Harpp and Hogan (1993) suggested a response similarity index defined as Response Similarity Index Explanation EEIC denote the number of exact errors in common or identically wrong, EIC is the number of errors in common. This is calculated for all pairs of examinees that the researcher wishes to compare. One advantage of this approach is […]
This index evaluates error similarity analysis (ESA), namely estimating the probability that a given pair of examinees would have the same exact errors in common (EEIC), given the total number of errors they have in common (EIC) and the aggregated probability P of selecting the same distractor. Bellezza and Bellezza utilize the notation of k=EEIC […]
The Frary, Tideman, and Watts (1977) g2 index is a collusion (cheating) detection index, which is a standardization that evaluates a number of common responses between two examinees in the typical standardized format: observed common responses minus the expectation of common responses, divided by the expected standard deviation of common responses. It compares all pairs […]
Wollack (1997) adapted the standardized collusion index of Frary, Tidemann, and Watts (1977) g2 to item response theory (IRT) and produced the Wollack Omega (ω) index. It is clear that the graphics in the original article by Frary, Tideman, and Watts (1977) were crude classical approximations of an item response function, so Wollack replaced the […]
Wesolowsky’s (2000) index is a collusion detection index, designed to look for exam cheating by finding similar response vectors amongst examinees. It is in the same family as g2 and Wollack’s ω. Like those, it creates a standardized statistic by evaluating the difference between observed and expected common responses and dividing by a standard error. […]
Wise and Kong (2005) defined an index to flag examinees not putting forth minimal effort, based on their response time. It is called the response time effort (RTE) index. Let K be the number of items in the test. The RTE for each examinee j is where TCji is 1 if the response time on […]
The Holland K index and variants are probability-based indices for psychometric forensics, like the Bellezza & Bellezza indices, but make use of conditional information in their calculations. All three estimate the probability of observing wij or more identical incorrect responses (that is, EEIC, exact errors in common) between a pair of examinees in a directional […]
Guttman errors are a concept derived from the Guttman Scaling approach to evaluating assessments. There are a number of ways that they can be used. Meijer (1994) suggests an evaluation of Guttman errors as a way to flag aberrant response data, such as cheating or low motivation. He quantified this with two different indices, G […]
Test security is an increasingly important topic. There are several causes, including globalization, technological enhancements, and the move to a gig-based economy driven by credentials. Any organization that sponsors assessments that have any stakes tied to them must be concerned with security, as the greater the stakes, the greater the incentive to cheat. And threats […]
Psychometric forensics is a surprisingly deep and complex field. Many of the indices are incredibly sophisticated, but a good high-level and simple analysis to start with is overall time vs. scores, which I call Time-Score Analysis. This approach uses simple flagging on two easily interpretable metrics (total test time in minutes and number correct raw score) […]
