The authors describe a method for statistically analyzing a student's proficiency at reading one of the distinct orthographies of Japanese, known as katakana. They provide a brief introduction to how a student model is constructed by analyzing a student's responses. A method is then presented for statistically analyzing a student model assuming that all of the phonological rules that would be required to completely transform these katakana into English contributed equally to the student's failure to understand. With this assumption, the student model becomes a binomial distribution for which the Bayes theorem is used to estimate the student's current knowledge state. A variety of techniques for assessing prior information is then proposed. The correlation between the probability of comprehension and the phonetic properties of transformation rules is addressed. It is shown that combining the binomial model with these factors allows the tutorial system to more accurately estimate a student's knowledge state and thus provide more efficient instruction. >