Studies investigating the power of person-fit statistics often assume that the item parameters that are used to calculate the statistics are estimated in a sample without misfitting item score patterns. However, in practical test applications calibration samples likely will contain such patterns. In the present study, the influence of the type and the number of misfitting patterns in the calibration sample on the detection rate of the ZU3 statistic was investigated by means of simulated data. An increase in the number of misfitting simulees resulted in a decrease in the power of ZU3. Furthermore, the type of misfit and the test length influenced the power of ZU3. The use of an iterative procedure to remove the misfitting patterns from the dataset was investigated. Results suggested that this method can be used to improve the power of ZU3. Index terms: aberrance detection, appropriateness measurement, nonparametric item response theory, person fit, person-fit statistic ZU3.