Expected a posteriori has a number of advantages over maximum likelihood estimation or maximum a posteriori (MAP) estimation methods. These include ability estimates (thetas) for all response patterns, less regression towards the mean than MAP ability estimates, and a lower average squared error. R. D. Bock and R. J. Mislevy (1982) state that the posterior standard deviation (PSD theta) is virtually interchangeable with the standard error (SEE). A typical criterion for terminating an adaptive test is when the theta's SEE is equal to or less than a predetermined value. However, if there are conditions in which the PSD theta is not interchangeable with the SEE, then the adaptive test may not be validly terminated. The use of the PSD theta in situations where an examinee is classified on the basis of his or her ability may lead to incorrect classifications if the PSD theta does not agree with the SEE. Results of this Monte Carlo study showed that the use of 10 quadrature points tends to result in PSD thetas which underestimate the observed standard error. The use of 80 quadrature points, given the test's length, is recommended where accurate PSD thetas are required. (Contains 8 figures, 14 tables, and 14 references.) (Author/SLD)