In "Maths for Business," a large first-year mathematics module, the continuous assessment component comprises 10 weekly quizzes which combine to contribute 40% of the final module mark. If students did not receive the full five marks on their weekly quiz, they were provided with the opportunity to resubmit their corrected weekly quiz…

This paper deals with a brief history of probability theory and its applications to Jacob Bernoulli's famous law of large numbers and theory of errors in observations or measurements. Included are the major contributions of Jacob Bernoulli and Laplace. It is written to pay the tricentennial tribute to Jacob Bernoulli, since the year 2013…

This paper reviews recent research on causal inference with large-scale assessments in education from a Bayesian perspective. I begin by adopting the potential outcomes model of Rubin ("J Educ Psychol" 66:688-701, 1974) as a framework for causal inference that I argue is appropriate with large-scale educational assessments. I then…

Models of category learning have been extensively studied in cognitive science and primarily tested on perceptual abstractions or artificial stimuli. In this paper, we focus on categories acquired from natural language stimuli, that is, words (e.g., "chair" is a member of the furniture category). We present a Bayesian model that, unlike…

This study models graduation rates at 4-year broad access institutions (BAIs). We examine the student body, structural-demographic, and financial characteristics that best predict 6-year graduation rates across two time periods (2008-2009 and 2014-2015). A Bayesian model averaging approach is utilized to account for uncertainty in variable…

Stan is a flexible probabilistic programming language providing full Bayesian inference through Hamiltonian Monte Carlo algorithms. The benefits of Hamiltonian Monte Carlo include improved efficiency and faster inference, when compared to other MCMC software implementations. Users can interface with Stan through a variety of computing…

Multilayer perceptron neural networks, Gaussian naive Bayes, and logistic regression classifiers were compared when used to make early predictions regarding one-year college student persistence. Two iterations of each model were built, utilizing a grid search process within 10-fold cross-validation in order to tune model parameters for optimal…

Specialized imputation routines for multilevel data are widely available in software packages, but these methods are generally not equipped to handle a wide range of complexities that are typical of behavioral science data. In particular, existing imputation schemes differ in their ability to handle random slopes, categorical variables,…

This article presents a multilevel longitudinal nested logit model for analyzing correct response and error types in multilevel longitudinal intervention data collected under a pretest-posttest, cluster randomized trial design. The use of the model is illustrated with a real data analysis, including a model comparison study regarding model…

Educational stakeholders are keen to know the magnitude and importance of different interventions. However, the way evidence is communicated to support understanding of the effectiveness of an intervention is controversial. Typically studies in education have used the standardised mean difference as a measure of the impact of interventions. This…

Natural languages make prolific use of conventional constituent-ordering patterns to indicate "who did what to whom," yet the mechanisms through which these regularities arise are not well understood. A series of recent experiments demonstrates that, when prompted to express meanings through silent gesture, people bypass native language…

We present an active-learning strategy for undergraduates that applies Bayesian analysis to candy-covered chocolate m&m's®. The exercise is best suited for small class sizes and tutorial settings, after students have been introduced to the concepts of Bayesian statistics. The exercise takes advantage of the nonuniform distribution of…

The educational recommendation system to provide support for academic guidance and adaptive learning has always been an important issue of research for smart education. A bad guidance can give rise to difficulties in further studies and can be extended to school dropout. This paper explores the potential of Educational Data Mining for academic…

Background: Within undergraduate science courses, instructors often assess student thinking using closed-ended question formats, such as multiple-choice (MC) and multiple-true-false (MTF), where students provide answers with respect to predetermined response options. While MC and MTF questions both consist of a question stem followed by a series…

The main thesis of the present study is to use the Bayesian structural equation modeling (BSEM) methodology of establishing approximate measurement invariance (A-MI) using data from a national examination in Saudi Arabia as an alternative to not meeting strong invariance criteria. Instead, we illustrate how to account for the absence of…