Interdirection Tests for Simple Repeated-Measures Designs

• Published in: Journal of the American Statistical Association Vol. 91; no. 436; pp. 1611 - 1618
• Main Authors: Jan, Show-Li, Randles, Ronald H.
• Format: Journal Article
• Language: English
• Published: Alexandria, VA Taylor & Francis Group 01.12.1996; American Statistical Association; Taylor & Francis Ltd
• Subjects: Analysis of variance; Applied statistics; Covariance matrices; Degrees of freedom; Distribution; Exact sciences and technology; Expected values; Experimental design; Gaussian distributions; Interdirection test; Mathematics; Matrices; Measurement; Nonparametric inference; Null hypothesis; Parametric inference; Probability and statistics; Rank tests; Repeated measures; Sampling distributions; Sciences and techniques of general use; Statistical methods; Statistics; Tests; Theory and Methods; Variance; Wilcoxon test; Monte Carlo method; Interdirection test; Test statistic; Repeated measurement; Density function; Asymptotic distribution; Rank test; Variance analysis; Sign test
• ISSN: 0162-1459; 1537-274X
• DOI: 10.1080/01621459.1996.10476729

Interdirection tests are proposed for a simple repeated-measures design. The test statistics proposed are applications of the one-sample interdirection sign test and interdirection signed-rank test to a repeated-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 interdirection signed-rank test includes the two-sided univariate Wilcoxon signed-rank test as a special case. The proposed statistics are shown to have a limiting X p−1 2 null distribution when the underlying distribution is elliptically symmetric. In addition, the asymptotic distributions of the proposed statistics under certain contiguous alternatives are obtained for elliptically symmetric distributions with a particular density function form. Pitman asymptotic relative efficiencies and Monte Carlo studies show the proposed interdirection tests to be robust as compared to several competitors. The sign test performs particularly well when the underlying distribution is heavy tailed or skewed, especially for non-H-type variance-covariance. For normal to light-tailed distributions, Hotelling's T 2 test and the signed-rank test have good powers when the variance-covariance structure of the underlying distribution is non-H-type; otherwise analysis of variance (ANOVA) F and the rank transformation test RT perform well.