CopyDetect

Fraud on standardized tests has been an increasing concern (Crouch, 2012; Hildebrand, 2012) because it invalidates the inferences made from test scores. The large-scale, self-report survey results consistently revealed that about 35% of high school students engaged in some type of test fraud two or more times in the previous year (Josephson Institute of Ethics, 2006, 2008, 2010), and answer exchange between two examinees is a type of test fraud commonly observed in multiple-choice examinations (Bopp, Gleason, & Misicka, 2001; Brimble & Clarke, 2005; Hughes & McCabe, 2006; Rakovski & Levy, 2007).

Identifying answer copying is an essential part of maintaining the integrity of test scores, and additional evidence is always necessary when a pair of examinees is suspected of exchanging answers on a multiple-choice test. Many scholars have developed a variety of analytical procedures and addressed the issue from a statistical perspective to provide additional evidence of answer copying between two examinees (Angoff, 1972; Bay, 1995; Bellezza & Bellezza, 1989; Cody, 1985; Frary, Tideman, & Watts, 1977; Hanson, Harris, & Brennan, 1987; Holland, 1996; Saupe, 1960; Sotaridona & Meijer, 2002, 2003; van der Linden & Sotaridona, 2006; Wollack, 1996). However, few of these indices have been shown to be effective and reliable based on the results from simulation studies (Bay, 1995; Hanson et al., 1987; Sotaridona & Meijer, 2002, 2003; Wollack, 1996, 2003, 2006; Wollack & Cohen, 1998; Zopluoglu & Davenport, 2012).

The simulation studies showed that the ω index (Wollack, 1996) and generalized binomial test (GBT; van der Linden & Sotaridona, 2006) provide the highest detection rates, while holding the empirical Type I error rates below the nominal level. In addition, the K index (Holland, 1996), K₁ and K₂ (Sotaridona & Meijer, 2002), and S₁ and S₂ indices (Sotaridona & Meijer, 2003) have provided reasonable detection rates and held Type I error rates below the nominal level in simulation studies. Although much effort has been put into developing statistical indices for detecting answer copying, so far little effort has been made to develop accessible software for practitioners to compute statistical indices that have been found effective in the literature. To my knowledge, none of these useful indices are available for practitioners in any accessible software, either commercial or otherwise, for detecting answer copying (Integrity, 2005; ScanexII, 2008; Scrutiny!, 2005).

An R package, CopyDetect, is now available to compute the ω, GBT, K, K₁, K₂, S₁, and S₂ indices. The package has two separate functions to compute these indices for dichotomous and nominal response outcomes. The functions require the raw data matrix with either dichotomous or nominal response outcomes, IRT model parameters (1PL, 2PL, 3PL, and nominal response IRT models), and the row numbers of suspected examinees in the data file. If dichotomous responses are provided and users are not able to obtain dichotomous IRT model item parameters from external software, the package internally uses the ltm engine (Rizopoulos, 2006) for estimating 2PL IRT model item parameters and uses them as input. However, if nominal responses are provided, the nominal IRT model item parameters must be obtained from external software and provided to the functions.

The CopyDetect package is available at no charge from the website http://www.r-project.org and works under Windows, Linux, and MacOS platforms. A reference manual is also available from the website. Version 2.14.1 (or later) of the R software (R Development Core Team, 2012) should be installed to be able to use the CopyDetect package.