Diagnostic judgments are often based on the comparison of two measures in order to judge whether the individual shows a genuine discrepancy in the traits or characteristics that the two measures represent. Until a perfect psychometric battery comes along, psychometricians can offer some guidance on the level of confidence to be placed in diagnostic judgments. In setting a level of confidence, three things have to be considered: (1) the size of the standard errors of measurement for the two variables, (2) the size of the observed difference between the two scores, and (3) the correlation between the measures of the two attributes one is studying. From an illustrative example of a child whose score was one standard deviation lower on a paragraph test than a word test, a procedure is worked out for preparing tables showing the "betting odds" for representative combinations of reliability, intercorrelation, and size of difference. The implications of these tables and the type of thinking they represent are applied to some samples of actual tests with the reliabilities and intercorrelations that characterize them. The texts examined briefly are the Davis reading tests, the Standard Diagnostic Reading Tests, and the reading tests of the Stanford Achievement Battery. A conclusion from the preceding analyses is that diagnosticians' hypotheses should be very tentative. (AMH)