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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

【作者】 戴步云

【导师】 罗照盛;

【作者基本信息】 江西师范大学 , 应用心理学, 2011, 硕士

【摘要】 在测验研究领域内寻找测量同一心理品质的两个测验形式之间分数转换关系的统计技术,叫等值。等值来源于实际工作的需要,其目的是为了使得两个不同测验形式之间的分数具有可比性。迄今,学者们已经提出了多种等值方法,其中基于经典测验理论(CTT)的方法主要有线性等值和等百分位等值两种。不同的等值方法会产生不同的等值结果。于是,到底用哪种等值方法得到的结果更加精确,就成为学者们关注的问题。对此,国内外已经有过许多研究,但由于每个研究所采用的研究情境各不相同,因此结论也各不相同。本研究用蒙特卡洛模拟研究方法,用单组非锚测验设计,以真分数等值为依据,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,在本研究所设情境中:(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。本研究的结论和以往研究有一些不同之处,为此本文也进行了一些讨论。

【Abstract】 The statistical techniques used for converting two different test scores into a comparable scale is called equating when the test scores serve to measure the same psychological trait. Equating comes from practical jobs with the purpose of making the scores of two different tests comparable.Until now, the 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. Thus, scholars are much concerned about which method would produce the most accurate results. To this end, there are many researches conducted at home and abroad. However, due to different research contexts, the conclusions are not the same.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.The conclusions here were somewhat different from the previous results. They were also discussed in the paper.

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