The use of Bayesian statistics as the basis of classical analysis of data is described. Bayesian analysis is a set of procedures for changing opinions about a given phenomenon based upon rational observation of a set of data. The Bayesian arrives at a set of prior beliefs regarding some states of nature; he observes data in a study and then modifies his beliefs into posterior probabilities. The computational vehicle for determining posterior probabilities based upon observed data and prior beliefs is Bayes' theorem. Because of the problem of putting numerical values on prior information, the value of Bayesian ideas might ultimately be in the clarification of the classical approach rather than in substituting one for another. Application of the procedure to the concept of personal probability is used as an example of how the technique might apply to education. (DJ)