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CHAPTER THIRTEEN
Simple Mixed Design
13.1 COMBINING BETWEEN-SUBJECTS AND
WITHIN-SUBJECTS FACTORS
A mixed design is one that contains at least one between-subjects inde-
pendent 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 vari-
ables are combined factorially. The number of levels of each independent
variable is not constrained by the design. Thus, we could have a 2
×
2, a
×
×
4
7 factorial design. Chapters 14 and 15 will address
two complex mixed designs that contain three independent variables.
Because there are two independent variables, there are three effects of
interest: the main effect of the between-subjects variable ( A ), the main
effect of the within-subjects variable ( B ), and the two-way interaction
( A
3, or even a 3
B ). Note that this is analogous to what we have seen in the two-way
between-subjects and two-way within-subjects designs. Furthermore, the
conceptual understanding of main effects and interactions in those designs
carries forward to the simple mixed design. Main effects focus on the mean
differences of the levels of each independent variable (e.g., a 1 vs. a 2 )and
interactions focus on whether or not the patterns of differences are parallel
(e.g., a 1 vs. a 2 under b 1 compared to a 1 vs. a 2 under b 2 ).
The primary difference between a simple mixed design and the
between-subjects and within-subjects designs is in the way that the total
variance of the dependent variable is partitioned. As is true for within-
subjects designs, the total variance in a mixed design is divided into
between-subjects variance and within-subjects variance. The three effects
of interest break out as follows:
×
Themaineffectof A : The between-subjects variable A is subsumed in
the between-subjects portion of the variance. It has its own between-
subjects error term that is used in computing the F ratio associated
with A .
Themaineffectof B : The within-subjects variable B is subsumed in
the within-subjects portion of the variance. It has its own within-
subjects error term that is used in computing the F ratio associated
with B . This error term is associated with the B factor and thus it
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