Educational Testing Service, Princeton, New Jersey, USA.
Br J Math Stat Psychol. 2020 Nov;73(3):397-419. doi: 10.1111/bmsp.12187. Epub 2019 Aug 16.
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 χ 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.
根据 Wollack 和 Schoenig（2018 年，《 Sage 教育研究、测量和评估百科全书》。千橡市，CA：Sage，第 260 页）的说法，从项目先验知识中受益是教育评估中发生的三种广泛的考试作弊类型之一。我们使用受约束统计推断的工具来建议一种新的统计量，该统计量基于项目得分和反应时间，可以用于检测可能从项目先验知识中受益的考生，前提是已知受影响的项目集。在没有先验知识的情况下，新统计量的渐近分布被证明是两个 χ 分布的简单混合。我们进行了详细的模拟研究，表明新统计量的Ⅰ型错误率非常接近名义水平，并且与基于项目得分和反应时间的现有基于项目先验知识的检测统计量相比，新统计量的功效令人满意。我们还包括一个真实数据示例，以演示建议的统计量的有用性。
