The Optimal Spacing of Repeated Measurements

The treatments in a repeated measurements design can frequently be ordered along some natural continuum (e.g. time), and as a consequence the expected values and covariance structure of the responses can be represented as functions of their positions on the scale. We shall consider rules for spacing the treatments so as to maximize the power of the T2 test for equal treatment effects, as well as general two-sample T2 tests for the equality of mean vectors. These results will be obtained under the assumptions of covariance structures of the kinds associated with Wiener and Markov stochastic processes, and alternative hypothesis mean vectors whose elements are linear or quadratic functions of the scale variable.