Statistical Methodology 6 (2009) 397–407 Contents lists available at ScienceDirect Statistical Methodology journal homepage: www.elsevier.com/locate/stamet The matched pair sign test using bivariate ranked set sampling for different ranking based schemes Hani M. Samawi a,* , Mohammad F. Al-Saleh b , Obaid Al-Saidy c a Jiann-Ping Hsu College of Public Health, Biostatistics Center, PO Box 8015, Georgia Southern University, Statesboro, GA 30460, USA b Department of Statistics, Yarmouk University, Irbid-Jordan, 211-63, Jordan c Department of Mathematics and Statistics, Sultan Qaboos University, P.O. Box 36, Al-khod 123, Oman article info Article history: Received 21 August 2007 Received in revised form 16 February 2009 Accepted 18 February 2009 Keywords: Bootstrap method Bivariate ranked set sample Pitman’s relative efficiency Sign test abstract Bivariate rank set sample (BVRSS) matched pair sign test is introduced and investigated for different ranking based schemes. We show that this test is asymptotically more efficient and more powerful than its counterpart sign test based on a bivariate simple random sample (BVSRS) for different ranking schemes. The asymptotic null distribution and the efficiency of the test are derived. Pitman’s asymptotic relative efficiency is used to compare the asymptotic performance of the matched pair sign test using BVRSS versus using BVSRS in all ranking cases. For small sample sizes, the bootstrap method is used to estimate P -values. Numerical comparisons are used to gain insight about the efficiency of the BVRSS sign test compared to the BVSRS sign test. Our numerical and theoretical results indicate that using any ranking scheme of BVRSS for the matched pair sign test is more efficient than using BVSRS. Published by Elsevier B.V. 1. Introduction Matching is a necessary technique for the control of confounding factors in many epidemiological and experimental studies. It has great intuitive appeal and has been widely used over the years. ‘‘Unlike randomization and restriction, which used to control confounding in the design stage of a study, matching is a strategy that must include elements of both design and analysis’’, [1]. Examples of matched pair studies can be found in [1]. Matched pair studies produce data consisting of observations in a bivariate (ordered pairs) random sample such as {(X i , Y i ), i = 1, 2,..., n}. Within each pair * Corresponding author. Tel.: +1 912 536 9655; fax: +1 912 681 5811. E-mail addresses: hsamawi@georgiasouthern.edu (H.M. Samawi), m-saleh@yu.edu.jo (M.F. Al-Saleh), obiad@squ.edu.om (O. Al-Saidy). 1572-3127/$ – see front matter. Published by Elsevier B.V. doi:10.1016/j.stamet.2009.02.002