When performing an analysis of variance with a one-factor, repeated-measurement design, the effect of the independent variable is tested by computing an F statistic, which is computed as the ratio of the mean square of effect by the mean square of the interaction between the subject factor and the independent variable. For a design with S subjects and A experimental treatments, when some assumptions are met, the sampling distribution of this F ratio is a Fisher distribution with v1 = A–1 and v2 = (A–1)(S–1) degrees of freedom.

In addition to the usual assumptions of normality of the error and homogeneity of variance, the F test for repeated-measurement designs assumes a condition called sphericity. Intuitively, this condition indicates that the ranking of the subjects does not ...

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