Rank methods

Abstract

AbstractOne of the major goals of statistics is to use data collected from a population to make inferences (hypothesis tests, confidence regions, and point estimators) about unknown attributes of the population. When there are good reasons to believe that the basic features of a population can be well approximated by a standard probability distribution, such as the commonly used Gaussian distribution, then a variety of approaches are available to construct procedures with optimal properties. When, however, a particular distribution is not an appropriate model for a population, the statistical procedures that are optimal for that distribution may not perform well; that is, model‐based statistical procedures may not be robust to departures from the assumed model. In such situations, one can use nonparametric procedures that maintain important stipulated properties (such as nominal significance level for hypothesis tests and coverage probability for confidence regions) over broad classes of probability distributions. While such nonparametric procedures are not optimal for a specific probability model, they are generally robust to deviations from that model. Many nonparametric procedures rely on simple counting and ranking processes applied either directly to the sample data or to some natural function of it and they are commonly known in the statistical literature as rank methods. In this article, we discuss the two basic approaches that lead to distribution‐free test procedures based on ranks and then illustrate how distribution‐free confidence intervals and robust point estimators can be derived directly from these hypothesis tests. Copyright © 2009 John Wiley & Sons, Inc.This article is categorized under: Statistical and Graphical Methods of Data Analysis > Nonparametric Methods