Bootstrap tests for two independent samples under ranked set sampling

Alexandre Souza MAGRO1

Maria Cecília Mendes BARRETO[1]

§     ABSTRACT: Ranked set sampling is more efficient than single random sampling for several statistical procedures when the measurement of the main variable is costly or difficult to obtain. Bohn and Wolfe (1990, 1992) presented a modified statistic of the Mann-Whitney-Wilcoxon test to compare two independent samples under a ranked set sample procedure. This paper considers an original implementation of the bootstrap resampling method to compare the location parameters of two independent samples under the ranked set design. A Monte Carlo study is conducted to validate the size and the power of the bootstrap test using the modified statistic of Mann-Whitney-Wilcoxon and the difference of sample means and the difference of sample medians as the statistic test. Our results are quite equivalent in size and power to those of the modified statistic of Bohn and Wolfe. The bootstrap tests for the modified statistic of Mann-Whitney-Wilcoxon can be used as a successful alternative to Bohn and Wolfe´s asymptotic test.

§     KEYWORDS: Ranked set sampling; bootstrap; modified statistic of Mann-Whitney-Wilcoxon test; tests for two independent samples.

 



[1]Departamento de Estatística, Universidade Federal de São Carlos – UFSCar, CEP 13565-905, São Carlos, SP, Brasil, E-mail: cbarreto@power.ufscar.br.