This articles discusses ways to respond to the need for criterion referenced information using Bayes' theorem, a method coupled with criterion referenced testing in the early 1970s. The theorem determines the most likely classification for an examinee from a dichotomous choice or through placement on a categorical or interval scale. A discussion is included on the application of the theorem to computer adaptive tests, in which an examinee's ability level is estimated during the testing process. Bayesain adaptive testing requires less pretesting; needs smaller item pool; can be applied to criterion referenced and diagnostic testing; can generate classifications based on multiple skills; and requires relatively little statistical knowledge relative to item response testing. The basic framework of this testing can be applied to a range of settings, and several classroom applications are presented. The framework can also be embedded in an intelligence tutoring system to determine mastery after each instructional unit. (Contains 16 references.) (JDM)