Abstract #300504

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JSM 2003 Abstract #300504
Activity Number: 126
Type: Contributed
Date/Time: Monday, August 4, 2003 : 10:30 AM to 12:20 PM
Sponsor: IMS
Abstract - #300504
Title: Asymptotics for a Large Number of Factor Levels
Author(s): Arne C. Bathke*+
Companies: University of Kentucky
Address: 875 Patterson Office Tower 0027, Lexington, KY, 40506-0001,
Keywords: ANOVA ; rank tests ; nonparametric methods ; Type I Error robustness ; heteroscedasticity
Abstract:

The common asymptotic results for ANOVA or nonparametric rank-based procedures have been derived in the literature under the assumption that the number of replications per treatment (n) tends to infinity while the number of treatments (k) is fixed. We derive the asymptotic distribution of the ANOVA and "ANOVA on ranks" F tests for factorial models with arbitrarily many factors in the situation where the number of replications is limited whereas the number of treatments goes to infinity (large k, small n case). The effect of heteroscedasticity on the validity of the tests is also discussed. The derivation of the asymptotic distribution of the rank test involves proving a novel result about the asymptotic distribution of a class of rank score statistics that can be applied to the large k, small n case. Simulation results supplement the theoretical findings.

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