By comparing two large-scale professional development programs' content and impact on student achievement, we contribute to research on critical features of high quality professional development, especially content focus. Even though the programs are conducted in the same context and are highly similar if characterized according to established research frameworks, our results suggest that they differ in their impact on student achievement. We therefore develop an analytical framework that allow us to characterize the programs' content and delivery in detail. Through this approach, we identify important differences between the programs that provide explanatory value in discussing reasons for their differing impacts.

Test equating is used to ensure that test scores from different test forms can be used interchangeably. This paper aims to compare the statistical and computational properties from three equating frameworks: item response theory observed-score equating (IRTOSE), kernel equating and kernel IRTOSE. The real data applications suggest that IRT-based frameworks tend to providemore stable and accurate results than kernel equating. Nonetheless, kernel equating can provide satisfactory results if we can find a good model for the data, while also being much faster than the IRT-based frameworks. Our general recommendation is to try all methods and examine how much the equated scores change, always ensuring that the assumptions are met and that a good model for the data can be found.

When using kernel equating to equate two test forms, a bandwidth needs to be selected. The bandwidth parameter determines the smoothness of the continuized score distributions and has been shown to have a large effect on the kernel density estimate. There are a number of suggested criteria for selecting the bandwidth, and currently four of them have been implemented in kernel equating. In this paper, all four of the existing bandwidth selectors suggested for kernel equating are evaluated and compared against each other using real test data together with a new criterion that implements leave-one-out cross-validation. Although the bandwidth methods generally were similar in terms of equated scores, there were potentially important differences in the upper part of the score scale where critical admission decisions are typically made.

Multilevel modeling is an important tool for analyzing large-scale assessment data. However, the standard multilevel modeling will typically give biased results for such complex survey data. This bias can be eliminated by introducing design weights which must be used carefully as they can affect the results. The aim of this paper is to examine different approaches and to give recommendations concerning handling design weights in multilevel models when analyzing large-scale assessments such as TIMSS (The Trends in International Mathematics and Science Study). To achieve the goal of the paper, we examined real data from two countries and included a simulation study. The analyses in the empirical study showed that using no weights or only level 1 weights sometimes could lead to misleading conclusions. The simulation study only showed small differences in estimation of the weighted and unweighted models when informative design weights were used. The use of unscaled or not rescaled weights however caused significant differences in some parameter estimates.

This paper discusses the use of optimal scores as an alternative to sum scores and expected sum scores when analyzing test data. Optimal scores are built on nonparametric methods and use the interaction between the test takers´ responses on each item and the impact of the corresponding items on the estimate of their performance. Both theoretical arguments for optimal score as well as arguments built upon simulation results are given. The paper claims that in order to achieve the same accuracy in terms of mean squared error and root mean squared error, an optimally scored test needs substantially fewer items than a sum scored test. The top-performing test takers and the bottom 5% test takers are by far the groups that benefit most from using optimal scores.

This article promotes the use of modern test theory in testing situations where sum scores for binary responses are now used. It directly compares the efficiencies and biases of classical and modern test analyses and finds an improvement in the root mean squared error of ability estimates of about 5% for two designed multiple-choice tests and about 12% for a classroom test. A new parametric density function for ability estimates, the tilted scaled , is used to resolve the nonidentifiability of the univariate test theory model. Item characteristic curves (ICCs) are represented as basis function expansions of their log-odds transforms. A parameter cascading method along with roughness penalties is used to estimate the corresponding log odds of the ICCs and is demonstrated to be sufficiently computationally efficient that it can support the analysis of large data sets.

This book describes how to use test equating methods in practice. The non-commercial software R is used throughout the book to illustrate how to perform different equating methods when scores data are collected under different data collection designs, such as equivalent groups design, single group design, counterbalanced design and non equivalent groups with anchor test design. The R packages equate, kequate and SNSequate, among others, are used to practically illustrate the different methods, while simulated and real data sets illustrate how the methods are conducted with the program R. The book covers traditional equating methods including, mean and linear equating, frequency estimation equating and chain equating, as well as modern equating methods such as kernel equating, local equating and combinations of these. It also offers chapters on observed and true score item response theory equating and discusses recent developments within the equating field. More specifically it covers the issue of including covariates within the equating process, the use of different kernels and ways of selecting bandwidths in kernel equating, and the Bayesian nonparametric estimation of equating functions. It also illustrates how to evaluate equating in practice using simulation and different equating specific measures such as the standard error of equating, percent relative error, different that matters and others.