Testing Equality of Means Under Order Restrictions Using Multiple Contrasts

Abstract

The likelihood ratio test for equality of ordered means is known to have power characteristics that are generally superior to those of competing procedures. Difficulties in implementing this test have led to the development of alternative approaches, most of which are based on contrasts. While orthogonal contrasts can be chosen to simplify the distribution theory, we propose a class of tests that is easy to implement even if the contrasts used are not orthogonal. An overall measure of significance may be obtained by using Fisher's combination statistic to combine the dependent p-values arising from these contrasts. This method can be easily implemented for testing problems involving unequal sample sizes and any partial order, and has power properties that compare well with those of the likelihood ratio test and other contrast-based tests.

Keywords:

• Combining dependent p-values
• Fisher's combination method
• Order restricted inference
• Polyhedral cone
• Scaled χ² approximation

Mathematics Subject Classification:

• Primary 62F03
• Secondary 62F30

Acknowledgments

The work of James Kost was supported in part by National Institutes of Health Grant T32 ES07271.