African Journal of
Environmental Science and Technology

  • Abbreviation: Afr. J. Environ. Sci. Technol.
  • Language: English
  • ISSN: 1996-0786
  • DOI: 10.5897/AJEST
  • Start Year: 2007
  • Published Articles: 1014

Full Length Research Paper

On the matched pairs sign test using bivariate ranked set sampling: an application to environmental issues

Hani M. Samawi1*, Mohammad F. Al-Saleh2 and Obaid Al-Saidy3
  1Jiann-Ping Hsu College of Public Health, PO Box 8015, Georgia Southern University Statesboro, GA 30460, USA. 2Department of Statistics, Yarmouk University, Irbid-Jordan, 211-63 3Department of Mathematics and Statistics, Sultan Qaboos University, P. O. Box 36, Al-khod 123, Sultanate of OMAN
Email: [email protected]

  •  Accepted: 15 January 2008
  •  Published: 31 January 2008



The matched pairs sign test using bivariate ranked set sampling (BVRSS) is introduced and investigated. We show that this test is asymptotically more efficient than its counterpart sign test based on a bivariate simple random sample (BVSRS). The asymptotic null distribution and the efficiency of the test are derived. The Pitman asymptotic relative efficiency is used to compare the asymptotic performance of the matched pairs sign test using BVRSS versus using BVSRS. 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 BVRSS for the matched pairs sign test is substantially more efficient than using BVSRS. Illustration using palm trees data from sultanate of Oman is provided.


Key words: Bootstrap method, bivariate ranked set sample, power of the test, P-value of the test, Pitman’s relative efficiency, sign test