Department of Educational Psychology, The University of Georgia, 323 Aderhold Hall, Athens, GA, 30602, USA.
Psychometrika. 2018 Jun;83(2):376-386. doi: 10.1007/s11336-017-9583-8. Epub 2017 Aug 22.
This paper demonstrates that, after applying a simple modification to Li and Stout's (Psychometrika 61(4):647-677, 1996) CSIBTEST statistic, an improved variant of the statistic could be realized. It is shown that this modified version of CSIBTEST has a more direct association with the SIBTEST statistic presented by Shealy and Stout (Psychometrika 58(2):159-194, 1993). In particular, the asymptotic sampling distributions and general interpretation of the effect size estimates are the same for SIBTEST and the new CSIBTEST. Given the more natural connection to SIBTEST, it is shown that Li and Stout's hypothesis testing approach is insufficient for CSIBTEST; thus, an improved hypothesis testing procedure is required. Based on the presented arguments, a new chi-squared-based hypothesis testing approach is proposed for the modified CSIBTEST statistic. Positive results from a modest Monte Carlo simulation study strongly suggest the original CSIBTEST procedure and randomization hypothesis testing approach should be replaced by the modified statistic and hypothesis testing method.
本文证明，在对 Li 和 Stout（Psychometrika 61(4):647-677, 1996）的 CSIBTEST 统计量进行简单修改后，可以实现该统计量的改进变体。结果表明，CSIBTEST 的这个修改版本与 Shealy 和 Stout（Psychometrika 58(2):159-194, 1993）提出的 SIBTEST 统计量有更直接的关联。特别是，SIBTEST 和新的 CSIBTEST 的渐近抽样分布和效应大小估计的一般解释是相同的。鉴于与 SIBTEST 的更自然联系，结果表明 Li 和 Stout 的假设检验方法对于 CSIBTEST 是不够的；因此，需要改进假设检验程序。基于提出的论点，为修改后的 CSIBTEST 统计量提出了一种新的基于卡方的假设检验方法。适度的蒙特卡罗模拟研究的积极结果强烈表明，原始的 CSIBTEST 程序和随机化假设检验方法应该被修改后的统计量和假设检验方法所取代。
