Likelihood Ratio Tests for the Non Equivalence of Means

Abstract

We derive likelihood ratio (LR) tests for the null hypothesis of equivalence that the normal means fall into a practical indifference zone. The LR test can easily be constructed and applied to k ≥ 2 treatments. Simulation results indicate that the LR test might be slightly anticonservative statistically, but when the sample sizes are large, it always produces the nominal level for mean configurations under the null hypothesis. More powerful than the studentized range test, the LR test is a straightforward application that requires only current existing statistical tables, with no complicated computations.

Keywords:

• Bioequivalence hypothesis
• Composite hypothesis
• Coverage probability
• Interval hypotheses
• Range statistic

Mathematics Subject Classification:

• 62F03
• 62P10

Acknowledgments

The authors are grateful for helpful comments from the Editor and a reviewer that led to significantly improved presentation of the work.

Notes

‡The range of the standard errors of the estimated levels is (.001, .003).

‡The range of the standard errors of the estimated levels is (.001, .003).

‡The range of the standard errors of the estimated powers is (.002, .005).