The Power of a Rank-Based Test for Non-Location Differences in Treatment Distributions in a Randomized Complete Block Design

• Activity Number: 532
• Type: Contributed
• Date/Time: Wednesday, August 7, 2013 : 10:30 AM to 12:20 PM
• 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 ; exact distribution

Abstract

The authors have previously discussed the development of a rank-based alternative to Friedman's test as a method for detecting differences among t treatment distributions in a randomized complete block (RCB) design on b blocks. The proposed test is an application of the Pearson goodness-of-fit test X^2 to the distribution of the t! possible permutations of the treatment ranks within a block (assuming no ties). Based on extensive numerical work using the exact distributions of the competing test statistics, for t = 3, 4 and 6, and small to moderate numbers of blocks (b=5, 10, 20 and 40), we show that when one or more of the t treatment distributions differ in scale, or a combination of scale and location, our proposed X^2 test can have greater power than both Friedman's test and the RCB analysis of variance F test.