A note on testing the sphericity hypothesis with Bartlett's test
Reddon, J. R., Jackson, D. N. (1984). A Note on Testing the Sphericity Hypothesis with Bartlett's Test. Multivariate Experimental Clinical Research, 7(1), 49-52.
This study employs computer simulations of correlations matrices to evaluate sample size requirements with different numbers of variables for testing departures from sphericity, implying the presence of group factors. Inductive approximation of average off-diagonal correlations due to Lawley (1940) and to Baggaley (1982) were found to be biased for correlation matrices with homogeneous elements. This bias led to some error in estimation by Baggaley of the appropriate sample size for evaluating departures from sphericity. Lawley's approximation was clearly inferior to Baggaley's approximation.