Date of Award

6-1-2023

Degree Name

Doctor of Philosophy

Department

Statistics

First Advisor

Jeff Terpstra, Ph.D.

Second Advisor

Kevin Lee, Ph.D.

Third Advisor

Joshua Naranjo, Ph.D.

Fourth Advisor

Mike Tarn, Ph.D.

Keywords

Experimental design, Jonckheere-Terpstra, nonparametrics

Abstract

Two classes of nonparametric procedures for a replicated Latin square design that test for both general and increasing alternatives are developed. The two classes of procedures are similar in the sense that both transform the data so that existing well-known tests for randomized complete block designs can be utilized. On the other hand, the two classes differ in the way that the data is transformed - one class essentially aggregates the data while the other class aligns the data. Within these contexts, the exact distributions and asymptotic distributions are discussed, when applicable. The exact distributions are easily computed using the R statistical software. Type I error rates and power estimates were computed via simulation for several design variations (including error terms that follow a contaminated normal distribution). The simulations show that the proposed methods have stable Type I error rates. Regarding power, the simulation results indicate that the proposed ordered alternative tests outperform their general alternative counterparts when the treatment effects are indeed ordered. Moreover, the proposed methods can outperform the parametric versions of the tests for heavily contaminated normal distributions; although the class of tests based on aligning observations tend to have higher power than the tests based on aggregating the data. The proposed methods are illustrated with data from the existing literature.

Access Setting

Dissertation-Open Access

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