of factorial studies can include significant main effects, interactions, both, or neither. When a study yields both main effects and interactions, the interactions should be interpreted first; sometimes an interaction is the important result, while the main effects in the study are irrelevant.
varieties of factorial designs
All of the independent variables in a factorial design can be between‐subjects factors or all can be within‐subjects factors. Completely between‐subjects factorial designs can include independent groups, matched groups, or ex post facto designs. Completely within‐subjects factorial designs are also called repeated‐measures factorial designs. A mixed factorial design includes at least one factor of each type (between and within). Factorial designs with at least one subject variable and at least one manipulated variable allow for the discovery of Person × Environment (P × E) interactions. When these interactions occur, they show how stimulus situations affect one type of person one way and a second type of person another way. A main effect for the P factor (i.e., subject variable) indicates important differences between types of individuals that exist in several environments. A main effect for the E factor (i.e., manipulated variable) indicates important environmental influences that exist for several types of persons. In educational research and research on the effectiveness of psychotherapy, these interactions between persons and environments are sometimes called Aptitude‐Treatment‐ Interactions (ATIs). In a mixed P × E design, the E factor is a within‐subjects variable.
