Power Comparisons of Eight Tests for Sphericity in Repeated Measures Designs

John E. Cornell, Dean M. Young, Samuel L. Seaman and Roger E. Kirk

Journal of Educational and Behavioral Statistics, 1992, vol. 17, issue 3, 233-249

Abstract: A Monte Carlo simulation was conducted to investigate the relative power of eight tests for sphericity in randomized block designs. Box’s (1954) epsilon values º = .35, .55, .75, .80, .85, .90, .95, and 1.00 were used to quantify departures from sphericity for rank-1 population covariance matrices of dimension p = 3, 5, 7, and 9. Sample covariance matrices were generated for samples of size n = 10, 15, 20, and 30. The locally best invariant test demonstrated substantial power to detect departures from sphericity—regardless of p— for both small and large samples for rank-1 alternatives. Recommendations are made regarding the use of preliminary tests.

Keywords: sphericity; likelihood ratio test; locally best invariant test (search for similar items in EconPapers)
Date: 1992
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Persistent link: https://EconPapers.repec.org/RePEc:sae:jedbes:v:17:y:1992:i:3:p:233-249

DOI: 10.3102/10769986017003233

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