A Rank-Based Test for Nonlocation Differences Between Treatment Distributions in a Randomized Complete Block Design

• Activity Number: 124
• Type: Contributed
• Date/Time: Monday, July 30, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Roy St. Laurent*+ and Philip Turk
• Companies: Northern Arizona University and West Virginia University
• Keywords: Friedman's Test ; nonparametric test ; power ; non-location shift ; goodness-of-fit

Abstract

Friedman's test is a rank-based procedure that can be used to test for differences among t treatment distributions in a randomized complete block design on b blocks. It is well-known that the test has reasonably good power under location-shift alternatives to the null hypothesis of no difference in the t treatment distributions. However the power of Friedman's test when the alternative hypothesis consists of a non-location, or not purely location, difference in treatment distributions can be poor. We develop an alternative rank-based test that has greater power than Friedman's test in these circumstances. Our proposed test is based on the joint distribution of the t! possible permutations of the treatment ranks within a block (assuming no ties). We show when and why our proposed test will have greater power than Friedman's test, and provide results from extensive numerical work comparing the power of the two tests under various configurations for the underlying treatment distributions.