A new ranked set sampling protocol for the signed rank test |
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| Institution: | 1. College of Forestry, Guizhou University, Guiyang, Guizhou 550025, PR China;2. Bijie City Qixingguan District Forestry Bureau, Bijie, Guizhou 551700, PR China;3. Huaxi District Water Administration, Guiyang, Guizhou 550025, PR China;1. Department of Respiratory and Critical Care Medicine, China-Japan Friendship Hospital, Beijing 100029, China;2. School of Public Health, The University of Queensland, Brisbane 4006, Australia;3. Center for Disease Surveillance & Research, Institute of Disease Control and Prevention, Academy of Military Medical Science, Beijing 102206, China;4. Department of Epidemiology and Preventive Medicine, School of Public Health and Preventive Medicine, Monash University, Melbourne 3004, Australia;5. Navy General Hospital of PLA, Beijing 100048, China;1. Imperial College School of Medicine, Faculty of Medicine, Imperial College London, London, UK;2. Guy''s, King''s and St Thomas’ School of Medicine, King''s College London, London, UK;3. Department of Vascular Surgery, Countess of Chester Hospital, Chester, UK;4. Department of Cardiothoracic Surgery, Liverpool Heart and Chest Hospital, Liverpool, UK |
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| Abstract: | In this paper, we construct a new ranked set sampling protocol that maximizes the Pitman asymptotic efficiency of the signed rank test. The new sampling design is a function of the set size and independent order statistics. If the set size is odd and the underlying distribution is symmetric and unimodal, then the new sampling protocol quantifies only the middle observation. On the other hand, if the set size is even, the new sampling design quantifies the two middle observations. This data collection procedure for use in the signed rank test outperforms the data collection procedure in the standard ranked set sample. We show that the exact null distribution of the signed rank statistic WRSS+ based on a data set generated by the new ranked set sample design for odd set sizes is the same as the null distribution of the simple random sample signed rank statistic WSRS+ based on the same number of measured observations. For even set sizes, the exact null distribution of WRSS+ is simulated. |
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