A Note on Determining the p-Value of Bartlett's Test of Homogeneity of Variances

Abstract

Bartlett's test for homogeneity of variances is rather nonrobust. However, when it is applicable, it is more powerful than various other tests. Dyer and Keating (1980) tabulate the exact critical values for Bartlett's test based on equal sample sizes from several normal populations. Moreover, they use these values to obtain highly accurate approximations to the critical values for unequal sample sizes. In this note, a simple and accurate method is proposed to obtain the p-value for Bartlett's test. Theoretically, the proposed method has third order accuracy. Numerical examples illustrate that it is extremely accurate even for very small sample sizes and a large number of populations. Furthermore, the proposed method can easily be implemented with standard statistical softwares.

Keywords:

• Bartlett's test
• Homogeneity of variances
• p-Value
• Saddlepoint approximation

Acknowledgments

The first author's research was supported in part by Cancer Center Support Grant CA 21765 and American Lebanese Syrian Associated Charities (ALSAC).The second author's reasearch was supported in part by National Science and Engineering Research Council of Canada. The authors would also like to thank the referrees, and the associate editor for their insightful recommendations that greatly improved this article.