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More on Sphericity

The general algorithm implemented will attempt to generate, for each effect, a set of independent (orthogonal) contrasts. In repeated measures ANOVA, these contrasts specify a set of hypotheses about differences between the levels of the repeated measures factor. However, if these differences are correlated across subjects, then the resulting contrasts are no longer independent. For example, in a study where we measured learning at three times during the experimental session, it may happen that the changes from time 1 to time 2 are negatively correlated with the changes from time 2 to time 3: subjects who learn most of the material between time 1 and time 2 improve less from time 2 to time 3. In fact, in most instances where a repeated measures ANOVA is used, one would probably suspect that the changes across levels are correlated across subjects. However, when this happens, the compound symmetry and sphericity assumptions have been violated, and independent contrasts cannot be computed.

(Taken from http://www.statsoft.com/textbook/stanman.html.)

None: FAQ/MANOVA/manrm/sphericity (last edited 2013-03-08 10:17:18 by localhost)