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Psychometrika. 2019 Dec;84(4):1129-1151. doi: 10.1007/s11336-019-09674-5. Epub 2019 Jul 1.
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.
平均测试重叠率通常被计算和报告，作为计算机自适应测试（CAT）的测试安全性风险或项目池利用率的度量。尽管这个样本统计量在文献和操作中都被广泛使用，但它的抽样分布从未被真正了解或研究过。有鉴于此，本文提出了一种在固定长度 CAT 中平均测试重叠率的线性变换的渐近分布的证明。理论结果可以用于估计标准误差和构建置信区间。此外，实际的模拟研究表明了两种具有不同暴露控制方法的 CAT 设计之间的平均测试重叠率的统计比较。
