Outlier Detection in Test and Questionnaire Data

Abstract

Classical methods for detecting outliers deal with continuous variables. These methods are not readily applicable to categorical data, such as incorrect/correct scores (0/1) and ordered rating scale scores (e.g., 0, …, 4) typical of multi-item tests and questionnaires. This study proposes two definitions of outlier scores suited for categorical data. One definition combines information on outliers from scores on all the items in the test, and the other definition combines information from all pairs of item scores. For a particular item-score vector, an outlier score expresses the degree to which the item-score vector is unusual. For ten real-data sets, the distribution of each of the two outlier scores is inspected by means of Tukey's fences and the extreme studentized deviate procedure. It is investigated whether the outliers that are identified are influential with respect to the statistical analysis performed on these data. Recommendations are given for outlier identification and accommodation in test and questionnaire data.