Automatic Detection of Answer Copying via Kullback-Leibler Divergence and K-Index

Abstract

This article presents a new method to detect copying on a standardized multiple-choice exam. The method combines two statistical approaches in successive stages. The first stage uses Kullback-Leibler divergence to identify examinees, called subjects, who have demonstrated inconsistent performance during an exam. For each subject the second stage uses the K-Index to search for a possible source of the responses. Both stages apply a hypothesis test given a significance level. Monte Carlo methods are applied to approximate empirical distributions and then compute critical values providing a low Type I error rate and a good copying-detection rate. The results with both simulated and empirical data demonstrate the effectiveness of this approach.