According to Wollack and Schoenig (2018, The Sage encyclopedia of educational research, measurement, and evaluation. Thousand Oaks, CA: Sage, 260), benefiting from item preknowledge is one of the three broad types of test fraud that occur in educational assessments. We use tools from constrained statistical inference to suggest a new statistic that is based on item scores and response times and can be used to detect examinees who may have benefited from item preknowledge for the case when the set of compromised items is known. The asymptotic distribution of the new statistic under no preknowledge is proved to be a simple mixture of two χ² distributions. We perform a detailed simulation study to show that the Type I error rate of the new statistic is very close to the nominal level and that the power of the new statistic is satisfactory in comparison to that of the existing statistics for detecting item preknowledge based on both item scores and response times. We also include a real data example to demonstrate the usefulness of the suggested statistic.

中文翻译：

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使用项目分数和响应时间来检测可能从项目预知中受益的考生。

根据 Wollack 和 Schoenig（2018 年，Sage 教育研究、测量和评估百科全书。加利福尼亚州千橡市：Sage，260），受益于项目预知是教育评估中发生的三大测试欺诈类型之一。我们使用来自受约束的统计推断的工具来建议基于项目分数和响应时间的新统计数据，并且可用于在已知受损项目集的情况下检测可能从项目预知中受益的考生。在没有预知的情况下，新统计量的渐近分布被证明是两个 χ ²的简单混合分布。我们进行了详细的模拟研究，以表明新统计量的 I 类错误率非常接近名义水平，并且与基于两者的检测项目预知识的现有统计量相比，新统计量的功效令人满意项目分数和响应时间。我们还包括一个真实的数据示例，以证明建议的统计数据的有用性。