Under certain conditions, statistical evidence is more persuasive than anecdotal evidence in supporting a claim about the probability that a certain event will occur. In three experiments, it is shown that the type of argument is an important condition in this respect. If the evidence is part of an argument by generalization, statistical evidence…

In a recent study, G. Kuhn and Z. Dienes (2005) reported that participants previously exposed to a set of musical tunes generated by a biconditional grammar subsequently preferred new tunes that respected the grammar over new ungrammatical tunes. Because the study and test tunes did not share any chunks of adjacent intervals, this result may be…

In many cognitive, metacognitive, and perceptual tasks, measurement of performance or prediction accuracy may be influenced by response bias. Signal detection theory provides a means of assessing discrimination accuracy independent of such bias, but its application crucially depends on distributional assumptions. The Goodman-Kruskal gamma…

This paper uses log-linear models with latent variables (Hagenaars, in "Loglinear Models with Latent Variables," 1993) to define a family of cognitive diagnosis models. In doing so, the relationship between many common models is explicitly defined and discussed. In addition, because the log-linear model with latent variables is a general model for…

Substantial evidence indicates that information is distorted during decision making, but very few studies have assessed the distortion of probability and outcome information in risky decisions. In two studies involving six binary decisions (e.g., banning blood donations from people who have visited England, because of "mad cow disease"),…

We extend the nonparametric literature on partially identified probability distributions and use our analytical results to provide sharp bounds on the impact of universal health insurance on provider visits and medical expenditures. Our approach accounts for uncertainty about the reliability of self-reported insurance status as well as uncertainty…

Risk propensity (RP) is a trait characterized by an increased probability of engaging in behaviors that have some potential danger or harm but also provide an opportunity for some benefit. In the present study, a new RP task with several dilemmas was explored. Each dilemma includes the initial set plus successive approximations for estimating the…

Given the increasing costs associated with commercial textbooks and decreasing financial support of public schools, it is important to better understand the impacts of open educational resources on student outcomes. The purpose of this quantitative study is to analyze whether the adoption of open science textbooks significantly affects science…

Many students struggle with fractions and must understand them before learning higher-level math. Veteran educator David B. Spangler provides research-based tools that are aligned with NCTM and Common Core State Standards. He outlines powerful diagnostic methods for analyzing student work and providing timely, specific, and meaningful…

"It's All Connected" provides teachers of mathematics the support they need to improve their instruction. This in-demand collection of lessons for grades 6-8 explores proportionality, proportional relationships, and proportional reasoning, acknowledging that the ability to reason proportionally is crucial in the middle school mathematics…

This paper tabulates the correlation of Virginia's mathematics performance expectations with Virginia's 2009 mathematics standards of learning.

In this dissertation, I study economics textbook markets as an example of durable goods monopoly. Textbooks are protected by copyrights, and from a student's point of view, different textbooks are not good substitutes because students wish to use the textbook adopted by their instructors. Therefore sellers have market power. Textbooks can be…

The Type I error rates and the power of IRT likelihood ratio test and cumulative logit ordinal logistic regression procedures in detecting differential item functioning (DIF) for polytomously scored items were investigated in this Monte Carlo simulation study. For this purpose, 54 simulation conditions (combinations of 3 sample sizes, 2 sample…

One of the author's undergraduate students recently asked him whether it was possible to generate a random positive integer. After some thought, the author realised that there were plenty of interesting mathematical ideas inherent in her question. So much so in fact, that the author decided to organise a workshop, open both to undergraduates and…

Bayes's theorem is notorious for being a difficult topic to learn and to teach. Problems involving Bayes's theorem (either implicitly or explicitly) generally involve calculations based on two or more given probabilities and their complements. Further, a correct solution depends on students' ability to interpret the problem correctly. Most people…