Bootstrap and permutation tests in ANOVA for directional data
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The problem of testing the null hypothesis of a common direction across several populations defined on the hypersphere arises frequently when we deal with directional data. We may consider the Analysis of Variance (ANOVA) for testing such hypotheses. However, for the Watson distribution, a commonly used distribution for modeling axial data, the ANOVA test is only valid for large concentrations. So we suggest to use alternative tests, such as bootstrap and permutation tests in ANOVA. Then, we investigate the performance of these tests for data from Watson populations defined on the hypersphere.
KeywordsHypersphere Monte Carlo methods Simulation Watson distribution Resampling methods
The author is grateful to the Professors Michael Stephens and Richard Lockhart for their suggestions to this paper. The author also thanks the helpful comments given by the referees of this journal, that helped to improve this paper. This work is financed by the FCT - Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) within project UID/EEA/50014/2013.
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