Literature Index

Statistics and probability have become an integral part of mathematics education. Therefore it is important to understand whether curricular materials adequately represent statistical ideas. The Guidelines for Assessment and Instruction in Statistics Education (GAISE) report (Franklin, Kader, Mewborn, Moreno, Peck, Perry, & Scheaffer, 2007), endorsed by the American Statistical Association, provides a two-dimensional (process and level) framework for statistical learning. This paper examines whether the statistics content contained in the NSF funded elementary curricula Investigations in Number, Data, and Space, Math Trailblazers, and Everyday Mathematics aligns with the GAISE recommendations. Results indicate that there are differences in the approaches used as well as the GAISE components emphasized among the curricula. In light of the fact that the new Common Core State Standards have placed little emphasis in statistics in the elementary grades, it is important to ensure that the minimal amount of statistics that is presented aligns well with the recommendations put forth by the statistics community. The results in this paper provide insight as to the type of statistical preparation students receive when using the NSF funded elementary curricula. As the Common Core places great emphasis on statistics in the middle grades, these results can be used to inform whether students will be prepared for the middle school Common Core goals.

The use of statistics and probabilities as legal evidence has recently come under increased scrutiny. Judges' and jurors' ability to understand and use this type of evidence has been of special concern. Finkelstein and Fairley (1970) proposed introducing Bayes' theorem into the courtroom to aid the fact-finder evaluate this type of evidence. The present study addressed individuals' ability to use statistical information as well as their ability to understand and use an expert's Bayesian explanation of that evidence. One hundred and eighty continuing education students were presented with a transcript purportedly taken from an actual trial and were asked to make several subjective probabiliy judgments regarding blood-grouping evidence. The results extend to the trial process previous psychological research suggesting that individuals generally underutilize statistical information, as compared to a Bayesian model. In addition, subjects in this study generally ignored the expert's Bayesian explanation of the statistical evidence.

The use of The Three Stooges' films as a source of data in an introductory statistics class is described. The Stooges' films are separated into three populations. Using these populations, students may conduct hypothesis tests with data they collect.

We focus on the problem of ignoring statistical independence. A binomial experiment is used to determine whether judges could match, based on looks alone, dogs to their owners. The experimental design introduces dependencies such that the probability of a given judge correctly matching a dog and an owner changes from trial to trial. We show how this dependence alters the probability of a successful match of dog to owner, and thus alters the expected number of successful matches and the variance of this expected quantity. Finally, we show that a false assumption of independence that results in incorrect probability calculations changes the probability of incorrectly rejecting the null hypothesis (i.e. the Type I error).