Bayes Theorem leads to three indexes of item effectiveness: 1) probability that an examinee knows the content given that the correct response was selected; 2) probability that an examinee does not know that content given that an incorrect response was selected; and 3) probability of making a correct decision about the examinee's knowledge given the performance on that item. These indexes and classical item discrimination were compared for three definitions of "high" and "low" knowledge groups. The results indicated that the way of defining groups does make a difference and that there are two quite distinct characteristics of item effectiveness. (Author)