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Ranked-set samples have been shown to lead to improved methods of estimation in parametric settings under specific distributional forms when actual measurement of the sample observations is difficult but ranking them is relatively easy. The earliest work with ranked-set data concentrated on estimating a population mean or variance. More recently, a ranked-set sample estimator of a cumulative distribution function was developed and used to obtain a simultaneous confidence interval for the function. In this article, we take the next logical step and use this ranked-set empirical distribution function to construct distribution-free competitors to the standard Mann-Whitney-Wilcoxon estimation and testing procedures. The appropriate null distribution tables for the associated test are presented for the case of perfect ranking. Asymptotic relative efficiency comparisons between the simple random sample Mann-Whitney-Wilcoxon procedures and their ranked-set analogues are discussed, and the results of a small-sample Monte Carlo simulation study of the same arc presented. [ABSTRACT FROM AUTHOR]

The techniques of exploratory data analysis include a resistant rule for identifying possible outliers in univariate data. Using the lower and upper fourths, F[sub L] and F[sub U] (approximate quartiles), it labels as "outside" any observations below F[sub L] - 1.5(F[sub U] - F[sub L]) or above F[sub U] + 1.5( F[sub U] - F[sub L]). For example, in the ordered sample -5, -2, 0, l, 8, F[sub L] = -2 and F[sub U] = 1, so any observation below -6.5 or above 5.5 is outside. Thus the rule labels 8 as outside. Some related rules also use cutoffs of the form F[sub L] -k(F[sub U] - F[sub L]) and F[sub U] + k(F[sub U] - F[sub L]). This approach avoids the need to specify the number of possible outliers in advance; as long as they are not too numerous, any outliers do not affect the location of the cutoffs. To describe the performance of these rules, we define the some-outside rate per sample as the probability that a sample will contain one or more outside observations. Its complement is the all-inside rate per sample. We also define the outside rate per observation as the average fraction of outside observations. For Gaussian data the population all-inside rate per sample (0) and the population outside rate per observation (.7%) substantially understate the corresponding small-sample values. Simulation studies using Gaussian samples with n between 5 and 300 yield detailed information on the resistant rules. The main resistant rule (k = 1.5) has an all-inside rate per sample between 67% and 86% for 5 less than or equal to n less than or equal to 20, and corresponding estimates of its outside rate per observation range from 8.6% to 1.7%. Both characteristics vary with n in ways that lead to good empirical approximations. Because of the way in which the fourths are defined, the sample sizes separate into four classes, according to whether dividing n by 4 leaves a remainder of 0, 1, 2, or 3. Within these... [ABSTRACT FROM AUTHOR]