A Mark-Recapture Approach to Estimating Item Pool Compromise

Abstract

Testing organizations routinely investigate if secure exam material has been compromised and is consequently invalid for scoring and inclusion on future assessments. Beyond identifying individual compromised items, knowing the degree to which a form is compromised can inform decisions on whether the form can no longer be administered or when an item pool is compromised to such an extent that serious action on a broad scale must be taken to ensure the validity of score interpretations. Previous research on estimating the population of item compromise is sparse; however, this is a more generally long-studied problem in ecological research. In this note, we exemplify the utility of the mark-recapture technique to estimate the population of compromised items, first through a brief demonstration to introduce the fundamental concepts and then a more realistic scenario to illustrate applicability to large-scale testing programs. An effective use of this technique would be to longitudinally track changes in the estimated population to inform operational test security strategies. Many variations on mark-recapture exist and interpretation of the estimated population depends on several factors. Thus, this note is only meant to introduce the concept of mark-recapture as a useful application to evaluate a testing organization's compromise mitigation procedures.

Keywords: test security, item compromise, mark-recapture.

Figure 1.

Illustration of the interaction among mark-recapture parameters in the Chapman estimator of the Peterson method (Chapman, 1951).

Figure 2.

Illustration of the Jolly-Seber method to estimate the compromised population.