Chapter 11 Experimental Research: Factorial Designs

Factorial Experimental Designs Experimental designs with more than one independent (manipulated) variable are known as Factorial Experimental Designs. The term Factor refers to each of the manipulated independent variables. Experiments with two independent variables are called two-way designs. Experiments with three independent variables are called three-way designs, etc…

Factorial Notation Factorial research designs are described with a notational system that concisely indicates both how many factors there are in the design and how many levels there are in each factor. Two independent variables with two levels each: 2 X 2 (read two-by- two). Three independent variables, one with two levels, one with four levels, and one with three levels: 2 X 4 X 3

Factorial Notation In a 2 X 2 design, there are four conditions (number of groups) In a 3 X 3 design, there are nine conditions In a 2 X 4 X 2 design, there are sixteen conditions

Main Effects When means are combined across the levels of another factor in this way, they are said to control for or to collapse across the effects of the other factor and are called Marginal Means. Differences on the dependent measure across the levels of any one factor, controlling for all other factors in the experiment, are known as the Main Effect of that factor. If significance is found for an independent variable in a factorial design, it will be stated that there is a “Main Effect” for that variable.

Interactions For a 2 X 2 factorial design: Main effect for factor 1 (or no main effect) Main effect for factor 2 (or no main effect) Interaction between factors ( or no interaction)

Post-hoc Comparisons When factors (Ivs) have more than two levels, the F statistic does not indicate where the significant differences exist. To avoid familywise error or experimentwise error – Post-hoc comparisons must be performed Otherwise alpha will inflate and risk of type I error increases