Abstract

The focus of this dissertation is the comparison of some orthodox statistical methods of analysis to Bayesian methods. The comparison is made in terms of inferences about the support afforded alternative models by an extensive set of genuine data from an experiment in educational psychology. ;Scientists need a generally reliable measure of the relative degree to which competing models are supported by experimental evidence. Such a measure, to be useful, must be computationally tractable, and concisely stateable for reporting in scientific journals and in informal communication with colleagues. These considerations were the basis for judging the relative value of the orthodox and Bayesian methodologies. ;The orthodox method applied in the dissertation was the use of an F-test based on chi-square statistics. No one method appears to be universally accepted by Bayesians. After considering several candidates, the method of average likelihood was selected as the Bayesian methodology. ;It was shown that both methodologies have serious problems. The orthodox methodology is computationally simpler but suffers from some conceptual difficulties. The Bayesian analysis suffers from overwhelming computational difficulties. The principal difficulty for both methodologies appeared to be an inability to handle stochastic dependencies in the data. ;The problems with both methodologies make them unreliable, in the sense that a practicing scientist could not accept the implications of the methods without questioning the validity of those results. A further complication is that the Bayesian and orthodox procedures give extremely different results for the comparison of the models on the data at hand. It is evident both methodologies need further development and testing, particularly with data exhibiting dependencies