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The Asymptotic Distribution of Average Test Overlap Rate in Computerized Adaptive Testing

机译：计算机式自适应测试中平均测试重叠率的渐近分布

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摘要

The average test overlap rate is often computed and reported as a measure of test security risk or item pool utilization of a computerized adaptive test (CAT). Despite the prevalent use of this sample statistic in both literature and operations, its sampling distribution has never been known nor studied in earnest. In response, a proof is presented for the asymptotic distribution of a linear transformation of the average test overlap rate in fixed-length CAT. The theoretical results enable the estimation of standard error and construction of confidence intervals. Moreover, a practical simulation study demonstrates the statistical comparison of average test overlap rates between two CAT designs with different exposure control methods.
机译：通常计算平均测试重叠速率并报告为计算机化自适应测试（CAT）的测试安全风险或项目池利用率的量度。 尽管在文献和运营中使用了这种样本统计数据，但其采样分布从未知道也没有得到认真的。 作为响应，呈现了固定长度猫平均测试重叠速率的线性变换的渐近分布的证据。 理论结果使得标准误差估计和置信区间的构建。 此外，实际仿真研究表明，两只猫设计与不同曝光控制方法的两只猫设计之间的平均测试重叠速率的统计比较。

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