JSM 2004 - Toronto

Abstract #301072

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Activity Number: 341
Type: Contributed
Date/Time: Wednesday, August 11, 2004 : 10:30 AM to 12:20 PM
Sponsor: Section on Nonparametric Statistics
Abstract - #301072
Title: A Nonparametric Alternative to Analysis of Covariance
Author(s): Arne C. Bathke*+
Companies: University of Kentucky
Address: 875 Patterson Office Tower, Lexington, KY, 40506-0027,
Keywords: nonparametric model ; rank test ; analysis of covariance ; ordered categorical data ; ordinal data ; dependent observations
Abstract:

The Analysis of Covariance (ANCOVA) is designed for the many practical situations in which factor effects are obscured by concomitant variables, or the main purpose of the investigation lies in assessing the effect of the concomitant variables. We consider a nonparametric model with covariates. The information contained in the covariates is used to minimize the variance of certain nonparametric estimators for the response variable. This model combines the power gain through introduction of covariates into a factorial design with the robustness of nonparametric procedures. We discuss asymptotic inference for factor effects as well as the effect of covariates. Application of the suggested methods to real data is demonstrated using a SAS-IML macro. The tests can be used for data with ties, and even for purely ordinal data, including ordinal covariates. The number of covariates that can be included into the model is not restricted. Simulations show extremely good small-sample performance. In many situations, the proposed tests only require sample sizes around 10.

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