We consider two-level models where a continuous response R and continuous covariates C are assumed missing at random. Inferences based on maximum likelihood or Bayes are routinely made by estimating their joint normal distribution from observed data R[subscript obs] and C[subscript obs]. However, if the model for R given C includes random…

Using simulation-based inference (SBI), such as randomization tests, as the primary vehicle for introducing students to the logic and scope of statistical inference has been advocated with the potential of improving student understanding of statistical inference and the statistical investigative process. Moving beyond the individual class…

Bayesian item response theory (IRT) modeling stages include (a) specifying the IRT likelihood model, (b) specifying the parameter prior distributions, (c) obtaining the posterior distribution, and (d) making appropriate inferences. The latter stage, and the focus of this research, includes model criticism. Choice of priors with the posterior…

We developed a method for using Coh-Metrix to automatically analyze tutorial dialogues. Coh-Metrix, a web-based tool for automatically evaluating text, is freely available to researchers. We applied the method to 190 tutorial dialogues between women and "BRCA Gist" from two experiments. "BRCA Gist" is an intelligent tutoring…

Acquiring the correct meanings of words expressing quantities ("seven, most") and qualities ("red, spotty") present a challenge to learners. Understanding how children succeed at this requires understanding, not only of what kinds of data are available to them, but also the biases and expectations they bring to the learning…

Most natural domains can be represented in multiple ways: we can categorize foods in terms of their nutritional content or social role, animals in terms of their taxonomic groupings or their ecological niches, and musical instruments in terms of their taxonomic categories or social uses. Previous approaches to modeling human categorization have…

Forces are experienced in actions on objects. The mechanoreceptor system is stimulated by proximal forces in interactions with objects, and experiences of force occur in a context of information yielded by other sensory modalities, principally vision. These experiences are registered and stored as episodic traces in the brain. These stored…

In recent years, the educational data mining and user modeling communities have been aggressively introducing models for predicting student performance on external measures such as standardized tests as well as within-tutor performance. While these models have brought statistically reliable improvement to performance prediction, the real world…

Using exogenous characteristics to identify endogenous subgroups, the approach discussed in this method note creates symmetric subsets within treatment and control groups, allowing the analysis to take advantage of an experimental design. In order to maintain treatment--control symmetry, however, prior work has posited that it is necessary to use…

In order to examine metacognitive accuracy (i.e., the relationship between metacognitive judgment and memory performance), researchers often rely on by-participant analysis, where metacognitive accuracy (e.g., resolution, as measured by the gamma coefficient or signal detection measures) is computed for each participant and the computed values are…

People often make inferences with incomplete information. Previous research has led to a mixed picture of how people treat missing information. To explain these results, the authors follow the Brunswikian perspective on human inference and hypothesize that the mechanism's accuracy for treating missing information depends on how it is distributed…

In 4 studies, the authors examined the hypothesis that the structure of the informational environment makes small samples more informative than large ones for drawing inferences about population correlations. The specific purpose of the studies was to test predictions arising from the signal detection simulations of R. B. Anderson, M. E. Doherty,…

Causal reasoning represents one of the most basic and important cognitive processes that underpin all higher-order activities, such as conceptual understanding and problem solving. Hume called causality the "cement of the universe" [Hume (1739/2000). Causal reasoning is required for making predictions, drawing implications and…

Bayesian inference on multinomial probabilities is conducted based on data collected from the game Pass the Pigs[R]. Prior information on these probabilities is readily available from the instruction manual, and is easily incorporated in a Dirichlet prior. Posterior analysis of the scoring probabilities quantifies the discrepancy between empirical…