Cited by 177Statistical Methods and Bayesian InferenceProbability and Statistical ResearchStatistical Methods in Clinical Trials

Approximate Power for Repeated-Measures ANOVA Lacking Sphericity

Muller, Keith E., Barton, Curtis N.·1989·Journal of the American Statistical Association

Abstract

Violation of sphericity of covariance across repeated measures inflates Type I error rates in univariate repeated-measures analysis of variance. Hence the use of Geisser—Greenhouse or Huynh—Feldt is now common (to provide improved Type I error rate). With nonsphericity, no method has been available to compute power. A convenient method is suggested for approximating power and test size under nonsphericity. New approximations are suggested for (a) a weighted sum of independent noncentral χ2,s, (b) the trace of a noncentral Wishart (or pseudo-Wishart) matrix, (c) the expected values of and , and (d) the noncentral test statistic, whether corrected or uncorrected. The new approximations are extensions of the work of Box (1954a,b) and Satterthwaite (1941). The method performed well when evaluated against published and new simulations.

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Crossref · 10.1080/01621459.1989.10478802

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Authors
Muller, K. E., & Barton, C. N.
Affiliations
  • University of North Carolina at Chapel Hill (US)
  • United States Food and Drug Administration (US)
Venue
Journal of the American Statistical Association
Published
1989-06
Volume
84
Issue
406
Pages
549-555
ISSN
  • 0162-1459 (ISSN-L)
  • 1537-274X
OpenAlex
W2151286374
Cited by
177
References
26
Citations by year
2026: 3 · 2025: 4 · 2024: 5 · 2023: 6 · 2022: 4 · 2021: 8 · 2020: 4 · 2019: 4 · 2018: 10 · 2017: 1 · 2016: 6 · 2015: 5 · 2014: 8 · 2013: 10 · 2012: 10
FWCI
5.58
Type
journal article
Language
en
Open access
closed
Locations
Journal of the American Statistical Association (publishedVersion)
Topics
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
  • Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
Keywords
statistical power, repeated measures ANOVA, nonsphericity, type I error rate, noncentral chi-square distribution, noncentral Wishart distribution, Satterthwaite approximation

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