320

REPEATED-MEASUREMENT AND OTHER EXPERIMENTAL DESIGNS

(2—1)(5—1) <4. The S/R term is the variation within subjects
summed over groups, and the degrees of freedom are R(n— 1) <
2(4— 1) —6. The SC/R term is the subject-by-column interactions summed
over rows, and the degrees of freedom are R(n— idte-t)<
U(4—- I)(5— 1) < M4.

The appropriate error term for testing row effects is the S/R variance
estimate. The appropriate error term for testing column effects and R x C
interaction is the SC/R variance estimate. The F ratios are as follows:

Sr 3240
seo 31.53
F. st 436 7.23 p<.OI
AT
Fezipo- ze —644 pel

In this illustrative example the row effects are not significant, whereas the
column effects, row-by-column effects, and row-by-column interaction
are significant at better than the .01 level.

19.40 ASSUMPTIONS UNDERLYING REPEATED-

MEASUREMENT DESIGNS

A basic assumption in the analysis of variance is the homogeneity of
variance assumption. In, for example, a simple analysis of variance in-
volving k independent groups this assumption may be stated in the form
oj? co? << <agyi—a?. It has been shown that reasonable violations
of this assumption will not seriously bias the F test. The analysis-of-
variance procedures are said to be robust with respect to violations of the
homogeneity of variance assumption. In the analysis of variance involving
repeated measurements, assumptions are made not only regarding the
homogeneity of variance but also regarding the homogeneity of covariance.
To illustrate, in a one-factor experiment with repeated measurements N
subjects are measured under C treatments. Al! the covariances, r;js;S;,
between pairs of treatments may be calculated. "The homogeneity of
covariance assumption is that all r;;s;s; are čstimates of the same population
covariance. If, for example, repeated measurements were made for N sub-
jects on four conditions, the following covariance table, or matrix, might be
calculated.

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