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…

Benefiting from item preknowledge (e.g., McLeod, Lewis, & Thissen, 2003) is a major type of fraudulent behavior during educational assessments. This paper suggests a new statistic that can be used for detecting the examinees who may have benefitted from item preknowledge using their response times. The statistic quantifies the difference in…

This dissertation is composed of a study of estimation methods in classical and test theories and the elaboration and application of a cluster-robust variance estimator. Variance estimators derived from generalized estimating equations are known to be robust to most covariance structures and are therefore well suited for psychometric analysis of…

We investigate the reliability of data from the Wage Indicator (WI), the largest online survey on earnings and working conditions. Comparing WI to nationally representative data sources for 17 countries reveals that participants of WI are not likely to have been representatively drawn from the respective populations. Previous literature has…

Background/Context: Pass/fail standardized exams frequently selectively rescore failing exams and retest failing examinees. This practice distorts the test score distribution and can confuse those who do analysis on these distributions. In 2011, the Wall Street Journal showed large discontinuities in the New York City Regent test score…

BASIE is a framework for interpreting impact estimates from evaluations. It is an alternative to null hypothesis significance testing. This guide walks researchers through the key steps of applying BASIE, including selecting prior evidence, reporting impact estimates, interpreting impact estimates, and conducting sensitivity analyses. The guide…

A strong foundation in early number concepts is crucial for students' future success in statistics. Despite its importance in statistics, many first-year students struggle to comprehend the normal distribution due to a lack of basic number sense. Students get confused about the order and magnitude of negative z-scores on a standard normal curve or…

Classical automated test assembly (ATA) methods assume fixed and known coefficients for the constraints and the objective function. This hypothesis is not true for the estimates of item response theory parameters, which are crucial elements in test assembly classical models. To account for uncertainty in ATA, we propose a chance-constrained…

Lord's (1980) equity theorem claims observed-score equating to be possible only when two test forms are perfectly reliable or strictly parallel. An analysis of its proof reveals use of an incorrect statistical assumption. The assumption does not invalidate the theorem itself though, which can be shown to follow directly from the discrete nature of…

One important issue in Bayesian estimation is the determination of an effective informative prior. In hierarchical Bayes models, the uncertainty of hyperparameters in a prior can be further modeled via their own priors, namely, hyper priors. This study introduces a framework to construct hyper priors for both the mean and the variance…

Background: Network meta-analysis (NMA) of survival data with a multidimensional treatment effect has been introduced as an alternative to NMA based on the proportional hazards assumption. However, these flexible models have some limitations, such as the use of an approximate likelihood based on discrete hazards, rather than a likelihood for…

Contribution: This article describes how a peer learning strategy called student-led tutorials (SLTs) can improve student performance in an electromagnetism course (EM). This study provides empirical evidence on how promoting student active participation in collaborative problem-solving activities improves performance rates. Background: In 2019,…

Children have limited exposure to statistical concepts and processes, yet researchers have highlighted multiple benefits of experiences in which they design and/or engage informally with statistical modelling. A study was conducted with a classroom in which students developed and utilised data-based models to respond to the inquiry question,…

The aim of this study was to examine the precision of item parameter estimation in different sample sizes and test lengths under three parameter logistic model (3PL) item response theory (IRT) model, where the trait measured by a test was not normally distributed or had a skewed distribution. In the study, number of categories (1-0), and item…

The purpose of the present study is to compare nonnormal distributions (i.e., t, skew-normal, skew-t with equal skew and skew-t with unequal skew) in growth mixture models (GMMs) based on diverse conditions of a number of time points, sample sizes, and skewness for intercepts. To carry out this research, two simulation studies were conducted with…