Ll. Bohn et Da. Wolfe, THE EFFECT OF IMPERFECT JUDGMENT RANKINGS ON PROPERTIES OF PROCEDURESBASED ON THE RANKED-SET SAMPLES ANALOG OF THE MANN-WHITNEY-WILCOXON STATISTIC, Journal of the American Statistical Association, 89(425), 1994, pp. 168-176
In this article we address the issue of imperfect judgment rankings in
ranked-set sampling and, in particular, their effect on the propertie
s of test procedures based on the ranked-set samples analog of the Man
n-Whitney-Wilcoxon statistic, U(RSS). We consider the impact of these
imperfect rankings on the null distribution of the statistic and the r
esulting effect on the nominal level of associated hypothesis tests. W
e propose a model for the probabilities of imperfect judgment rankings
based on the concept of expected spacings and use this model to study
the properties of tests based on U(RSS). This investigation includes
both small-sample Monte Carlo power simulations and a detailed analysi
s of the asymptotic relative efficiency properties of the U(RSS) proce
dure. We also examine, as an indication of the merits of using ranked-
set sampling, the relative cost of measuring the value of a sample ite
m as compared to obtaining a judgment ordering of a set of sample item
s.