An Extension to Two Populations of an Analogue of Student's $t$-Test Using the Sample Range

Abstract

The modified $t$-test considered by Daly$^1$ (see [1]) is used to develop one-sided significance tests to decide whether the mean of a new normal population exceeds the mean of an old normal population having the same variance. Significance tests are also developed to decide whether the mean of the new population is less than the mean of the old population. These tests require very little computation for their application and are approximately as powerful as the most powerful tests of these hypotheses.