A Comprehensive Review and Comparison of CUSUM and Change-Point-Analysis Methods to Detect Test Speededness

Abstract

Cumulative sum (CUSUM) and change-point analysis (CPA) are two well-established statistical process control methods to detect changes in a sequence. Both have been used in psychometric research to detect aberrant responses in a response sequence, e.g., test speededness, inattentiveness, or cheating. However, the pros and cons of CUSUM and CPA in different testing settings still remain unclear. In this paper, we conduct a comprehensive comparison of the performance of twelve CUSUM-based statistics and three CPA-based procedures in detecting test speededness. Two speededness mechanisms are considered, namely the graduate change model (GCM) and the hybrid model (HM), to test the robustness and flexibility of the two methods. Simulation studies show that the performances of the statistics are affected by the underlying data generating model, the severity of speededness, and the test length. Generally, under HM some CUSUM statistics perform much better than the CPA-based statistics. Under the GCM, the performance of the CPA statistics is dramatically improved. Taken together, due to the unknown mechanism of speededness in real applications, two CUSUM-based statistics are recommended when the test length is long (e.g., 80 items), regardless of the underlying mechanism being HM or GCM. In a relatively short (e.g., 40 items) or medium-length (e.g., 60 items) test, no statistic always ends up in the top three under both HM and GCM. In those cases, either one of the two CUSUM-based statistics mentioned above can be a reasonable choice because of their good (though not necessarily the best) performance in a wide range of conditions.

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