This study addressed 2 issues of using loglinear models for smoothing univariate test score distributions and for enhancing the stability of equipercentile equating functions. One issue was a comparative assessment of several statistical strategies that have been proposed for selecting 1 from several competing model parameterizations. Another…

Nine statistical strategies for selecting equating functions in an equivalent groups design were evaluated. The strategies of interest were likelihood ratio chi-square tests, regression tests, Kolmogorov-Smirnov tests, and significance tests for equated score differences. The most accurate strategies in the study were the likelihood ratio tests…

This article discusses a particular type of concordance table and the potential for test score misuse that may result from employing such a table. The concordance that is discussed is typically created between scores on different, nonequatable versions of a test that share the same or close to the same test title. These concordance tables often…

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 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…

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…

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…

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…

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.…

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…