This paper lays out a framework for comparing the qualities and the quantities of information about student competence provided by multiple-choice and free-response test items. After discussing the origins of multiple-choice testing and recent influences for change, the paper outlines an "inference network" approach to test theory, in which students are characterized in terms of levels of understanding of key concepts in a learning area. It then describes how to build inference networks to address questions concerning the information about various criteria conveyed by alternative response formats. The types of questions that can be addressed in this framework include those that can be studied within the framework of standard test theory. Moreover, questions can be asked about generalized kinds of reliability and validity for inferences cast in terms of recent developments in cognitive psychology. (54pp.)