ABSTRACT
Two data characteristics, the mean and the standard deviation, are the primary descriptors of continuous data in practice. Therefore, tests for means have very important roles in health-related experiments. It is frequently of interest to compare two independent groups with respect to their mean scores of a continuous measure. This chapter presents an exact likelihood ratio test for the joint equality of means and variances of two populations. In clinical trials, the generalized treatment effect can be used to compare treatments or interventions based on the difference in mean outcomes between pre-and post-treatment measurements. The chapter outlines a limited number of publications in which health-related researches may be interested. In many practical scenarios, due to the cost of the sampling procedures, the skewness of the parent distribution can be greater than those studied by Johnson and the sample sizes can be quite small, possibly as small as 10, under which cases Johnson's test can be quite inaccurate.
