Testing Homogeneity of Mean Directions for Circular Dispersion Models

Abstract

Tests for equality of mean directions in independent circular populations is an important practical problem in many areas of applied research, for which results are yet to be obtained. Dispersion model approach with analysis of deviance is an appealing approach for testing equality of parameters under non-normal setups. In view of its wide applicability, the present endeavour is to examine whether standard circular models for describing directional data can be viewed as special cases of dispersion model. The answer is affirmative and this leads us to explore whether analysis of deviance can be employed for circular observations. Special emphasis is given on circular normal and wrapped Cauchy distributions for carrying out deviance analysis. Interestingly, we demonstrate that the Watson-Williams ad-hoc test (1956) proposed for independent von Mises distributions is equivalent to the analysis of deviance test. We thereby also exhibit the rare property possessed by von Mises distributions with high concentrations, that the nuisance concentration parameter can be ignored for this test in such a case.