Distribution-free tests for cluster samples of ordinal responses |
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| Institution: | 1. Department of Orthopedic Surgery, Spine Lab, The First Affiliated Hospital, Zhejiang University School of Medicine, Hangzhou, People''s Republic of China;2. Department of Physical Therapy, Faculty of Health Sciences, University of Western Ontario, London, Ontario, Canada;1. Department of Psychosis Studies, Institute of Psychiatry, Psychology and Neuroscience, King''s College London, UK;2. Department of Neuroimaging, Institute of Psychiatry, Psychology and Neuroscience, King''s College London, UK;3. Department of Psychological Medicine, Institute of Psychiatry, Psychology and Neuroscience, King''s College London, UK;4. Neuropsychology and Applied Cognitive Neuroscience Laboratory, Institute of Psychology, Chinese Academy of Sciences, Beijing, China;5. National Institute for Health Research (NIHR) Mental Health Biomedical Research Centre at South London and Maudsley NHS Foundation Trust and King''s College London, UK;6. Social Genetic and Developmental Psychiatry, Institute of Psychiatry, Psychology and Neuroscience, King''s College London, UK;1. Faculty of Life Sciences, University of Manchester, Manchester, UK;2. NEUROcom, Depto de Medicina, Univ da Coruña, Campus de Oza, A Coruña, Spain; The Institute for Biomedical Research of Coruña (INIBIC), A Coruña, Spain |
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| Abstract: | A simulation comparison is done of Mann–Whitney U test extensions recently proposed for simple cluster samples or for repeated ordinal responses. These are based on two approaches: the permutation approach of Fay and Gennings (four tests, two exact), and Edwardes’ approach (two asymptotic tests, one new). Edwardes’ approach permits confidence interval estimation, unlike the permutation approach. An appropriate parameter for estimation is P(X<Y)−P(X>Y), where X is the rank of a response from group 1 and Y is from group 2. The permutation tests are shown to be unsuitable for some survey data, since they are sensitive to a difference in cluster intra-correlations when there is no distribution difference between groups at the individual level. The exact permutation tests are of little use for less than seven clusters, precisely where they are most needed. Otherwise, the permutation tests perform well. |
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