A Modified Friedman Test for Randomized Complete Block Designs
Document Type
Article
Publication Date
3-25-2015
Publication Title
Communications in Statistics - Simulation and Computation
Abstract
The Friedman test is often used for a randomized complete block design when the normality assumption is not satisfied or the data are ordinal. The Friedman test can be viewed as an extension of the sign test for multiple measurements within each subject or block. We propose a modified Friedman test based on the Wilcoxon sign rank approach. Coincidentally, Tukey proposed a test statistic similar to our proposed test, but blocks are ranked by the minimum difference within each block. In the proposed test, we use the variance of block to rank the blocks, with the least variance being ranked the smallest. In both Tukey test and the modified Friedman test, linear ranks are used for blocks and treatments. The Tukey test belongs to the family of weighted-ranking test from Quade. The modified Friedman test, the Friedman test and the Tukey test are compared under various conditions and the results indicate that the proposed test is generally more powerful than the Friedman test and the Tukey test when the number of groups is small.
Keywords
Friedman test; Nonparametric test; Power study; Randomized complete block design; Repeated measurements
Repository Citation
Xu, J.,
Shan, G.,
Amei, A.,
Zhao, J.,
Young, D.,
Clark, S.
(2015).
A Modified Friedman Test for Randomized Complete Block Designs.
Communications in Statistics - Simulation and Computation
http://dx.doi.org/10.1080/03610918.2015.1006777