Approximate Power for Repeated-Measures ANOVA Lacking Sphericity
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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If all distributional assumptions are met, the univariate approach is the most powerful method.
“If all the distributional assumptions are met, then the univariate approach is the most powerful method (Muller & Barton, 1989;O'Brien & Kaiser, 1985).”
From G*Power 3: A flexible statistical power analysis program for the social, behavioral, and biomedical sciences (2007) · cites this paper as Muller & Barton, 1989
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González, M. J., Knoll, L. B., & Vanni, M. J. (2009) · Freshwater Biology · doi:10.1111/j.1365-2427.2009.02304.x · Cited by 11 · see citing works
Aberrant visual circuitry associated with normal spatial match-to-sample accuracy in schizophrenia
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Lang, A., & Yegiyan, N. S. (2014) · Journal of Health Communication · doi:10.1080/10810730.2013.872728 · Cited by 10 · see citing works
Prodan, A., Imangaliyev, S., Brand, H. S., Rosema, N., Levin, E., Wim Crielaard, A., Keijser, B. J. F., & Veerman, E. C. I. (2016) · Metabolomics · doi:10.1007/s11306-016-1096-4 · Cited by 10 · see citing works
- 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
- Publisher
- Informa UK Limited
- 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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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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