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Published online by Cambridge University Press: 05 June 2012
Overview
A mixed design is one that contains at least one between-subjects independent variable and at least one within-subjects independent variable. In a simple mixed design, there are only two independent variables, one a between-subjects factor and the other a within-subjects factor; these variables are combined factorially. Because there are two independent variables, there are three effects of interest: the main effect of the between-subjects variable, the main effect of the within-subjects variable, and the two-way interaction.
The partitioning of the variance in a mixed design
The total variance of the dependent variable is partitioned into between-subjects variance and within-subjects variance. The three effects of interest are as follows.
The main effect of the between-subjects variable: The between-subjects variable is subsumed in the between-subjects portion of the variance. It has its own between-subjects error term that is used in computing its F ratio.
The main effect of the within-subjects variable: The within-subjects variable is subsumed in the within-subjects portion of the variance. It has its own within-subjects error term that is used in computing its F ratio.
The two-way interaction: The interaction effect is subsumed in the within-subjects portion of the variance. We use the within-subjects error term to compute its F ratio for this effect.
26.3 Numerical example
The following hypothetical study illustrates a 2 × 2 simple mixed design.
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