Within-subjects ANOVA assumes that the scores in all conditions are normally distributed. It is also assumed that each subject is sampled independently from each other subject. Naturally, it is not assumed that the scores of a given subject are independent of each other since the whole point of the analysis is that they are dependent.

In addition to the assumption of normality, within-subject analysis of variance is based on assumptions about the variances of the measurements and the correlations among the measurements. Taken together, these assumptions are called the assumption of sphericity. Although a complete description of sphericity is beyond the scope of this text, there is sphericity if (a) the population variances of the repeated measurements are equal and (b) the population correlations among all pairs of measures are equal. Other complex and unusual patterns of variances and correlations can also produce sphericity. Violation of the assumption of sphericity is serious: It results in an increase in the Type I error rate.