A modified Friedman test for randomized complete block designs

Authors

J Xu, University of Nevada, Las Vegas
G Shan, University of Nevada, Las VegasFollow
A Amei, University of Nevada, Las VegasFollow
J Zhao, University at BuffaloFollow
D Young, University of Nevada, Las VegasFollow
S Clark, University of Nevada, Las VegasFollow

Document Type

Article

Publication Date

1-1-2017

Publication Title

Communications in Statistics: Simulation and Computation

Volume

46

Issue

2

First page number:

1508

Last page number:

1519

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 (1979).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. © 2017 Taylor & Francis Group, LLC.

Language

english

Repository Citation

Xu, J., Shan, G., Amei, A., Zhao, J., Young, D., Clark, S. (2017). A modified Friedman test for randomized complete block designs. Communications in Statistics: Simulation and Computation, 46(2), 1508-1519.
http://dx.doi.org/10.1080/03610918.2015.1006777