In this article, I introduce a novel applet ("module") for exploring probability distributions, their samples, and various related statistical concepts. The module is primarily designed to be used by the instructor in the introductory course, but it can be used far beyond it as well. It is a free, cross-platform, stand-alone interactive…

The current study examined the impacts on students' cognitive performance of the key versus ordinary school system in China, using an analytic approach that combines hierarchical linear modeling with propensity score stratification. The results show that students from key schools score significantly higher on a mathematical achievement test than…

In this international collaborative case study, American and Italian authors applied a hypothetical philanthropic case scenario to the recent graduation of the first student with nonverbal autism at the University of Central Italy in order to examine the potential impact a private donation would have on various institutional constituents. A series…

Many view mathematics as a rich and wonderfully elaborate game. In turn, games can be used to illustrate mathematical ideas. Fibber's Dice, an adaptation of the game Liar's Dice, is a fast-paced game that rewards gutsy moves and favors the underdog. It also brings to life concepts arising in the study of probability. In particular, Fibber's Dice…

This research examines issues regarding model estimation and robustness in the use of Bayesian Inference Networks (BINs) for measuring Learning Progressions (LPs). It provides background information on LPs and how they might be used in practice. Two simulation studies are performed, along with real data examples. The first study examines the case…

Performance in the stop-signal paradigm involves a balance between going and stopping, and one way that this balance is struck is through shifting priority away from the go task, slowing responses after a stop signal, and improving the probability of inhibition. In 6 experiments, the authors tested whether there is a corresponding shift in…

Using a sample of youth who graduated from high school in the late 1990s and early 2000s, this paper examines the impact of high school math curriculum on the decision to go to college. Results that control for unobserved differences between students and their families suggest that a more rigorous high school math curriculum is associated with a…

The "radioactive dice" experiment is a commonly used classroom analogue to model the decay of radioactive nuclei. However, the value of the half-life obtained from this experiment differs significantly from that calculated for real nuclei decaying exponentially with the same decay constant. This article attempts to explain the discrepancy and…

We present two simple, one-dimensional, stochastic models that lead to a qualitative understanding of very complex systems from biology, nanoscience and social sciences. The first model explains the complicated dynamics of microtubules, stochastic cellular highways. Using the theory of random walks in one dimension, we find analytical expressions…

We examined how decision makers generate and evaluate hypotheses when data are presented sequentially. In the first 2 experiments, participants learned the relationship between data and possible causes of the data in a virtual environment. Data were then presented iteratively, and participants either generated hypotheses they thought caused the…

Is optimism real, or are optimistic forecasts just cheap talk? To help answer this question, we investigated whether optimistic predictions persist in the face of large incentives to be accurate. We asked National Football League football fans to predict the winner of a single game. Roughly half (the partisans) predicted a game involving their…

In a temporal double bisection task, animals learn two discriminations. In the presence of Red and Green keys, responses to Red are reinforced after 1-s samples and responses to Green are reinforced after 4-s samples; in the presence of Blue and Yellow keys, responses to Blue are reinforced after 4-s samples and responses to Yellow are reinforced…

The probability of test takers changing answers upon review of their initial choices is modeled. The primary purpose of the model is to check erasures on answer sheets recorded by an optical scanner for numbers and patterns that may be indicative of irregular behavior, such as teachers or school administrators changing answer sheets after their…

Many models of cognitive diagnosis, including the "least squares distance model" (LSDM), work under the "conjunctive" assumption that a correct item response occurs when all latent attributes required by the item are correctly performed. This article proposes a "disjunctive" version of the LSDM under which the correct item response occurs when "at…

Logistic regression is slowly gaining acceptance in the social sciences, and fills an important niche in the researcher's toolkit: being able to predict important outcomes that are not continuous in nature. While OLS regression is a valuable tool, it cannot routinely be used to predict outcomes that are binary or categorical in nature. These…