An Approximate Likelihood Ratio Test for Comparing Several Treatments to a Control

Abstract

Abstract Some parametric tests for comparing several treatments to a control are examined. Those tests developed earlier tend to rest on a single principle: Simplicity or power; those developed later attempt to fill the gap. We propose a new test that represents another such attempt. The basic idea is to find a simple statistic that is a good approximation to the likelihood ratio statistic. This leads to a power function similar to that of the likelihood ratio test, which is optimal among the available competitors. Like the orthogonal contrast test, the new test is built on an orthogonal relationship, resulting in a relatively simple null distribution that depends on the sample sizes only through their total. Thus critical values can be easily computed and a detailed listing results in only a moderately large table. Computing the statistic is elementary when the sample sizes of the new treatments are equal; otherwise, some matrix operations are needed. A simple procedure is given to estimate the sample size required to achieve a given power level. To compete with Dunnett's test in terms of pairwise comparison, the new test (or any of the other tests) can be applied according to the closed testing procedure. In this setting the new test is compared to Dunnett's test by simulation.