Power Comparisons of Eight Tests for Sphericity in Repeated Measures Designs

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.

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