Rank Score Tests

Abstract

Nonparametric statistical methods are useful tools for data analysis when there is reason to believe that the outcome variables of interest may fail certain distributional assumptions required for parametric methods. Variables may be ordered categories in nature and thereby not suitable for analysis methods that assume normally distributed variables, such as t tests or analyses of variance and covariance. Variables may also be metric or continuous but subject to excessive variability or the presence of outliers. When the research hypothesis involves comparing a sample of subjects under 2 conditions or at 2 time points or comparing 2 samples of subjects with respect to an outcome variable of interest, then univariate nonparametric methods based on rank score tests can be invoked. A study design feature such as random assignment of conditions or treatments is typically all that is required for these methods to be valid. Furthermore, the methods can be quite powerful under a number of alternatives, particularly those involving shifts in the median. The Wilcoxon signed rank test, the Spearman rank correlation coefficient, and the Wilcoxon rank sum test are among the most commonly used nonparametric tests and cover a variety of research questions. These tests are described here. Although the focus is on hypothesis testing, related methods for estimation of confidence intervals are also presented. Extensions of nonparametric methods to handle stratification and covariate adjustment are also described. Scenarios in which nonparametric methods may be most useful and the power they can be expected to yield are discussed. The methods are illustrated with data from a clinical trial assessing the impact of exposure to low levels of carbon monoxide on exercise capacity in patients with ischemic heart disease. When the response variable of interest is a metric measurement that follows a symmetrical distribution with substantial variability or outliers, then …