Outlier Measures and Norming Methods for Computerized Adaptive Tests

The problem of identifying outliers has two important aspects: the choice of outlier measures, and the method to assess the degree of outlyingness (norming) of those measures. We introduce several classes of measures for identifying outliers in Computerized Adaptive Tests (CATs). Some of these measures are new and are constructed to take advantage of CAT's sequential choice of items; other measures are taken directly from paper and pencil (P&P) tests and are used for baseline comparisons. Assessing the degree of outlyingness of CAT responses however can not be applied directly from P&P tests because stopping rules associated with CATs yield examinee responses of varying lengths. Standard outlier measures are highly correlated with the varying lengths which makes comparison across examinees impossible. Therefore, we present and compare four methods which map outlier statistics to a familiar probability scale (a p-value). The application of these methods to CAT data is new. The methods are explored in the context of CAT data from the 1995 National Council Licensure EXamination (NCLEX).