INTERDIRECTION TESTS FOR SIMPLE REPEATED-MEASURES DESIGNS

Interdirection tests are proposed for a simple repeated-measures desig n. The test statistics proposed are applications of the one-sample int erdirection sign test and interdirection signed-rank test to a repeate d-measurement setting. The interdirection sign test has a small-sample distribution-free property and includes the two-sided univariate sign test and Blumen's bivariate sign test as special cases. The interdire ction signed-rank test includes the two-sided univariate Wilcoxon sign ed-rank test as a special case. The proposed statistics are shown to h ave a limiting chi(p-1)(2) null distribution when the underlying distr ibution is elliptically symmetric. In addition, the asymptotic distrib utions of the proposed statistics under certain contiguous alternative s are obtained for elliptically symmetric distributions with a particu lar density function form. Pitman asymptotic relative efficiencies and Monte Carlo studies show the proposed interdirection tests to be robu st as compared to several competitors. The sign test performs particul arly well when the underlying distribution is heavy tailed or skewed, especially for non-H-type variance-covariance. For normal to light-tai led distributions, Hotelling's T-2 test and the signed-rank test have good powers when the variance-covariance structure of the underlying d istribution is non-H-type; otherwise analysis of variance (ANOVA) F an d the rank transformation test RT perform well.