Educational assessment concerns inference about students' knowledge, skills, and accomplishments. Because data are never so comprehensive and unequivocal as to ensure certitude, test theory evolved in part to address questions of weight, coverage, and import of data. The resulting concepts and techniques can be viewed as applications of more general principles for inference in the presence of uncertainty. Issues of evidence and inference in educational assessment are discussed from this perspective. Apprehending the evidential value of assessment data means defining what the researcher wishes to accomplish or the purposes for assessment and specifying what is needed to find out about students. Then a principled framework can be constructed to evaluate and improve efforts. As a general framework for reasoning in the presence of uncertainty, the paradigm of mathematical probability provides tools and concepts. (Contains 5 tables, 18 figures, and 69 references.) (Author/SLD)