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|
Chair and Professor, Department of Statistics, North Dakota State University, Fargo, USA
Neuropsychiatric Research Institute, Fargo, USA
Ph.D. student, Statistics, North Dakota State University, Fargo, USA