Douglas A. Wolfe

Nonparametric Statistical Methods.

This Second Edition of Myles Hollander and Douglas A. Wolfes successful Nonparametric Statistical Methods meets the needs of a new generation of users, with completely up-to-date coverage of this important statistical area. Like its predecessor, the revised edition, along with its companion ftp site, aims to equip readers with the conceptual and technical skills necessary to select and apply the appropriate procedures for a given situation. An extensive array of examples drawn from actual experiments illustrates clearly how to use nonparametric approaches to handle one- or two-sample location and dispersion problems, dichotomous data, and one-way and two-way layout problems. An ideal text for an upper-level undergraduate or first-year graduate course, Nonparametric Statistical Methods, Second Edition is also an invaluable source for professionals who want to keep abreast of the latest developments within this dynamic branch of modern statistics.

An Asymptotically Distribution-Free Test for Symmetry versus Asymmetry

Abstract An asymptotically distribution-free procedure is proposed for testing whether a univariate population is symmetric about some unknown value versus a broad class of asymmetric distribution alternatives. The consistency class of the test is discussed and two competing tests are described, one based on the sample skewness, and the other on Guptas nonparametric procedure. A Monte Carlo study shows that the proposed test is superior to either competitor since it maintains the designated α levels fairly accurately even for sample sizes as small as 20, while displaying good power for detecting asymmetric distributions.

K-Sample Rank Tests for Umbrella Alternatives

Abstract Distribution-free test procedures are proposed for the k-sample problem, where the alternatives of interest are of the form F 1 (x) ≥ ··· ≥ Fl(x) ≤ ··· ≤ Fk (x) for all x, with at least one strict inequality. These are referred to as umbrella alternatives, and both the l (point of umbrella) known and l unknown settings are considered. Small sample null distributions are discussed, and the results of a Monte Carlo power study are presented. A detailed example illustrating the use of the unknown umbrella point procedure is also given.

Nonparametric Two-Sample Procedures for Ranked-Set Samples Data

Abstract 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 s...

The Effect of Imperfect Judgment Rankings on Properties of Procedures Based on the Ranked-Set Samples Analog of the Mann-Whitney-Wilcoxon Statistic

Abstract In this article we address the issue of imperfect judgment rankings in ranked-set sampling and, in particular, their effect on the properties of test procedures based on the ranked-set samples analog of the Mann-Whitney-Wilcoxon statistic, U rss. We consider the impact of these imperfect rankings on the null distribution of the statistic and the resulting effect on the nominal level of associated hypothesis tests. We 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 analysis of the asymptotic relative efficiency properties of the U rss procedure. We also examine, as an indication of the merits of using ranked-set sampling, the relative cost of measuring the value of a sample item as compared to obtaining a judgment ordering of a set of sample items.

Nonparametric statistical procedures for the changepoint problem

Abstract Let X 1 ,…, X r −1 , X r , X r +1 ,…, X n be independent, continuous random variables such that X i , i = 1,…, r , has distribution function F ( x ), and X i , i = r +1,…, n , has distribution function F ( x − Δ ), with -∞ Δ r is unknown, this is refered to as a change point problem with at most one change. The unknown parameter Δ represents the magnitude of the change and r is called the changepoint. In this paper we present a general review discussion of several nonparametric approaches for making inferences about r and Δ .

A new ranked set sample estimator of variance

Summary. We develop an unbiased estimator of the variance of a population based on a ranked set sample. We show that this new estimator is better than estimating the variance based on a simple random sample and more efficient than the estimator based on a ranked set sample proposed by Stokes. Also, a test to determine the effectiveness of the judgment ordering process is proposed.

A Class of Distribution-Free Two-Sample Tests Based on Placements

Abstract We consider a class of two-sample distribution-free tests that are appropriate for situations where one of the sample sizes is large relative to the other. These procedures are based on the placements of the observations in the smaller sample among the ordered observations in the larger sample, and this class of tests generalizes the Mann-Whitney (1947) procedure in much the same way that the class of linear rank tests generalizes the equivalent Wilcoxon (1945) rank sum form. Optimality criteria for choosing a test from this class are discussed and limiting distributions for the associated class of test statistics are determined for the case where only one of the sample sizes goes to infinity.

Ranked Set Sampling: Its Relevance and Impact on Statistical Inference

Ranked set sampling (RSS) is an approach to data collection and analysis that continues to stimulate substantial methodological research. It has spawned a number of related methodologies that are active research arenas as well, and it is finally beginning to find its way into significant applications beyond its initial agricultural-based birth in the seminal paper by McIntyre (1952). In this paper, we provide an introduction to the basic concepts underlying ranked set sampling, in general, with specific illustrations from the one- and two-sample settings. Emphasis is on the breadth of the ranked set sampling approach, with targeted discussion of the many options available to the researcher within the RSS paradigm. The paper also provides a thorough bibliography of the current state of the field and introduces the reader to some of the most promising new methodological extensions of the RSS approach to statistical data analysis.

Test for qualitative interaction of clinical significance

We generalize the problem of detecting qualitative interaction between treatments and subsets in a two treatment clinical trial to the more practical problem of detecting a qualitative interaction greater than a non-negative value d, corresponding to the minimal treatment difference of clinical significance. We develop a test based on simultaneous confidence intervals for the generalized problem under the assumption of normality. The proposed test is easy to implement, either by hand calculation or through the use of virtually any existing statistical software. We derive explicit power function for the proposed test and give examples to illustrate the procedures.