APPLICATION OF A BIVARIATE t DISTRIBUTION TO HYPOTHESIS TESTING IN CROSSOVER

PAUL WILDER STEWART. Application of a Bivariate t Distribution to Hypothesis Testing in Crossover Designs. Under the direction of RONALD H. HELMS, Ph.D. The joint distribution of a pair of Student-t variates, (tl ,t2), is investigated and methods of computing Pr{tl £ setl and t 2 E set2} are developed. The resulting algorith~s are used to evaluate the power and actual significance level of two-sided tests which are based on the test statistic max Iti I and the Bonferroni inequality. It is assumed that the numerators of t l and t 2 are dependent, that the denominators are dependent, and that nu~erators are independent of denominators. This research is motivated by an alternative 'by-period' analysis for crossover experiments recently suggested by Helms, Kempthorne and Shen (1980). Conceptual advantages of the byperiod analysis over the traditional analysis are discussed and a comparison is made with respect to the power of tests against alternative hypotheses. An original crossover experiment is report and analyzed according to the by-period method. The power of the treatment effects test is computed. A messy-data subset of the complete data is then re-analyzed and power is computed. The power of the analogous test in the traditional analysis is also computed and comparisons are made between the two analyses. It is found that the by-period testing procedure is more powerful than that in the traditional analysis for this problem.