Publication Date


Document Type


First Advisor

Saunders, Roy (Professor of mathematics)

Degree Name

M.S. (Master of Science)

Legacy Department

Department of Mathematical Sciences


Experimental design; Binary system (Mathematics)


This thesis addresses the analysis of binary data for two cases of the two-period crossover design. The first case, the complete crossover, is the more common one in which each subject receives both treatments. The second case, the incomplete crossover, occurs when it is not possible to give the second treatment if a response to the first administered treatment was observed. In both cases, estimation and test procedures for hypotheses concerning treatment differences are discussed as well as differences due to sequence. For the complete crossover, intuitively appealing procedures for estimating treatment differences assuming no sequence effect are formulated by the method of maximum likelihood. Large sample normal approximation and generalized likelihood-ratio (GLR) tests are given for testing treatment differences. Similar tests are given for assessing sequence differences. Other procedures found in the literature for testing treatment and sequence effect are reviewed. For the incomplete crossover, current methodology and test procedures for treatment effect are discussed and a new approach is suggested. Shortcomings of the current methodology are brought to attention, some of which are negative variance estimates of treatment differences and a hidden assumption of independence of response. The new estimators suggested do not require this assumption and are derived by the method of maximum likelihood. Variance estimators of the treatment difference estimators are derived and two testing procedures are proposed, the large-sample normal test and the GLR test. A simulation study supports the use of the large-sample normal approximation for testing treatment differences. In the small-sample setting, analogues to the tests given for the complete crossover are suggested.


Bibliography: pages 64-65.


vii, 73 pages




Northern Illinois University

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