The Effects Of Difficulty Distributions Of Items And Sample Sizes On Two CTT Equating Methods

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.