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The Power of the K-Index (or PMIR) to Detect Copying

Lewis, Charles; Thayer, Dorothy T.
Publication Year:
Report Number:
ETS Research Report
Document Type:
Page Count:
Subject/Key Words:
Cheating, Multiple-Choice Tests, Statistical Significance, Probability


At the 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 suggested, based on the Bonferroni inequality. The resulting value is referred to as a 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 concluded that the power of the PMIR to detect substantial amount of unit is quite low, even when the Source has relatively large number of incorrect responses.

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