JSM 2005 - Toronto

Abstract #302873

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Activity Number: 67
Type: Contributed
Date/Time: Sunday, August 7, 2005 : 4:00 PM to 5:50 PM
Sponsor: Biopharmaceutical Section
Abstract - #302873
Title: A Test for Monotonicity of Normal Means with Unequal Variances
Author(s): Arthur Roth*+
Companies: Pfizer, Inc.
Address: 2800 Plymouth Rd 50M129, Ann Arbor, MI, 48105, United States
Keywords: Monotonicity tests ; Heteroscedasticity ; Ebar square test ; Amalgamation ; Order restrictions / Isotonic regression ; Simulations
Abstract:

The Brown-Forsythe (BF) test for monotonicity of normal means is constructed by combining properties of two other tests on normal means---namely the Ebar Square (ES) test for monotonicity, which tests the hypothesis of interest assuming equal variances, and the BF nontrend test (BFN), which tests a different hypothesis without assuming equal variances. The resulting BF monotonicity test addresses the hypothesis of interest but avoids assuming equal variances. An analogous technique was previously used by the author (1983) to construct the BF trend test, which assumes monotonicity of normal means and tests their equality without assuming equal variances as an alternative to the ES trend test, which tests the same hypothesis under the same assumption but with the additional assumption of equal variances. Simulations show almost all aspects of comparing the BF and ES monotonicity tests are analogous to the earlier comparison between the BF and ES trend tests. In particular, the ES monotonicity test has poor Type I error rates when the variances are unequal, and the BF monotonicity test outperforms it except with equal variances and tiny sample sizes.

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