Testing sphericity using small samples

Abstract

It is shown here that with small sample sizes, the null distribution of the ellipticity, or sphericity, likelihood criterion W(n, p) can be obtained very accurately, either by computation using the Meijer function, or by Monte Carlo simulation. Testing in repeated measures design can now be carried out with much more accuracy.

Keywords:

• sphericity
• Meijer function
• beta distribution
• simulation
• percentiles
• computation
• non-null distribution
• zonal polynomials

AMS Classification :

• 62H10
• 62H15

Acknowledgements

This research is supported in part by the NSERC grant A9249 (Canada). The authors wish to thank Professor Robert Chou of the Department of Applied Psychology, U. de M., for bringing this problem to their attention. Two dedicated referees have also helped a great deal in improving the paper by giving their constructive remarks and suggestions. Also thanks to Professor S. Thomas for sending us their preprint article.