Two New Statistics to Detect Answer Copying
Abstract
Two new indices to detect answer copying on a multiple‐choice test—S1 and S2—were proposed. The S1 index is similar to the K index (Holland, 1996) and the K2 index (Sotaridona & Meijer, 2002) but the distribution of the number of matching incorrect answers of the source and the copier is modeled by the Poisson distribution instead of the binomial distribution to improve the detection rate of K and K2. The S2 index was proposed to overcome a limitation of the K and K2 index, namely, their insensitiveness to correct answers copying. The S2 index incorporates the matching correct answers in addition to the matching incorrect answers. A simulation study was conducted to investigate the usefulness of S1 and S2 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 S1 and S2 were compared with those of the K2 and the ω copying index (Wollack, 1997). Results showed that all four indices were able to maintain their Type I errors, with S1 and K2 being slightly conservative compared to S2 and ω. Furthermore, S1 had higher detection rates than K2. The S2 index showed a significant improvement in detection rate compared to K and K2.
Citing Literature
Number of times cited according to CrossRef: 30
- Qingping He, Michelle Meadows, Beth Black, An introduction to statistical techniques used for detecting anomaly in test results, Research Papers in Education, 10.1080/02671522.2020.1812108, (1-19), (2020).
- Kaiwen Man, Jeffrey R. Harring, Sandip Sinharay, Use of Data Mining Methods to Detect Test Fraud, Journal of Educational Measurement, 10.1111/jedm.12208, 56, 2, (251-279), (2019).
- Cengiz Zopluoglu, Detecting Examinees With Item Preknowledge in Large-Scale Testing Using Extreme Gradient Boosting (XGBoost), Educational and Psychological Measurement, 10.1177/0013164419839439, (001316441983943), (2019).
- Tobias Cagala, Ulrich Glogowsky, Johannes Rincke, Commitment to a No-Cheating Rule Can Increase Cheating, SSRN Electronic Journal, 10.2139/ssrn.3111855, (2018).
- César Martinelli, Susan W. Parker, Ana Cristina Pérez-Gea, Rodimiro Rodrigo, Cheating and Incentives: Learning from a Policy Experiment, American Economic Journal: Economic Policy, 10.1257/pol.20150066, 10, 1, (298-325), (2018).
- Hotaka Maeda, Bo Zhang, An Algorithm to Improve Test Answer Copying Detection Using the Omega Statistic, International Journal of Testing, 10.1080/15305058.2016.1217418, 17, 1, (55-73), (2016).
- Jeff Allen, Andrew Ghattas, Estimating the Probability of Traditional Copying, Conditional on Answer-Copying Statistics, Applied Psychological Measurement, 10.1177/0146621615622780, 40, 4, (258-273), (2016).
- Cengiz Zopluoglu, Classification Performance of Answer-Copying Indices Under Different Types of IRT Models, Applied Psychological Measurement, 10.1177/0146621616664724, 40, 8, (592-607), (2016).
- Marcelo Perlin, Creating and Grading Latex Exams with Randomized Content Using RndTexExams, SSRN Electronic Journal, 10.2139/ssrn.2806570, (2016).
- Mauricio Romero, Álvaro Riascos, Diego Jara, On the Optimality of Answer-Copying Indices, Journal of Educational and Behavioral Statistics, 10.3102/1076998615595628, 40, 5, (435-453), (2016).
- James A. Wollack, Computer Software Review: Cheating Detection at Your Fingertips, Applied Psychological Measurement, 10.1177/0146621607300853, 31, 3, (233-239), (2016).
- Leonardo S. Sotaridona, Wim J. van der Linden, Rob R. Meijer, Detecting Answer Copying Using the Kappa Statistic, Applied Psychological Measurement, 10.1177/0146621606288891, 30, 5, (412-431), (2016).
- Rob R. Meijer, A. Susan M. Niessen, Jorge N. Tendeiro, A Practical Guide to Check the Consistency of Item Response Patterns in Clinical Research Through Person-Fit Statistics, Assessment, 10.1177/1073191115577800, 23, 1, (52-62), (2015).
- CCsar A Martinelli, Susan Parker, Ana Cristina Perez-Gea, Rodimiro Rodrigo, Cheating and Incentives: Learning from a Policy Experiment, SSRN Electronic Journal, 10.2139/ssrn.2606487, (2015).
- Mauricio Romero, Alvaro Riascos, Diego Jara, A Derivation of the Optimal Answer-Copying Index and Some Applications, SSRN Electronic Journal, 10.2139/ssrn.2414058, (2014).
- Mauricio Romero, Alvaro Riascos, Diego Jara, A Derivation of the Optimal Answer-Copying Index and Some Applications, SSRN Electronic Journal, 10.2139/ssrn.2489178, (2014).
- Zhan Shu, Robert Henson, Richard Luecht, Using Deterministic, Gated Item Response Theory Model to Detect Test Cheating due to Item Compromise, Psychometrika, 10.1007/s11336-012-9311-3, 78, 3, (481-497), (2013).
- Jorge N. Tendeiro, Rob R. Meijer, Lolle Schakel, Annette M. Maij-de Meij, Using Cumulative Sum Statistics to Detect Inconsistencies in Unproctored Internet Testing, Educational and Psychological Measurement, 10.1177/0013164412444787, 73, 1, (143-161), (2012).
- Cengiz Zopluoglu, CopyDetect, Applied Psychological Measurement, 10.1177/0146621612463119, 37, 1, (93-95), (2012).
- Cengiz Zopluoglu, Ernest C. Davenport, The Empirical Power and Type I Error Rates of the GBT and ω Indices in Detecting Answer Copying on Multiple-Choice Tests, Educational and Psychological Measurement, 10.1177/0013164412442941, 72, 6, (975-1000), (2012).
- Stephen J. Zaccaro, Gia A. Dirosa, The Processes of Team Staffing: A Review of Relevant Studies, International Review of Industrial and Organizational Psychology 2012, 10.1002/9781118311141, (197-229), (2012).
- Carlos Zerpa, Krystal Hachey, Christina van Barneveld, Marielle Simon, Modeling Student Motivation and Students’ Ability Estimates From a Large-Scale Assessment of Mathematics, SAGE Open, 10.1177/2158244011421803, 1, 2, (215824401142180), (2011).
- Brian H. Kim, Deception and Applicant Faking: Putting the Pieces Together, International Review of Industrial and Organizational Psychology 2011, 10.1002/9781119992592, (181-217), (2011).
- Robert Liebler, Action and Ethics Education, Journal of Academic Ethics, 10.1007/s10805-010-9114-z, 8, 2, (153-160), (2010).
- Diego Jara, Alvaro Riascos, Mauricio Romero, Detecting Answer Copying in Standardized Tests (In Spanish), SSRN Electronic Journal, 10.2139/ssrn.1625509, (2010).
- Wim J. van der Linden, A Bivariate Lognormal Response-Time Model for the Detection of Collusion Between Test Takers, Journal of Educational and Behavioral Statistics, 10.3102/1076998609332107, 34, 3, (378-394), (2009).
- L. Andries van der Ark, Wilco H. M. Emons, Klaas Sijtsma, Detecting Answer Copying Using Alternate Test Forms and Seat Locations in Small‐Scale Examinations, Journal of Educational Measurement, 10.1111/j.1745-3984.2007.00055.x, 45, 2, (99-117), (2008).
- Walter M. Haney, Michael J. Clarke, Cheating on Tests, Psychology of Academic Cheating, 10.1016/B978-012372541-7/50015-2, (255-287), (2007).
- James A. Wollack, Simultaneous Use of Multiple Answer Copying Indexes to Improve Detection Rates, Applied Measurement in Education, 10.1207/s15324818ame1904_3, 19, 4, (265-288), (2006).
- James A. Wollack, Comparison of Answer Copying Indices with Real Data, Journal of Educational Measurement, 10.1111/j.1745-3984.2003.tb01104.x, 40, 3, (189-205), (2006).
