On testing homogeneity of t normal means against ordered alternatives in r groups

Abstract

Given k=rt normal populations with a common but unknown variance consisting of t treatments applied to r different groups of units, and supposing that in each group the means are monoto-nically non-decreasing (or non-increasing), then the likelihood ratio test of homogeneity of the means in each group against the simple order alternative is considered. Critical values are provided when one observation is drawn from each of the k populations.

Keywords:

• likelihood ratio tests
• simple order alternatives
• simultaneous test procedures