THE POWER OF THE K‐INDEX (OR PMIR) TO DETECT COPYING

Abstract

ABSTRACTAt Educational Testing Service, the K‐Index is used to assess unusual agreement between the incorrect responses of two test takers on a multiple‐choice test. Since the Fall of 1996, the value of the K‐Index used for this assessment has been adjusted, based on the Bonferroni inequality. The resulting value is referred to as the Probability of Matching Incorrect Responses (PMIR). If a test taker copies from someone (a Source) with no incorrect responses, the PMIR is useless (i.e., has zero power) for detecting unusual agreement. Similarly, if a Source has relatively few incorrect responses, the power of the PMIR will be low. We propose a framework within which to study the power of the PMIR. The power function derived within this framework exhibits quite complex behavior; however, we conclude that the power of the PMIR to detect substantial amounts of copying is quite low, even when the Source has a relatively large number of incorrect responses.