Many item-fit statistics have been proposed for assessing whether the responses to test items ag gregated across examinees conform to IRT test models. Conversely, person-fit statistics have been proposed for assessing whether an examinee's re sponses aggregated across items are congruent with a specified IRT model. Statistical procedures to as sess item fit have differed from those to assess per son fit. This research compared a χ² item-fit index with a likelihood-based person-fit index. Eight 0,1 data matrices were simulated under the three- parameter logistic test model. Both the likelihood- based and χ² fit statistics were then computed for examinees and items, and Type I and Type II error rates were analyzed. With data simulated to fit the IRT model, the χ² test overidentified examinees and items as being misfitting, while the likelihood- based fit index held closer to the specified α levels. The two fit indices gave consistent (mis)fit-to- model results in 94 and 97 percent of cases for items and examinees, respectively, across simula tions. Under simulated conditions of data misfit, the χ² statistic detected misfit at a higher rate than the likelihood-based statistic, indicating that the χ² statistic was slightly more sensitive to response pat tern aberrancy. However, other considerations led to a recommendation for employing the likelihood- based index in applied fit analyses to evaluate both examinee and item model-data (mis)fit.