In many educational tests, both multiple-choice (MC) and constructed-response (CR) sections are used to measure different constructs. In many common cases, security concerns lead to the use of form-specific CR items that cannot be used for equating test scores, along with MC sections that can be linked to previous test forms via common items. In…

Adjustment by minimum discriminant information provides an approach to linking test forms in the case of a nonequivalent groups design with no satisfactory common items. This approach employs background information on individual examinees in each administration so that weighted samples of examinees form pseudo-equivalent groups in the sense that…

Recently, there has been an increasing level of interest in subscores for their potential diagnostic value. Haberman (2008b) suggested reporting an augmented subscore that is a linear combination of a subscore and the total score. Sinharay and Haberman (2008) and Sinharay (2010) showed that augmented subscores often lead to more accurate…

Continuous exponential families are applied to linking test forms via an internal anchor. This application combines work on continuous exponential families for single-group designs and work on continuous exponential families for equivalent-group designs. Results are compared to those for kernel and equipercentile equating in the case of chained…

For testing programs that administer multiple forms within a year and across years, score equating is used to ensure that scores can be used interchangeably. In an ideal world, samples sizes are large and representative of populations that hardly change over time, and very reliable alternate test forms are built with nearly identical psychometric…

A regression procedure is developed to link simultaneously a very large number of item response theory (IRT) parameter estimates obtained from a large number of test forms, where each form has been separately calibrated and where forms can be linked on a pairwise basis by means of common items. An application is made to forms in which a…

Sampling errors limit the accuracy with which forms can be linked. Limitations on accuracy are especially important in testing programs in which a very large number of forms are employed. Standard inequalities in mathematical statistics may be used to establish lower bounds on the achievable inking accuracy. To illustrate results, a variety of…

Grouped jackknifing may be used to evaluate the stability of equating procedures with respect to sampling error and with respect to changes in anchor selection. Properties of grouped jackknifing are reviewed for simple-random and stratified sampling, and its use is described for comparisons of anchor sets. Application is made to examples of item…

Continuous exponential families may be employed to find continuous distributions with the same initial moments as the discrete distributions encountered in typical applications of classical equating. These continuous distributions provide distribution functions and quantile functions that may be employed in equating. To illustrate, an application…

Continuous exponential families are applied to linking forms via a single-group design. In this application, a distribution from the continuous bivariate exponential family is used that has selected moments that match those of the bivariate distribution of scores on the forms to be linked. The selected continuous bivariate distribution then yields…

This study uses historical data to explore the consistency of SAT® I: Reasoning Test score conversions and to examine trends in scaled score means. During the period from April 1995 to December 2003, both Verbal (V) and Math (M) means display substantial seasonality, and a slight increasing trend for both is observed. SAT Math means increase more…