题目难度分布和样本容量对两种CTT等值结果的影响

The Effects of Difficulty Distributions of Items and Sample Sizes on Two CTT Equating Methods

基于经典测验理论(CTT)的等值方法主要有线性等值和等百分位等值两种。在不同情境下,不同的等值方法会产生不同的等值结果。本研究以真分数等值为依据,用蒙特卡洛模拟研究方法,综合比较了各种题目难度分布条件下和各种样本容量条件下两种CTT等值方法的等值结果。研究结果表明:(1)线性等值的误差受题目难度分布影响较大,等百分位等值的误差几乎不受题目难度分布影响。(2)线性等值的误差几乎不受样本容量的影响,等百分位等值的误差受样本容量影响较大。(3)不论题目难度分布如何,只要样本容量足够大,等百分位等值的效果都比线性等值更好。

Researchers have developed many kinds of equating methods,among which,linear equating and equipercentile equating are the two most common which are based on Classical Test Theory（CTT）.Different equating methods would lead to different equating results.Based on the true score equating and single group design without anchor test and employed Monte Carlo simulation method,this research comprehensively compared the two CTT equating methods in different difficulty distributions of test items and different sample sizes.The simulation results showed as follows：（1） The error of linear equating was much affected by difficulty distributions of test items,while the error of equipercentile equating was hardly affected.（2） The error of linear equating was hardly affected by sample sizes,while the error of equipercentile equating was much affected.（3） No matter how the difficulty distributions of test items were,equipercentile equating was better than linear equating as long as the sample sizes were large enough.