POWER STUDY OF CIRCULAR ANOVA TEST AGAINST NONPARAMETRIC ALTERNATIVES

Abstract

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.

Keywords

• Bootstrap, Circular Data, Circular ANOVA, von Mises Distribution, Seasonal Wind Directions, Uniform Scores Test, Rao’s Test.

POWER STUDY OF CIRCULAR ANOVA TEST AGAINST NONPARAMETRIC ALTERNATIVES

Abstract

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Keywords

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References

1. Agostinelli, C. and Ulric, L. (2009). Circular Package in R, http://cran.rproject.org/web/packages/circular/circular.pdf.
2. Batschelet, E. (1981). Circular Statistics in Biology, Academic Press, London.
3. Efron, B. (1979). Bootstrap methods: Another look at the Jackknife, Ann. Statist., 7,pp 1Efron, B. and Tibshirani, R.J. ( 1993).An introduction to the Bootstrap, Chapman and Hall, New York.
4. Fisher, N.I. and Hall, P. (1989). Bootstrap Confidence Regions for directional data. Journal of the American Statistical Association, 84, 408, pp. 996-1002.
5. Fisher, N. I. ( 1993). Statistical Analysis of Circular Data, Cambridge University Press, New York, USA.
6. Hall, P. (1988). On the Bootstrap and Symmetric Confidence Intervals. Journal of the Royal Statistical Socieity. Ser. B, 50, pp. 35-45.
7. Harrison, D., Kanji, G.K. and Gadsden, R.J.( 1986). Analysis of variance for circular data, Journal of Applied Statistics, vol 13,issue 2.
8. Jammalamadaka, S. R. and Sen Gupta, A. (2001). Topics in Circular Statistics, World Scientific Publishing Co. Pte. Ltd, London, England.

9. Mardia, K. V. (1967). A nonparametric test for the bivariate two-sample location problem,Jour. of Roy. Statis. Soc. Ser. B, B29, 320-342.
10. Mardia, K. V. (1972). Statistics of Directional Data, Academic Press, London and New York.
11. Okamura, H. and Takasuka, A. (2012). A bootstrap method for testing equality of peak months. Population Ecology 54,1, 169-176.
12. Rao, J.S. (1967). Large sample tests for the homogeneity of angular data, Sankhya, Ser, B., Stephens, M. (1969). Tests for the von Mises Distribution, Biometrika, 56,149-160.
13. Tasdan, F. (2013). Technical Report: R programs for Circular ANOVA and Nonparametric Alternatives, http://www.wiu.edu/users/ft100/WindRcode.pdf
14. Watson, G. S. (1983). Statistics on Spheres, Wiley, New York, USA.
15. Watson, G. S. and Williams, E. J. (1956). On the construction of significance tests on the circle and the sphere, Biometrika, 43,344-352.
16. Wheeler, S. and Watson, G. S. (1964). A distribution free two sample test on the circle, Biometrika 51, 256-7.
17. Appendix A R functions that are used in this paper can be found in Tasdan ([15]). These functions require ”circular” package to be installed first in order to run the functions.