A modified Friedman test for randomized complete block designs

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.

Keywords:

• Friedman test
• Nonparametric test
• Power study
• Randomized complete block design
• Repeated measurements

Mathematics Subject Classification:

• 62G30
• 62G10

Acknowledgments

The authors thank the referee and the editor for their knowledgeable comments to improve the manuscript. The authors also thank the Southern Nevada Health District for providing the trail usage data.