Assessments with a large amount of small, similar, or often repetitive tasks are being used in educational, neurocognitive, and psychological contexts. For example, respondents are asked to recognize numbers or letters from a large pool of those and the number of correct answers is a count variable. In 1960, George Rasch developed the Rasch…

This study investigated the extent to which class-specific parameter estimates are biased by the within-class normality assumption in nonnormal growth mixture modeling (GMM). Monte Carlo simulations for nonnormal GMM were conducted to analyze and compare two strategies for obtaining unbiased parameter estimates: relaxing the within-class normality…

Understanding exam score distributions has implications for item response theory (IRT), grade curving, and downstream modeling tasks such as peer grading. Historically, grades have been assumed to be normally distributed, and to this day the normal is the ubiquitous choice for modeling exam scores. While this is a good assumption for tests…

This paper describes a method for pooling grouped, ordered-categorical data across multiple waves to improve small-sample heteroskedastic ordered probit (HETOP) estimates of latent distributional parameters. We illustrate the method with aggregate proficiency data reporting the number of students in schools or districts scoring in each of a small…

Despite broad applications of growth curve models, few studies have dealt with a practical issue -- nonnormality of data. Previous studies have used Student's "t" distributions to remedy the nonnormal problems. In this study, robust distributional growth curve models are proposed from a semiparametric Bayesian perspective, in which…

Test score distributions of schools or demographic groups are often summarized by frequencies of students scoring in a small number of ordered proficiency categories. We show that heteroskedastic ordered probit (HETOP) models can be used to estimate means and standard deviations of multiple groups' test score distributions from such data. Because…

Describing the variation in test scores between and within school districts is critical for: (1) for policy-related and descriptive work that investigates the sorting of students among districts and the differential effectiveness of those districts; and (2) for methodological work planning future experiments or interventions. Intraclass…

Value-added models have been widely used to assess the contributions of individual teachers and schools to students' academic growth based on longitudinal student achievement outcomes. There is concern, however, that ignoring the presence of missing values, which are common in longitudinal studies, can bias teachers' value-added scores.…

In this study, eight statistical strategies were evaluated for selecting the parameterizations of loglinear models for smoothing the bivariate test score distributions used in nonequivalent groups with anchor test (NEAT) equating. Four of the strategies were based on significance tests of chi-square statistics (Likelihood Ratio, Pearson,…

With the coming of the information age, computer-based teaching model has had an important impact on English teaching. Since 2004, the trial instruction on Network-assisted Language Teaching (NALT) Model integrating the English instruction and computer technology has been launched at some universities in China, including China university of…

An evolved form of the Edwards and Beckworth (1989) model for probability selection for Scholastic Achievement Test takers using truncated normal distributions is presented. It is shown that the arguments of Holland and Wainer are not sufficient to reject this model. (SLD)

An optimization model is presented that allows test assemblers to control the shape of the observed-score distribution on a test for a population with a known ability distribution. An obvious application is for item response theory-based test assembly in programs where observed scores are reported and operational test forms are required to produce…