Nonparametric Methods for Detecting Treatment Effects in Repeated-Measures Designs

Abstract

Sufficient conditions are given that guarantee the limiting distribution of a test proposed by Agresti and Pendergast (1986) to detect treatment effects in repeated-measures designs. The test, which is appropriate for either the original or aligned data, is related to one proposed by Koch (1969) and to the rank-transformation statistic. Using Pitman asymptotic-relative-efficiency comparisons, situations are presented where these tests are more efficient than their standard parametric and nonparametric competitors. The problem of detecting ordered alternatives in repeated-measures designs is also considered. A rank transformation analog of Page's (1963) L is shown to be generally more efficient in the Pitman sense than the standard competitors when the number of treatments is not too large.

Key Words:

• Rank transformation
• Friedman's test
• Page's test
• Kepner-Robinson test
• Exchangeable distribution
• Conditional test
• Distribution-free test