Two modification formulas are presented for the test information function in order to provide better measures of local accuracies of the estimation of "theta" when maximum likelihood estimation is used to provide the estimate of ability "theta." A minimum bound of any estimator, biased or unbiased, is considered; and Formula 1 is proposed for the maximum likelihood estimator in place of the test information function. A minimum bound of the mean squared error is considered, and Modification Formula 2 is proposed. Examples are given using data from 2,356 subjects taking the Iowa Level 11 Vocabulary Subtest and 2,259 subjects taking Shiba's Tests of Word/Phrase Comprehension. The usefulness of these modified test information functions in computerized adaptive testing is discussed. These topics are also reviewed for the monotonically transformed latent variable. Fifteen graphs and 3 data tables are provided. (SLD)