POWER STUDY OF CIRCULAR ANOVA TEST AGAINST NONPARAMETRIC ALTERNATIVES
POWER STUDY OF CIRCULAR ANOVA TEST AGAINST NONPARAMETRIC ALTERNATIVES
Yazar: Taşdan, Feridun; Yeniay, Özgür
Dergi: Hacettepe Journal of Mathematics and Statistics, Vol. 43 No. 1, 2014
Anahtar kelimeler: Bootstrap, Circular Data, Circular ANOVA, von Mises Distribution, Seasonal Wind Directions, Uniform Scores Test, Rao’s Test.

This study compares circular ANOVA against bootstrap test, uniformscores test and Rao’s test of homogeneity which are considered nonparametric alternatives. Circular ANOVA is one-way analysis of variance method to test the equality of mean directions in circular dataanalysis, but it requires some assumptions. The main assumption forcircular ANOVA is that all r-independent samples must come from vonMises distribution with equal directional means and equal concentration parameters. On the other hand, nonparametric alternatives aredistribution free methods and, therefore, does not require having vonMises distribution or equality of parameters. Literature of circular statistics is very limited on the comparison of these tests; therefore, apower simulation study is performed to compute the power of circular ANOVA against the nonparametric alternatives under assumptionsof von Mises and non-von Mises populations. Power simulation studyshows that bootstrap and uniform scores tests perform slightly betterthan circular ANOVA if the common concentration parameter, κ, isless than 1 under the assumption of von Mises distribution. If κ ≥ 2,then bootstrap and circular ANOVA perform better than the other alternatives. Rao’s test of homogeneity requires very large samples inorder to reach the same power levels of competitive tests in this study.Finally, uniform scores tests performs better than circular ANOVA andbootstrap test if the sample sizes are small and the data comes frommixed von Mises distributions or wrapped Cauchy.

This study compares circular ANOVA against bootstrap test, uniformscores test and Rao’s test of homogeneity which are considered nonparametric alternatives. Circular ANOVA is one-way analysis of variance method to test the equality of mean directions in circular dataanalysis, but it requires some assumptions. The main assumption forcircular ANOVA is that all r-independent samples must come from vonMises distribution with equal directional means and equal concentration parameters. On the other hand, nonparametric alternatives aredistribution free methods and, therefore, does not require having vonMises distribution or equality of parameters. Literature of circular statistics is very limited on the comparison of these tests; therefore, apower simulation study is performed to compute the power of circular ANOVA against the nonparametric alternatives under assumptionsof von Mises and non-von Mises populations. Power simulation studyshows that bootstrap and uniform scores tests perform slightly betterthan circular ANOVA if the common concentration parameter, κ, isless than 1 under the assumption of von Mises distribution. If κ ≥ 2,then bootstrap and circular ANOVA perform better than the other alternatives. Rao’s test of homogeneity requires very large samples inorder to reach the same power levels of competitive tests in this study.Finally, uniform scores tests performs better than circular ANOVA andbootstrap test if the sample sizes are small and the data comes frommixed von Mises distributions or wrapped Cauchy.