JSM 2005 - Toronto

Abstract #304702

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Legend: = Applied Session, = Theme Session, = Presenter
Activity Number: 65
Type: Contributed
Date/Time: Sunday, August 7, 2005 : 4:00 PM to 5:50 PM
Sponsor: General Methodology
Abstract - #304702
Title: Exact Test Size in the General Univariate Linear Model under Violation of Homogeneity of Variance with Cluster Samples of Unequal Size
Author(s): Jacqueline Johnson*+ and Keith E. Muller
Companies: University of North Carolina, Chapel Hill and University of North Carolina, Chapel Hill
Address: CB 7420, Chapel Hill, NC, 27599, United States
Keywords: cluster sample ; linear models
Abstract:

We present a method to obtain exact test size for hypothesis tests in the general univariate linear model (GLUM) for Gaussian data with any covariance structure. The results apply to data that violate homogeneity and independence assumptions. We express the usual GLUM test statistic as a sum of weighted independent chi-square random variables. The exact distribution can be calculated using Davies' (1980) algorithm. We apply the method to assess the impact of using the GLUM to analyze Gaussian cluster means with unequal-sized clusters. The approach can inflate or deflate test size depending on the relative dimensions and covariance structure of the problem. Example designs from clinical trials, community-based trials, and laboratory studies illustrate the results. Although some scenarios cause no concern, others can greatly affect inference accuracy.

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Revised March 2005