Careful considerations are necessary when there is a need to choose an anchor test form from a list of old test forms for equating under the random groups design. The choice of the anchor form potentially affects the accuracy of equated scores on new test forms. Few guidelines, however, can be found in the literature on choosing the anchor form.…

The overall aim was to examine effects of differences in group ability and features of the anchor test form on equating bias and the standard error of equating (SEE) using both real and simulated data. Chained kernel equating, Postratification kernel equating, and Circle-arc equating were studied. A college admissions test with four different…

Recent research has suggested that re-setting the standard for each administration of a small sample examination, in addition to the high cost, does not adequately maintain similar performance expectations year after year. Small-sample equating methods have shown promise with samples between 20 and 30. For groups that have fewer than 20 students,…

The aim of this study was to compare, by simulation, the accuracy of mapping a cut-score from one test to another by expert judgement (using the Angoff method) versus the accuracy with a small-sample equating method (chained linear equating). As expected, the standard-setting method resulted in more accurate equating when we assumed a higher level…

In observed-score equipercentile equating, the goal is to make scores on two scales or tests measuring the same construct comparable by matching the percentiles of the respective score distributions. If the tests consist of different items with multiple categories for each item, a suitable model for the responses is a polytomous item response…

In common-item equating the anchor block is generally built to represent a miniature form of the total test in terms of content and statistical specifications. The statistical properties frequently reflect equal mean and spread of item difficulty. Sinharay and Holland (2007) suggested that the requirement for equal spread of difficulty may be too…

The purpose of this study was to evaluate the combined effects of reduced equating sample size and shortened anchor test length on item response theory (IRT)-based linking and equating results. Data from two independent operational forms of a large-scale testing program were used to establish the baseline results for evaluating the results from…

Mixed-format tests containing both multiple-choice (MC) items and constructed-response (CR) items are now widely used in many testing programs. Mixed-format tests often are considered to be superior to tests containing only MC items although the use of multiple item formats leads to measurement challenges in the context of equating conducted under…

Test equating is a statistical procedure for adjusting for test form differences in difficulty in a standardized assessment. Equating results are supposed to hold for a specified target population (Kolen & Brennan, 2004; von Davier, Holland, & Thayer, 2004) and to be (relatively) independent of the subpopulations from the target population (see…

The equity properties can be used to assess the quality of an equating. The degree to which expected scores conditional on ability are similar between test forms is referred to as first-order equity. Second-order equity is the degree to which conditional standard errors of measurement are similar between test forms after equating. The purpose of…

Holland and colleagues derived a formula for analytical standard error of equating using the delta-method for the kernel equating method. Extending their derivation, this article derives an analytical standard error of equating procedure for the conventional percentile rank-based equipercentile equating with log-linear smoothing. This procedure is…

Equating of tests composed of both discrete and passage-based items using the nonequivalent groups with anchor test (NEAT) design is popular in practice. This study investigated the impact of discrete anchor items and passage-based anchor items on observed score equating via simulation. Results suggested that an anchor with a larger proportion of…

Equating functions are supposed to be population invariant, meaning that the choice of subpopulation used to compute the equating function should not matter. The extent to which equating functions are population invariant is typically assessed in terms of practical difference criteria that do not account for equating functions' sampling…

The purpose of this study was to empirically evaluate the impact of loglinear presmoothing accuracy on equating bias and variability across chained and post-stratification equating methods, kernel and percentile-rank continuization methods, and sample sizes. The results of evaluating presmoothing on equating accuracy generally agreed with those of…

Studied whether circular equating could provide an adequate measure of various types of equating error when applied to different equating methods under different equating designs. Analyses and simluations show that circular equating is generally invalid as a criterion to evaluate the adequacy of equating. (SLD)