Testing the equality of quantiles for several normal populations

ABSTRACT

Many procedures exist for testing equality of means or medians to compare several independent distributions. However, the mean or median do not determine the entire distribution. In this article, we propose a new small-sample modification of the likelihood ratio test for testing the equality of the quantiles of several normal distributions. The merits of the proposed test are numerically compared with the existing tests—a generalized p-value method and likelihood ratio test—with respect to their sizes and powers. The simulation results demonstrate that proposed method is satisfactory; its actual size is very close to the nominal level. We illustrate these approaches using two real examples.

KEYWORDS:

• Actual size
• Generalized p-value
• Likelihood ratio test
• Quantiles

MATHEMATICS SUBJECT CLASSIFICATION:

• 62F03
• 62F30

Acknowledgment

The authors are grateful to the referee and the associate editor for their helpful comments and suggestions on improving this manuscript.