For more complicated designs, there are no new concepts to be learned. We will begin with the analysis of a two-factor mixed design.

A two-factor mixed design Mixed design ANOVAs are particularly versatile and are often used in psychology. These designs have at least one betweensubjects factor and at least one within-subjects factor. A simple expertise study of memory would normally use this design (see

Chapters 9 and 10). Expertise would be the between-subjects factor out of necessity, while position type, for a chess study, can be a within-subjects factor in order to increase the sensitivity of the experiment and save on the number of subjects. Recall that a between-subjects design uses the within-group variance as its error term, while a within-subjects design uses the residual variance as its error term. It therefore follows that a mixed design ANOVA will need at least two error terms; one for the between-subjects main effect and one for the within-subjects main effect. The imaginary experiment to be described will be the same task as described in Chapter 9. Hence, there are two factors: expertise (expert versus novice) and position type (real versus random). This time, each subject is briefly shown twenty chess positions one at a time. There are ten real positions and ten random positions, each with ten pieces on the board. After the

Box 11.1 Preliminary analysis for the expertise data

Finally, here is the ANOVA table for these data:

subject has been shown each, the task is to reproduce it from memory. The dependent variable is the number of boards remembered entirely correctly for each subject for each position type. Box 11.1 shows possible raw data, a table of means and an ANOVA table for the data (the end of this section gives the details of the actual calculations).