Date of Award


Degree Name

Doctor of Philosophy



First Advisor

Dr. Joseph W. McKean

Second Advisor

Dr. Je ffery T. Terpstra

Third Advisor

Dr. Jung Chao Wang

Fourth Advisor

Dr. Bradley E. Huitema


Ordered alternatives, rank based estimator, joint rank estimator, statistics, rank based procedures


The ordered alternatives in a one-way layout with k ordered treatment levels are appropriate for many applications, especially in psychology and medicine. There is extensive literature in this area, and many parametric and nonparametric approaches have been introduced. Abelson-Tukey (AT) test is a frequently used parametric method. Its coefficients provide an ideal way of combining means for the purpose of detecting a monotonic relationship between the independent and dependent variables. The AT method, though, is not robust. Furthermore, our initial empirical studies show that it is not more powerful than the Jonckheere-Terpstra (JT) and the Hettmansperger- Norton (HN) nonparametric tests at normal errors for moderate sample sizes. Theses nonparametric tests, unlike the AT test, are not easily extended to general linear and mixed models.

We have developed a rank-based procedure which has the same optimal efficacy properties as the HN procedure for the ordered and umbrella alternative problems, including the unknown peak problem. It is a rank-based procedure and is easily extended to linear, mixed and covariance models. The procedure can utilize general score functions.

Access Setting

Dissertation-Open Access