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…

Mixed-format tests containing both multiple-choice and constructed-response items are widely used on educational tests. Such tests combine the broad content coverage and efficient scoring of multiple-choice items with the assessment of higher-order thinking skills thought to be provided by constructed-response items. However, the combination of…

This article presents the author's rejoinder to thinking about linking from issue 8(1). Particularly within the more embracing linking frameworks, e.g., Holland & Dorans (2006) and Holland (2007), there appears to be a major disjunction between (1) classification discourse: the supposed basis for classification, that is, the underlying theory…

"Linking" is a term given to a general class of procedures by which one represents scores X on one test or measure in terms of scores Y on another test or measure. A recent taxonomy by Holland and Dorans (2006; Holland, 2007) organizes the various types of links into three broad categories: prediction, scale aligning, and equating. In…

The equating of scores on alternate forms of different achievement tests through the use of the three-parameter latent trait model, item-response theory (IRT) equating, was compared with the results of score equatings based on conventional linear and curvilinear equating models. Ten equatings were completed for pairs of alternate forms of the…

Scores on the multiple-choice sections of alternate forms are equated through anchor-test equating for the Advanced Placement Program (AP) examinations. There is no linkage of free-response sections since different free-response items are given yearly. However, the free-response and multiple-choice sections are combined to produce a composite.…

A special case of examinee choice, the Optional Essay Problem, is examined from the point of view of test equating. The Optional Essay Problem involves equating essay scores when the examinees are required to select an optional essay topic from a list of topics in addition to taking a mandatory test required of all examinees. The conditions that…

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…

The effects of applying different methods of determining different sets of subscore weights on the composite score ranking of examinees were investigated. Four sets of subscore weights were applied to each of three examination results. The scores were from Advanced Placement (AP) Examinations in History of Art, Spanish Language, and Chemistry. One…

The extent to which log-linear smoothing could improve the accuracy of common-item equating by the chained equipercentile method in small samples of examinees was investigated with responses from a 100-item test and 93,283 examinees. Smoothing reduced the sample size required for a given degree of accuracy. (SLD)

An increasingly popular test format allows examinees to choose the items they will answer from among a larger set. When examinee choice is allowed fairness requires that the different test forms thus formed be equated for their possible differential difficulty. For this equating to be possible it is necessary to know how well examinees would have…

This study investigated the extent to which log-linear smoothing could improve the accuracy of common-item equating by the chained equipercentile method in small samples of examinees. Examinee response data from a 100-item test (the Advanced Placement Examination in United States History) were used to create two overlapping forms of 58 items each,…

This report builds on and extends existent research on population invariance to new tests and issues. The authors lay the foundation for a deeper understanding of the use of population invariance measures in a wide variety of practical contexts. The invariance of linear, equipercentile and IRT equating methods are examined using data from five…

When an examination consists, in whole or in part, of constructed response items, it is a common practice to allow the examinee to choose among a variety of questions. This procedure is usually adopted so that the limited number of items that can be completed in the allotted time does not unfairly affect the examinee. This results in the de facto…

This paper discusses the assumptions required by the item response theory (IRT) true-score equating method (with Stocking & Lord, 1983; scaling approach), which is commonly used in the nonequivalent groups with an anchor data-collection design. More precisely, this paper investigates the assumptions made at each step by the IRT approach to…