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order rather than reacting to the music itself). By randomizing the order of
music trials and presuming that having just heard a snippet of classical or
rock music will not affect the students on the next trial, a within-subjects
design appears to be viable. Actually, it becomes the design of choice for
the study in that individual differences can be statistically accounted for
in a within-subjects design (because all subjects are measured under all
conditions) but cannot be so accounted for in a between-subjects design
(because different subjects are measured under each level of the indepen-
dent variable). Thus, in a within-subjects design, we can identify a type of
variance known as within-subjects variance.
10.5 BETWEEN- VERSUS WITHIN-SUBJECTS VARIANCE
10.5.1 BETWEEN-SUBJECTS VARIANCE IN A BETWEEN-
SUBJECTS DESIGN
In a one-way design, whether it is between subjects or within subjects, we
are interested in comparing the distributions of scores under each level of
the independent variable by using the means (and standard deviations)
as proxies for the distributions. For between-subjects designs, each level
of the independent variable is associated with different participants; we
therefore refer to the levels as “groups,” and presume, if individuals were
randomly assigned to the groups, that at least in the long run differ-
ences between participants will have been “randomized out” and will not
confound any mean differences we might observe between the treatment
conditions. The variance that we partition in such an ANOVA is therefore
called between-subjects variance.
Chapters 6 through 9 have presented
n-
way between-subjects designs.
The variance of the dependent variable that we have partitioned has all
been between-subjects variance. That is, because a subject contributed just
one score to the analysis, and because different subjects were measured
under each level of the independent variable, talking about differences
between the sets of scores was tantamount to talking about differences
between the sets of subjects. When we compared the means of different
groups, we were also comparing the differences in the performance of
different subjects. The situation is more complex in a within-subjects
design.
10.5.2 BETWEEN-SUBJECTS VARIANCE IN A WITHIN-SUBJECTS DESIGN
Within-subjects designs contain multiple participants who are measured
repeatedly on the dependent variable. With multiple subjects, one set
of scores (a set of repeated measures) will have resulted from the mea-
surement of Subject 1, another set of scores will have resulted from the
measurement of Subject 2, and so on. When we compare these sets of
scores to each other, we are comparing the subjects to each other. In
comparing different subjects to each other, we are dealing with between-
subjects variance. Thus, even when using a within-subjects design, some
