Various applications of item response theory often require linking to achieve a common scale for item parameter estimates obtained from different groups. This article used a simulation to examine the relative performance of four different item response theory (IRT) linking procedures in a random groups equating design: concurrent calibration with…

This study examined variations of the nonequivalent-groups equating design for mixed-format tests--tests containing both multiple-choice (MC) and constructed-response (CR) items--to determine which design was most effective in producing equivalent scores across the two tests to be equated. Four linking designs were examined: (a) an anchor with…

The standard errors of the 2 most widely used population-invariance measures of equating functions, root mean square difference (RMSD) and root expected mean square difference (REMSD), are not derived for common equating methods such as linear equating. Consequently, it is unknown how much noise is contained in these estimates. This paper…

This study investigated the subgroup invariance of equating functions for a licensure test in the context of a nonequivalent groups with anchor test (NEAT) design. Examinees who had taken a new, to-be-equated form of the test were divided into three subgroups according to their previous testing experience: (a) repeaters who previously took the…

We explain how to simulate both univariate and bivariate raw data sets having specified values for common summary statistics. The first example illustrates how to "construct" a data set having prescribed values for the mean and the standard deviation--for a one-sample t test with a specified outcome. The second shows how to create a bivariate data…

In this study, a data base containing the responses of 40,000 candidates to 90 multiple-choice questions was used to mimic data sets for 50-item tests under the "nonequivalent groups with anchor test" (NEAT) design. Using these smaller data sets, we evaluated the performance of five linear equating methods for the NEAT design with five levels of…

Score equity assessment is an important analysis to ensure inferences drawn from test scores are comparable across subgroups of examinees. The purpose of the present evaluation was to assess the extent to which the Grade 8 NAEP Math and Reading assessments for 2005 were equivalent across selected states. More specifically, the present study…

This article uses simulation to compare two test equating methods under the common-item nonequivalent groups design: the frequency estimation method and the chained equipercentile method. An item response theory model is used to define the true equating criterion, simulate group differences, and generate response data. Three linear equating…

This study addressed the sampling error and linking bias that occur with small samples in a nonequivalent groups anchor test design. We proposed a linking method called the synthetic function, which is a weighted average of the identity function and a traditional equating function (in this case, the chained linear equating function). Specifically,…

In this study we examined variations of the nonequivalent groups equating design for tests containing both multiple-choice (MC) and constructed-response (CR) items to determine which design was most effective in producing equivalent scores across the two tests to be equated. Using data from a large-scale exam, this study investigated the use of…

Item response theory (IRT) methods are generally used to create score scales for large-scale tests. Research has shown that IRT scales are stable across groups and over time. Most studies have focused on items that are dichotomously scored. Now Rasch and other IRT models are used to create scales for tests that include polytomously scored items.…

Operational testing programs employing item response theory (IRT) applications benefit from of the property of item parameter invariance whereby item parameter estimates obtained from one sample can be applied to other samples (when the underlying assumptions are satisfied). In theory, this feature allows for applications such as computer-adaptive…

While measurement precision is relatively easy to establish for single tests and assessments, it is much more difficult to determine for decision making with multiple tests on different subjects. This latter is the situation in the system of final examinations for secondary education in the Netherlands and is used as an example in this paper. This…

To ensure fairness, it is important to better understand the relationship of language proficiency with the standard procedures of psychometric analysis. This paper examines how equating results are affected by an increase in the proportion of examinees who report that English is not their first language, using the analysis samples for a…

The psychometric considerations and challenges associated with including constructed response items on tests are discussed along with how these issues affect the form assembly specifications for mixed-format exams. Reliability and validity, security and fairness, pretesting, content and skills coverage, test length and timing, weights, statistical…