Two new statistics to detect answer copying

Two new indices to detect answer copying on a multiple-choice test, S(1) and S(2) (subscripts), are proposed. The S(1) index is similar to the K-index (P. Holland, 1996) and the K-overscore(2), (K2) index (L. Sotaridona and R. Meijer, in press), but the distribution of the number of matching incorrect answers of the source (examinee s) and the copier (examinee c) is modeled by the Poisson distribution instead of the binomial distribution to improve the detection rate of K and K2. The S(2) index was proposed to overcome a limitation of the K and K2 indexes, namely their insensitiveness to correct answers copying. The S(2) index incorporates the matching correct answers in addition to the matching incorrect answers. A simulation study was conducted to investigate the usefulness of S(1) and S(2) for 40- and 80- item tests, 100 and 500 sample sizes, and 10%, 20%, 30% , and 40% answer copying. The Type I errors and detection rates of S(1) and S(2) were compared with those of the K2 and the w (omega) copying index (J. Wollack, 1997). Results show that all four indexes are able to maintain their Type I errors, with S(1) and K2 being slightly conservative compared to S(2) and w. Furthermore, S(1) had higher detection rates than K2. The S(2) index showed a significant improvement in detection rate compared to K and K2.