Humans implicitly pick up on probabilities of stimuli and events, yet it remains unclear how statistical learning builds expectations that affect perception. Across 29 experiments, we examine the influence of task-irrelevant distributions--defined across acoustic frequency--on both tone detection in noise and tone duration judgments. The shape and…

We present a variant of the Game of Pig to introduce the concepts of probability, simulation and expected value.

The authors analyzed the development of 4th-grade students' understanding of the transition from experimental relative frequencies of outcomes to theoretical probabilities with a focus on the foundational statistical concepts of variation and expectation. After observing the decreasing variation from the theoretical probability as the sample size…

We establish an interesting connection between the number of runs and the length of the first run when tossing a fair coin.

This study is motivated by the desire to address some of the enormous challenges faced by the students as well as the lecturer in fulfilling their respective expectations and duties demanded by the process of learning--teaching of mathematics and statistics within the framework of the constraining schedules laid down by the academic institutions…

When two sealed envelopes contain money, one twice as much as the other, a player should be indifferent between them. But when one envelope is opened, one's decision should vary as a function of the observed value and one's subjective probabilities.

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

This study presents the results of a partial credit Rasch analysis of in-depth interview data exploring statistical understanding of 73 school students in 6 contextual settings. The use of Rasch analysis allowed the exploration of a single underlying variable across contexts, which included probability sampling, representation of temperature…

The national lottery is often portrayed as a game of pure chance with no room for strategy. This misperception seems to stem from the application of probability instead of expectancy considerations, and can be utilized to introduce the statistical concept of expectation.

A series of 13 survey questions based on a 50-50 spinner is used to explore school students' understanding of statistical variation in a chance setting. Five questions set the context by assessing understanding of theoretical expectation and representation of repeated trials in a stacked dot (line) plot. Four questions provide opportunity to…

A numerical procedure is outlined for obtaining an interval estimate of a parameter in an empirical Bayes estimation problem. The case where each observed value x has a binomial distribution, conditional on a parameter zeta, is the only case considered. For each x, the parameter estimated is the expected value of zeta given x. The main purpose is…