Parametric hypothesis tests for the difference between two population means

Abstract

When one wishes to perform a statistical-hypothesis test, the first important step is to select the correct, most appropriate, test to perform. This article aims, firstly, to outline the test-selection criteria when one wishes to obtain statistical evidence about the equality of population means. Thereafter, Stata statistical software (StataCorp, USA) commands will be given for the various tests. If the population means of interest are numerical and have known probability-sampling distributions, then the standard recommended statistical-hypothesis test, with data from samples, is either the classic t-test, or a variant of it. In this article, the first part concentrates on the selection of the appropriate test to perform when using sample data to determine whether two population means are likely to differ. The selection criteria/steps are illustrated by a diagram (Fig. 1). The second part describes how to perform the tests using Stata. In that section, some Stata output is also presented, and the interpretation of the output is explained.