Abstract #301516

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JSM 2003 Abstract #301516
Activity Number: 216
Type: Contributed
Date/Time: Tuesday, August 5, 2003 : 8:30 AM to 10:20 AM
Sponsor: Biometrics Section
Abstract - #301516
Title: Exact and Approximate Power for Important Special Cases of Linear Mixed Models: Repeated-Measures ANOVA With or Without Sphericity
Author(s): Lloyd J. Edwards*+ and Keith E. Muller and Douglas Taylor
Companies: University of North Carolina, Chapel Hill and University of North Carolina, Chapel Hill and Family Health International
Address: 3819 Swarthmore Rd., Durham, NC, 27707-5437,
Keywords: balanced data ; medical imaging ; noncentral chi-square ; sample size
Abstract:

The convenience of linear mixed models for Gaussian data has led to their widespread use. Unfortunately, standard mixed model methods in small samples usually give very optimistic inference, including greatly inflated test size. The difficulties can be avoided in a wide range of useful special cases by reducing the analysis to the univariate approach to repeated measures (UNIREP). In contrast to mixed model tests, UNIREP tests allow strong control of test size and accurate power approximation, even in small samples (Muller and Barton, 1989). We describe new exact and approximate results for the null and non-null settings. A new expression for the distribution function of the test statistic gives exact test size and power for the uncorrected and conservative (Box) tests. New approximations include a two moment match for any positively weighted sum of noncentral chi-squares, approximations for the means of the Geisser-Greenhouse and Huynh-Feldt correction factors, and new noncentral F power approximations. One version performed far better than existing approximations, while retaining simplicity of computation and interpretation. Free software implements the new methods.

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