Optimal Identification of Mismeasured Individuals

Optimal appropriateness measurement statistically provides the most powerful methods for identifying individuals who are mismeasured by a standardized psychological test or scale. These methods use a likelihood ratio test to compare the hypothesis of normal responding versus the alternative hypothesis that an individual's responses are aberrant in some specified way. According to the Neyman-Pearson Lemma, no other statistic computed from an individual's item responses can achieve a higher rate of detection of the hypothesized measurement anomaly at the same false positive rate. Use of optimal methods requires a psychometric model for normal responding, which can be readily obtained from the item response theory literature, and a model for aberrant responding. In this article, several concerns about measurement anomalies are described and transformed into quantitative models. We then show how to compute the likelihood of a response pattern u* for each of the aberrance models.