Robustness of Mann-Whitney-Wilcoxon Test to Dependence in the Variables.

Abstract

Let (X,Y) have an unknown bivarite distribution function H(x,y) having continuous marginals F(x) and G(y). The Mann-Whitney-Wilcoxon test statistic can be studentized so as to be asymptotically distribution-free for testing (H sub 0): F(x) = G(x), for all x against the alternative (H sub 1: F > or = G (with strict inequality for some x). The test is consistent and its asymptotic efficiency relative to the t-test is evaluated and an explicit form for it is obtained when H(x,y) is bivariate normal with correlation coefficient rho. The relative efficiency is 3/pi when rho = -1 or 0, is increasing for -1 < or = rho < -.5, decreasing for -.5 < rho < or = 1 and is equal to square root (3)/2 = .866 when rho = 1. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1973
Accession Number
AD0762778

Entities

People

  • Z. Govindarajulu

Organizations

  • University of Kentucky

Tags

DTIC Thesaurus Topics

  • Coefficients
  • Computing-Related Activities
  • Data Science
  • Distribution Functions
  • Efficiency
  • Inequalities
  • Information Science
  • Interdisciplinary Science
  • Mathematical Analysis
  • Mathematics
  • Nonparametric Statistics
  • Square Roots
  • Statistical Analysis
  • Statistics

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Regression Analysis.