The Study Of Equating Problem Based On Item Response Theory

Equating is one of the important issues of the practice of Educational Measurement. Test equating is divided into horizontal equating and vertical equating according to the difficulty of the test paper and whether there is a significant difference in the distribution of the candidates’ ability. We need to adopt a suitable design and an appropriate method for a specific equating problem. The original equating methods are based on Classical Testing Theory, such as ”equipercentile equating”, ”linear equating” and so on. With Item Response Theory widely used in fields of Educational Statistical and Psychometric Measurement, a variety of equating methods based on IRT emerged, such as ”mean and mean method”, ”mean and sigma method”,”Item Characteristic Curve method” and so on. Compared with CTT equating methods, IRT equating methods can not only achieve score-equating between the different papers, but also calibrate the discrimination and difficulty of the questions on a unified measuring scale.This paper use IRT to solve two kinds of equating cases. In the horizontal equating case of IELTS, TOEFL and a Training test, we use ”single-group design” and ”equipercentile equating method” to give ”IRT equipercentile equating method”. This method uses the three-parameter logistic model and the Bayesian expected a posteriori estimation method to estimate item parameters and ability parameters. It converses score equating in different measuring scales to ability equating in the same measure in order to make the equating results are more reasonable.In the vertical equating case of the difference of ability during the period of compulsory education, we use ”anchor test design” and ”MM method” and ”MS method” based on IRT. Then we propose ”Weighted MM/MS equating method” in which the weight is related to Fisher Information. This method uses the two-parameter logistic model and Bayesian expected a posteriori estimation method to estimate item parameters and ability parameters. In this paper, we also introduce Stocking-Lord ”test characteristic curve equating method” and give Newton-Raphson interation process to estimate the equating conversion coefficient. At last, we analyze ability difference and give a kind of division of ability level during the period of compulsory education using ”Independent Sample Test”.