The effect of dimensionality on an adaptive test's ability estimation was examined. Two-dimensional data sets, which differed from one another in the interdimensional ability association, the correlation among the difficulty parameters, and whether the item discriminations were or were not confounded with item difficulty, were generated for 1,600 simulated examinees. The generated data were used for Bayesian computerized adaptive testing (CAT) simulations (three-parameter logistic model), and the CAT ability estimates were compared with the simulated examinees' known abilities. The dimensionality of response data shifted the focus for the minimization of measurement errors from known abilities (with unidimensional data) to the average of the latent abilities (with bidimensional data). Three tables and 24 graphs summarize the study results. (Author/SLD)