Criterion-referenced testing is an important area in the theory and practice of educational measurement. This study demonstrated that even these tests must be closely examined for construct validity. The dimensionality of a dataset will be affected by the examinee's cognitive processes as well as by the nature of the content domain. The methods of extracting a unidimensional subset from an achievement dataset were studied. A second purpose was to apply a general technique for detecting aberrant response patterns derived from wrong rules of operation. The Individual Consistency Index (ICI) was found effective in detecting the anomalous response patterns resulting from some misconceptions. However, it requires repeated measures. Applicability to tests that do not have several parallel items to measure the performance of a single task will be limited. Although computerized error diagnostic programs can identify misconceptions possessed by a student in the very specific domain of arithmetic, ICI can be applicable to more general domains. It can detect candidates to route to the expensive error-diagnostic programs. (Author/DWH)