Small sample power of multivariate nonparametric tests for monotone trend

Abstract

Bhattacharyya and Kioiz (1966) propose two multivariate nonparametric tests for monotone trend, one involving coordinate-wise Mann statistics and the other, coordinate-wise Spearman statistics. Dietz and Killeen (1981) propose a different test statistic based on coordinate-wise Mann statistics. The Pitman asymptotic relative efficiency of all three tests with respect to a normal theory competitor equals the cube root of the efficiency of a multivariate signed rank test with respect to Hotelling's T2. In this article, the small sample power of the nonparametric tests, the normal theory test, and a Bonferroni approach involving coordinate-wise univariate Mann or Spearman tests is examined in a simulation study. The Mann statistic of Dietz and Killeen and the Spearman statistic of Bhattacharyya and Klotz are found to perform well under both null and alternative hypotheses

Keywords:

• Mann test
• multivariate trend test
• nonparametric tests
• Spearman test