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Applied Psychological Measurement
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A Parametric Cumulative Sum Statistic for Person Fit

Ronald D. Armstrong

Rutgers University, New Jersey, r.d.armstrong{at}att.net

Min Shi

California State University, Los Angeles

This article develops a new cumulative sum (CUSUM) statistic to detect aberrant item response behavior. Shifts in behavior are modeled with quadratic functions and a series of likelihood ratio tests are used to detect aberrancy. The new CUSUM statistic is compared against another CUSUM approach as well as traditional person-fit statistics. A simulation study demonstrates the advantage of the proposed method. Also, the person-fit methods are applied to real response data from the administration of a high-stakes exam. The use of CUSUM charts to help visually identify types of aberrant behavior is demonstrated.

Key Words: aberrancy detection • cheating • test familiarization • guessing near time limit • item response theory model • 3PL model • likelihood ratio • cumulative sum statistic

Applied Psychological Measurement, Vol. 33, No. 5, 391-410 (2009)
DOI: 10.1177/0146621609331961
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