Rank-Based Procedures for Linear Models: Applications to Pharmaceutical Science Data
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0092-8615/2001 Copyright 0 2001 Drug Information Association Inc.
RANK-BASED PROCEDURES FOR LINEAR MODELS: APPLICATIONS TO PHARMACEUTICAL SCIENCE DATA ASHEBER ABEBE,KIMBERLY CRIMIN,AND JOSEPH W. MCKEAN Western Michigan University, Kalamazoo, Michigan
JOSEPH V. HAASAND THOMASJ. VIDMAR Pharmacia, Kalamazoo, Michigan
Rank-based procedures for linear models generalize the simple Wilcoxon rank tests in the simple location models, inheriting their robustness and high efficiency properties. Given a general linear model, these rank-based procedures form a complete analysis, including estimation, conjidence, and multiple comparison procedures, and tests of general linear hypotheses. In this article, these ranked-based procedures are reviewed in the context of pharmaceutical science data. Examples involving ANOVA- and ANCOVAtype designs are considered in some detail. We further present a Web-based interface incorporating the statistical software R and RGLM for the computation of these procedures. As discussed, the user need only visit our Web site to compute these procedures. Taken together these rank-based procedures offer the user an efJicient and robust alternative to standard least squares procedures for linear models. Key Words: Distribution free; Nonparametric methods; R Software; RGLM; Relative efficiency; Robust methods; Web-based software; Wilcoxon scores
INTRODUCTION NONPARAMETRIC STATISTICS OR distribution-free methods have historically referred to a collection of statistical tests whose null distributions do not depend on the underlying distribution of the data; hence the term nonparametric, that is, no parameters. Many of the early nonparametric (NP) procedures were based upon replacing the data by their ranks which, before the advent of the computer, facilitated hand calculation; see Wilcoxon (1). These procedures were thought to be quick and dirty but much less efficient than least squares (LS) methods. Work such as Hodges and Lehmann (2), however, showed that many of these NP procedures were quite efficient. If the data follow a normal distribution then many of these procedures have efficiency .955 relative to LS methods, while, if the data follow distributions with thicker tails than normal (have outliers like most real data), then these NP procedures are much more efficient than LS methods. The early NP procedures were essentially test statistics for simple location problems or at most one-way layouts. Theory for corresponding estimates and confidence intervals of Reprint address: Joseph W. McKean, Department of Statistics, Western Michigan University, Kalamazoo, MI 49008.
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Downloaded from dij.sagepub.com at University of Sussex Library on August 11, 2015
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A. Abebe, K. Crimin, J. McKean, J. V. Haas, and T. J. Vidmar
location effects was developed in the 1960s. Taken together, these NP procedures for simple location problems offer the user highly efficient and robust methods which form an attractive alternative to traditional LS procedures. LS procedures, though, generalize easily to any line
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