Moosai-Sitahal, Susan

In this thesis a comparative study of treatment and carryover effects is performed for five statistical tests as they apply to a three treatment, three period crossover design. These tests are two likelihood based tests, namely, Ordinary Least Squares and Modified F-Test Approximation; two non parametric tests, the one of Bellavance and Tardif (1995) and the other of Ohrvik (1998); and The Generalized Estimating Equations test. This crossover design consists of six possible treatment sequences, (123, 132, 213, 231, 312 and 321) made up of three treatments, say 1, 2 and 3, being assigned to six subjects per group, for n groups. For each sequence, observations are taken for each period following the treatment. The statistical tests were used to determine treatment effects and carryover effects. Data is simulated for group sizes of 4, 8, 12 and 24 subjects per sequence, and different covariance structures. For each simulation, 2000 independent samples were generated and significance tests using the above five methods were carried out. The empirical percentage of Type I error for each test was defined as the proportion of p-values smaller or equal to a specified nominal alpha level. Alpha levels of 0.01%, 0.05% and 0.1% were chosen in this study.

In this thesis a prediction model using graduation rate as the performance indicator is obtained for community colleges for three cohort years, 2003, 2004, and 2005 in the states of California, Florida, and Michigan. Multiple Regression analysis, using an aggregate of seven predictor variables, was employed in determining this prediction model. From this prediction model, a predicted graduation rate was obtained for each of the 142 institutions in this study. Using this predicted graduation rate, an Institutional Performance Ratio (IPR), was then calculated for each institution, by dividing the actual graduation rate for each institution by its predicted graduation rate. These IPR values were then used to classify the performance of each institution as meeting expectation, exceeding expectation or falling below expectation. Inter institutional comparisons were also made using these IPR values.