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Harpp, Hogan, and Jennings (1996): Response Similarity Index

response similarity index

Harpp, Hogan, and Jennings (1996) revised their Response Similarity Index somewhat from Harpp and Hogan (1993). This produced a new equation for a statistic to detect collusion and other forms of exam cheating:

where

EEIC denote the number of exact errors in common or identically wrong,

D is the number of items with a different response.

Note that D is calculated across all items, not just incorrect responses, so it is possible (and likely) that D>EEIC.  Therefore, the authors suggest utilizing a flag cutoff of 1.0 (Harpp, Hogan, & Jennings, 1996):

Analyses of well over 100 examinations during the past six years have shown that when this number is ~1.0 or higher, there is a powerful indication of cheating.  In virtually all cases to date where the exam has ~30 or more questions, has a class average <80% and where the minimum number of EEIC is 6, this parameter has been nearly 100% accurate in finding highly suspicious pairs.

However, Nelson (2006) has evaluated this index in comparison to Wesolowsky’s (2000) index and strongly recommends against using the HHJ.  It is notable that neither makes any attempt to evaluate probabilities or standardize.  Cizek (1999) notes that both Harpp-Hogan methods do not even receive attention in the psychometric literature.

This approach has very limited ability to detect cheating when the source has a high ability level. While individual classroom instructors might find the EEIC/D straightforward and useful, there are much better indices for use in large-scale, highstakes examinations.

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Nathan Thompson, PhD

CEO at Assessment Systems
Nathan Thompson, PhD, is CEO and Co-Founder of Assessment Systems Corporation (ASC). He is a psychometrician, software developer, author, and researcher, and evangelist for AI and automation. His mission is to elevate the profession of psychometrics by using software to automate psychometric work like item review, job analysis, and Angoff studies, so we can focus on more innovative work. His core goal is to improve assessment throughout the world. Nate was originally trained as a psychometrician, with an honors degree at Luther College with a triple major of Math/Psych/Latin, and then a PhD in Psychometrics at the University of Minnesota. He then worked multiple roles in the testing industry, including item writer, test development manager, essay test marker, consulting psychometrician, software developer, project manager, and business leader. He is also cofounder and Membership Director at the International Association for Computerized Adaptive Testing (iacat.org). He's published 100+ papers and presentations, but his favorite remains https://scholarworks.umass.edu/pare/vol16/iss1/1/.

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