Chapters 11 and 12 presented the mixed-model, or univariate, approach for analyzing data from within-subjects designs. Traditionally, this approach was the most frequently used method for analyzing within-subjects data in psychology, but research during the 1970s and 1980s pointed out the limitations of this approach. In particular, evidence accumulated that the mixed-model approach is quite sensitive to violations of the sphericity assumption required by the covariance matrix. Although the E adjustments discussed in Chapters 11 and 12 provide one potential solution to this problem, our belief is that this solution is usually less useful than yet another solution, namely the multivariate approach. We defer our justification for this statement until later in the chapter. Once we explain the logic of the multivariate approach, we are able to discuss why it is generally preferable to the E adjusted mixed-model approach. For the moment, however, we simply state that the multivariate approach requires no assumption of sphericity, can be substantially more powerful than the mixed-model approach (although under some circumstances, it can also be substantially less powerful), is straightforward to use with statistical packages, and leads naturally to appropriate tests of specific individual comparisons.