Comparing the Durbin, Wilcoxon Signed Ranks Test, and a Proposed Test in Balanced Incomplete Block Designs

By Rhonda Magel, Li Cao and Alfred Ndungu.

Published by The International Journal of Science in Society

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This study compares the powers of the Durbin test to those of the Wilcoxon Signed-Ranks Test for a Balanced Incomplete Block Design, with observations taken on two treatments per block, when it can be assumed that if some of the treatment effects do differ, they follow a nondecreasing (or nonincreasing) pattern. A new test is proposed allowing for two or more treatments to be applied in each block. Various combinations of treatment effects are considered for 3, 4, and 5 treatments when the underlying observations have normal distributions, t distributions with 3 degrees of freedom, or exponential distributions. The proposed test has higher powers when the treatment effects are nondecreasing (or nonincreasing). If the assumed ordering of the treatment effects is not correct, the Durbin test will have higher powers. Applications will be discussed.

Keywords: Nonparametric Statistical Tests, Assumed Ordering, Testing Treatment Effects

The International Journal of Science in Society, Volume 3, Issue 4, pp.1-16. Article: Print (Spiral Bound). Article: Electronic (PDF File; 838.224KB).

Dr. Rhonda Magel

Chair and Professor, Department of Statistics, North Dakota State University, Fargo, USA

I am a full professor and Chair of the Department of Statistics. I have been the major research advisor to many M.S. and Ph.D. students in statistics who have graduated. My primary research interest is in the area of nonparametric statistics. I have developed new nonparametric statistics for different types of mixed experimental designs. I have also developed new nonparametric statistics based on various order restricted assumptions for k populations, and nonparametric statistics for use with bivariate data.

Li Cao

Neuropsychiatric Research Institute, Fargo, USA

I am a statistical analyst of Neuropsychiatric Research Institute, Fargo, ND. Multilevel mixed model and generalizd linear model are my primary research interest. My research has maily been done in the eating disorder research area.

Alfred Ndungu

Ph.D. student, Statistics, North Dakota State University, Fargo, USA