Abstract #300197

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JSM 2003 Abstract #300197
Activity Number: 452
Type: Contributed
Date/Time: Thursday, August 7, 2003 : 8:30 AM to 10:20 AM
Sponsor: Biopharmaceutical Section
Abstract - #300197
Title: Should the One-Way ANOVA F-test be Retired? Presenting a Powerful Adaptive Strategy for Comparing Independent Means with Possibly Unequal Variances
Author(s): Robin Mogg*+ and Devan V. Mehrotra
Companies: Merck & Co., Inc. and Merck Research Laboratories
Address: 111 Hilltown Pike, Line Lexington, PA, 18932,
Keywords: adaptive test ; one-way ANOVA ; variance heterogeneity
Abstract:

The one-way analysis of variance (ANOVA) F test is known to be sensitive to heterogeneity of within group variances. The actual size of the test can differ substantially from the nominal level; in some scenarios it is overly conservative and in others extremely liberal. The effect becomes more severe when sample sizes are unequal. Numerous methods have been proposed to account for a lack of variance homogeneity, including the established Welch (W) and (modified) Brown-Forsythe (mBF) tests. These methods generally control the test size under normality, but none of them uniformly dominates the others in terms of power to detect differences in means. We propose a simple adaptive testing strategy that cleverly exploits the best features of the W and mBF tests. Based on an extensive simulation study, we demonstrate that our method provides excellent control of the test size, and is at least as powerful as its competitors. Under variance homogeneity, our procedure is about as powerful as the one-way ANOVA F test, but under variance heterogeneity it is substantially better. Accordingly, we answer the titled question in the affirmative. A numerical example is provided.

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