Detecting inappropriate test scores with optimal and practical appropriateness indices

Abstract

Several statistics have been proposed as quantitative indices of the appropriateness of a test score as a measure of ability. Two criteria have been used to evaluate such indices in previous research. The first criterion, standardization, refers to the extent to which the conditional distributions of an index, given ability, are invariant across ability levels. The second criterion, relative power, refers to indices’ relative effectiveness for detecting inappropriate test scores. In this paper the effectiveness of nine appropriateness indices is determined in an absolute sense by comparing them to optimal indices; an optimal index is the most powerful index for a particular form of aberrance that can be computed from item responses. Three indices were found to provide nearly optimal rates of detection of very low ability response patterns modified to simulate cheating, as well as very high ability response patterns modified to simulate spuriously low responding. Optimal indices had detection rates from 50% to 200% higher than any other index when average ability response vectors were manipulated to appear spuriously high and spuriously low.