The primary objective of this investigation is the formulation of random intercept latent profile transition analysis (RI-LPTA). Our simulation investigation suggests that the election between LPTA and RI-LPTA for examination has negligible impact on the estimation of transition probability parameters when the population parameters are generated…

Propensity score matching and weighting methods are applied to balance covariates and reduce selection bias in the analysis of observational study data, and ultimately estimate a treatment effect. We wish to evaluate the impact of a Supplemental Instruction (SI) program on student success in an Introductory Statistics course. In such student…

In 2015, the Australian Government's Excellence in Research for Australia (ERA) assessment of research quality declined to rate 1.5 per cent of submissions from universities. The public debate focused on practices of gaming or "coding errors" within university submissions as the reason for this outcome. The issue was about the…

While regression discontinuity has usually been applied retrospectively to secondary data, it is even more attractive when applied prospectively. In a prospective design, data collection can be focused on cases near the discontinuity, thereby improving internal validity and substantially increasing precision. Furthermore, such prospective…

Optimal assessment tools should measure in a limited time the knowledge of students in a correct and unbiased way. A method for automating the scoring is multiple choice scoring. This article compares scoring methods from a probabilistic point of view by modelling the probability to pass: the number right scoring, the initial correction (IC) and…

Model-based attempts to rigorously study the broad and imprecise concept of "discriminating power" are scarce, and generally limited to nonlinear models for binary responses. This paper proposes a comprehensive framework for assessing the discriminating power of item and test scores which are analyzed or obtained using Spearman's…

Experiments 1 and 2 involved independent groups that received primary reinforcement after a correct match with a probability of 1.0, 0.50 or 0.25. Correct matches that did not produce primary reinforcement produced a conditioned reinforcer. Both experiments revealed little evidence that acquisition or retention was adversely affected by use of…

There is much debate over the degree to which language learning is governed by innate language-specific biases, or acquired through cognition-general principles. Here we examine the probabilistic language acquisition hypothesis on three levels: We outline a novel theoretical result showing that it is possible to learn the exact "generative model"…

This study aimed to assess the effect of musical training in statistical learning of tone sequences using Magnetoencephalography (MEG). Specifically, MEG recordings were used to investigate the neural and functional correlates of the pre-attentive ability for detection of deviance, from a statistically learned tone sequence. The effect of…

This article discusses comparisons of means using exploratory and confirmatory approaches. Three methods are discussed: hypothesis testing, model selection based on information criteria, and Bayesian model selection. Throughout the article, an example is used to illustrate and evaluate the two approaches and the three methods. We demonstrate that…

We present an introduction to Bayesian inference as it is used in probabilistic models of cognitive development. Our goal is to provide an intuitive and accessible guide to the "what", the "how", and the "why" of the Bayesian approach: what sorts of problems and data the framework is most relevant for, and how and why it may be useful for…

We propose a new limited-information goodness of fit test statistic C[subscript 2] for ordinal IRT models. The construction of the new statistic lies formally between the M[subscript 2] statistic of Maydeu-Olivares and Joe (2006), which utilizes first and second order marginal probabilities, and the M*[subscript 2] statistic of Cai and Hansen…

Recently, the Northwest Evaluation Association (NWEA) completed a study to connect the scale of the North Carolina State End of Grade (EOG) Testing Program used for North Carolina's mathematics and reading assessments with NWEA's Rausch Interval Unit (RIT) scale. Information from the state assessments was used in a study to establish…

There have been many discussions of how Type I errors should be controlled when many hypotheses are tested (e.g., all possible comparisons of means, correlations, proportions, the coefficients in hierarchical models, etc.). By and large, researchers have adopted familywise (FWER) control, though this practice certainly is not universal. Familywise…

A principle of efficient language production based on information theoretic considerations is proposed: Uniform Information Density predicts that language production is affected by a preference to distribute information uniformly across the linguistic signal. This prediction is tested against data from syntactic reduction. A single multilevel…