In administration of individually administered intelligence tests, items are commonly presented in a sequence of increasing difficulty, and test administration is terminated after a predetermined number of incorrect answers. This practice produces stochastically censored data, a form of nonignorable missing data. By manipulating four factors (i.e., treatment of nonresponses, ability estimation method, test length, and stopping rule), this study investigated how accurately ability parameters are recovered under these conditions. The results suggest that there might be a complex interaction among these manipulated factors with respect to parameter estimation bias. The worst estimates occur when nonadministered items are treated as incorrect. Treating nonadministered items as not presented or fractionally correct appears to produce more accurate ability estimates. Among the ability estimation methods examined in this study, the Expected A Posterior and Maximum A posteriori methods tend to produce less estimation error in the presence of censored data. The differences in missing data treatment methods tend to have greater impact on ability estimate under maximum likelihood estimation than Bayesian methods. (Contains 1 note, 5 tables, and 6 figures.)