A general theory of hypothesis testing based on rankings |
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| Institution: | 1. Department of Epidemiology and Biostatistics, University of California, San Francisco, CA, USA;2. Center for Biostatistics in AIDS Research, Harvard T. H. Chan School of Public Health, Boston, MA, USA;3. Division of Infectious Diseases, Department of Medicine, Johns Hopkins University School of Medicine, Baltimore, MD, USA;4. Vitalant Research Institute, San Francisco, CA, USA;5. Department of Laboratory Medicine, University of California, San Francisco, San Francisco, CA, USA;6. University of California San Francisco, Department of Medicine, San Francisco, CA, USA;7. The Peter Doherty Institute for Infection and Immunity, The University of Melbourne and Royal Melbourne Hospital, Melbourne, Australia;8. Department of Infectious Diseases, Monash University and Alfred Hospital, Melbourne, Australia |
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| Abstract: | In nonparametric statistics, a hypothesis testing problem based on the ranks of the data gives rise to two separate permutation sets corresponding to the null and to the alternative hypothesis, respectively. A modification of Critchlow's unified approach to hypothesis testing is proposed. By defining the distance between permutation sets to be the average distance between pairs of permutations, one from each set, various test statistics are derived for the multi-sample location problem and the two-way layout. The asymptotic distributions of the test statistics are computed under both the null and alternative hypotheses. Some comparisons are made on the basis of the asymptotic relative efficiency. |
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