This paper presents a new equating method for the nonequivalent groups with anchor test design: poststratification equating based on true anchor scores. The linear version of this method is shown to be equivalent, under certain conditions, to Levine observed score equating, in the same way that the linear version of poststratification equating is…

Quantitative information about test score reliability can be presented in terms of the distribution of equated scores on an alternate form of the test for test takers with a given score on the form taken. In this paper, we describe a procedure for estimating that distribution, for any specified score on the test form taken, by estimating the joint…

In this study, I investigated 2 procedures intended to create test-taker groups of equal ability by poststratifying on a composite variable created from demographic information. In one procedure, the stratifying variable was the composite variable that best predicted the test score. In the other procedure, the stratifying variable was the…

This booklet grew out of a half-day class on equating that author Samuel Livingston teaches for new statistical staff at Educational Testing Service (ETS). The class is a nonmathematical introduction to the topic, emphasizing conceptual understanding and practical applications. The class consists of illustrated lectures, interspersed with…

This article describes a preliminary investigation of an empirical Bayes (EB) procedure for using collateral information to improve equating of scores on test forms taken by small numbers of examinees. Resampling studies were done on two different forms of the same test. In each study, EB and non-EB versions of two equating methods--chained linear…

A series of resampling studies investigated the accuracy of equating by four different methods in a random groups equating design with samples of 400, 200, 100, and 50 test takers taking each form. Six pairs of forms were constructed. Each pair was constructed by assigning items from an existing test taken by 9,000 or more test takers. The…

Score equating based on small samples of examinees is often inaccurate for the examinee populations. We conducted a series of resampling studies to investigate the accuracy of five methods of equating in a common-item design. The methods were chained equipercentile equating of smoothed distributions, chained linear equating, chained mean equating,…

This article suggests a method for estimating a test-score equating relationship from small samples of test takers. The method does not require the estimated equating transformation to be linear. Instead, it constrains the estimated equating curve to pass through two pre-specified end points and a middle point determined from the data. In a…

A simultaneous equating of four new test forms to each other and to one previous form was accomplished through a complex design incorporating seven separate equating links. Each new form was linked to the reference form by four different paths, and each path produced a different score conversion. The procedure used to resolve these inconsistencies…

This paper suggests two new, related methods for estimating a test-score equating relationship from small samples of test takers. These methods do not require the estimated equating transformation to be linear. Instead, they constrain the estimated equating curve to pass through 2 prespecified end-points and a middle point determined from the…

This report proposes an empirical Bayes approach to the problem of equating scores on test forms taken by very small numbers of test takers. The equated score is estimated separately at each score point, making it unnecessary to model either the score distribution or the equating transformation. Prior information comes from equatings of other…

A series of resampling studies was conducted to compare the accuracy of equating in a common item design using four different methods: chained equipercentile equating of smoothed distributions, chained linear equating, chained mean equating, and the circle-arc method. Four operational test forms, each containing more than 100 items, were used for…

Randomly equivalent forms (REF) of tests in listening and reading for nonnative speakers of English were created by stratified random assignment of items to forms, stratifying on item content and predicted difficulty. The study included 50 replications of the procedure for each test. Each replication generated 2 REFs. The equivalence of those 2…

This study examines how closely the kernel equating (KE) method (von Davier, Holland, & Thayer, 2004a) approximates the results of other observed-score equating methods--equipercentile and linear equatings. The study used pseudotests constructed of item responses from a real test to simulate three equating designs: an equivalent groups (EG)…

Kernel equating is a method of equating test scores devised by P. W. Holland and D. T. Thayer (1989). It takes its name from kernel smoothing, a process of smoothing a function by replacing each discrete value with a frequency distribution. It can be used when scores on two forms of a test are to be equated directly or when they are to be equated…