A new exact p-value approach for testing variance homogeneity

Abstract

To test variance homogeneity, various likelihood-ratio based tests such as the Bartlett's test have been proposed. The null distributions of these tests were generally derived asymptotically or approximately. We re-examine the restrictive maximum likelihood ratio (RELR) statistic, and suggest a Monte Carlo algorithm to compute its exact null distribution, and so its p-value. It is much easier to implement than most existing methods. Simulation studies indicate that the proposed procedure is also superior to its competitors in terms of type I error and powers. We analyse an environmental dataset for an illustration.

Keywords:

• Homogeneity of variances
• Bartlett's test
• restrictive maximum likelihood ratio test
• type I error rate

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The research of Li was supported by Grant 11871294 from National Natural Science Foundation of China. Liang's research was partially supported by NSF grant DMS-1620898.

Notes on contributors

Juan Wang

Juan Wang is an assistant professor of School of Mathematics and Statistics at Qingdao University.

Xinmin Li

Xinmin Li is a professor of School of Mathematics and Statistics at Qingdao University.

Hua Liang

Hua Liang is a professor of Department of Statistics at George Washington University.