Percentage points of the studentized range test for dispersion of normal means

Abstract

Consider k (≥ 2) independent populations such that observations obtained from π_i are independent and normally distributed with unknown mean μ_iand a common unknown variance σ², Let the standardized difference of the means be measured by is the maximum (minimum) of . In this paper, we provide tables for testing an interval hypothesis is a predetermined constant. The null hypothesis thus stipulates that the population means fall into a zone of indifference of size δ (standard units). As a test statistic for this hypothesis the studentized range is proposed and the least favorable configuration (LFC) for the test under H₀ is determined. umerical quadrature is employed to obtain percentage points of the test statistic under the LFC for testing the interval hypothesis H₀. These tables can also be used to construct a lower confidence bound for d(μ) if δ is not specified.

Keywords:

• Testing a composite hypothesis
• Studentized range test
• Confidence bound
• Percentage points
• Linear models