Oral reading fluency (ORF), used by teachers and school districts across the country to screen and progress monitor at-risk readers, has been documented as a good indicator of reading comprehension and overall reading competence. In traditional ORF administration, students are given one minute to read a grade-level passage, after which the…

The Monte Carlo method is one of the basic simulation statistical methods which can be used both to demonstrate basic probability and statistical concepts as well as to analyse the behaviour stochastic models. The introduction part of the article provides a brief description of the Monte Carlo method. The main part of the article is concentrated…

One of the most important goals in E-learning is to guarantee that participants reach the learning objectives. We have observed that having the knowledge of the subject is not sufficient for reaching learning objectives. The participants must also develop understanding that they know the subject, which we have named confidence. In this work, we…

In this article, a numerical method integrated with statistical data simulation technique is introduced to solve a nonlinear system of ordinary differential equations with multiple random variable coefficients. The utilization of Monte Carlo simulation with central divided difference formula of finite difference (FD) method is repeated n times to…

Purpose: This study aims to investigate the orthogonality assumption, which restricts the use of Bifactor item response theory under different conditions. Method: Data of the study have been obtained in accordance with the Bifactor model. It has been produced in accordance with two different models (Model 1 and Model 2) in a simulated way.…

When data for multiple outcomes are collected in a multilevel design, researchers can select a univariate or multivariate analysis to examine group-mean differences. When correlated outcomes are incomplete, a multivariate multilevel model (MVMM) may provide greater power than univariate multilevel models (MLMs). For a two-group multilevel design…

There has been growing interest in using statistical methods to analyze data and estimate effect size indices from studies that use single-case designs (SCDs), as a complement to traditional visual inspection methods. The validity of a statistical method rests on whether its assumptions are plausible representations of the process by which the…

We use Markov chain Monte Carlo (MCMC) analysis to construct a three-question math quiz to assess key skills needed for introductory finance. We begin with data collected from a ten-question criterion-referenced math quiz given to 314 undergraduates on the first day of class. MCMC indicates the top three questions for predicting overall course…

This study presents a new approach to synthesizing differential item functioning (DIF) effect size: First, using correlation matrices from each study, we perform a multigroup confirmatory factor analysis (MGCFA) that examines measurement invariance of a test item between two subgroups (i.e., focal and reference groups). Then we synthesize, across…

A multidimensional Bayesian item response model is proposed for modeling item position effects. The first dimension corresponds to the ability that is to be measured; the second dimension represents a factor that allows for individual differences in item position effects called persistence. This model allows for nonlinear item position effects on…

Online teaching evaluations have replaced in-class teaching evaluations as the new norm for assessing teaching performance. Faculty raise concerns regarding lower response rates compared to traditional in-class evaluations. A low response rate implies an underrepresentation of the target student population and threatens the validity of the…

Data simulation and Monte Carlo simulation studies are important skills for researchers and practitioners of educational and psychological measurement, but there are few resources on the topic specific to item response theory. Even fewer resources exist on the statistical software techniques to implement simulation studies. This article presents…

Monte Carlo simulations for uncertainty propagation take as inputs the uncertainty distribution for each variable and an equation for the calculation of a desired quantity. The desired quantity is then calculated by randomly drawing from the specified uncertainty distributions of the input variables. This calculation is then repeated many times…

The chiropractic clinical competency examination uses groups of items that are integrated by a common case vignette. The nature of the vignette items violates the assumption of local independence for items nested within a vignette. This study examines via simulation a new algorithmic approach for addressing the local independence violation problem…

Cognitive diagnostic models (CDMs) are a family of psychometric models designed to provide categorical classifications for multiple latent attributes. CDMs provide more granular evidence than other psychometric models and have potential for guiding teaching and learning decisions in the classroom. However, CDMs have primarily been conducted using…