Computer simulation can be used to demonstrate why the unbiased sample variance uses degrees of freedom (n-1). This is first demonstrated for sampling from a normal random variable, and in additional simulations for some selected non-normal random variables, namely, chi-square and binomial.

Recommended learning goals for students in introductory statistics courses include the ability to recognize and explain the key role of randomness in designing studies and in drawing conclusions from those studies involving generalizations to a population or causal claims (GAISE College Report ASA Revision Committee, 2016). The purpose of this…

While looking for an inexpensive technology package to help students in statistics classes, the author found StatKey, a free Web-based app. Not only is StatKey useful for students' year-end projects, but it is also valuable for helping students learn fundamental content such as the central limit theorem. Using StatKey, students can engage in…

The omega (?) statistic is reputed to be one of the best indices for detecting answer copying on multiple choice tests, but its performance relies on the accurate estimation of copier ability, which is challenging because responses from the copiers may have been contaminated. We propose an algorithm that aims to identify and delete the suspected…

This article presents the results of a qualitative research with a group of 15 university students of social sciences on informal inferential reasoning developed in a computer environment on concepts involved in the confidence intervals. The results indicate that students developed a correct reasoning about sampling variability and visualized…

Statistical inference relies heavily on the concept of sampling distributions. However, sampling distributions are difficult to teach. We present a series of short animations that are story-based, with associated assessments. We hope that our contribution can be useful as a tool to teach sampling distributions in the introductory statistics…

Consistent with the Common Core State Standards for Mathematics (CCSSI 2010), the authors write that they have asked students to do statistics projects with real data. To obtain real data, their students use the free Web-based app, Census at School, created by the American Statistical Association (ASA) to help promote civic awareness among school…

Most questions in social and biomedical sciences are causal in nature: what would happen to individuals, or to groups, if part of their environment were changed? In this groundbreaking text, two world-renowned experts present statistical methods for studying such questions. This book starts with the notion of potential outcomes, each corresponding…

The research reported here uses a pre/post-test model and stimulated recall interviews to assess teachers' statistical reasoning about comparing distributions, when enrolled in a graduate-level statistics education course. We discuss key aspects of the course design aimed at improving teachers' learning and teaching of statistics, and the…

Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This eighth installment of "Explorations in Statistics" explores permutation methods, empiric procedures we can use to assess an experimental result--to test a null hypothesis--when we are reluctant to trust statistical…

There is considerable research on the difficulties students have in conceptualising individual concepts of probability and statistics (see for example, Bryant & Nunes, 2012; Jones, 2005). The unit of work developed for the action research project described in this article is specifically designed to address some of these in order to help…

The purposes of this study were to investigate (a) undergraduate students' reasoning about the concepts of confidence intervals (b) undergraduate students' interactions with "well-designed" screencast videos on sampling distributions and confidence intervals, and (c) how screencast videos improve undergraduate students' reasoning ability…

Survey sampling is fundamentally an applied field. The goal in this book is to put an array of tools at the fingertips of practitioners by explaining approaches long used by survey statisticians, illustrating how existing software can be used to solve survey problems, and developing some specialized software where needed. This book serves at least…

We surveyed researchers in the health and exercise sciences to explore different areas and magnitudes of bias in researchers' decision making. Participants were presented with scenarios (testing a central hypothesis with p = 0.06 or p = 0.04) in a random order and surveyed about what they would do in each scenario. Participants showed significant…

Statistical studies are referenced in the news every day, so frequently that people are sometimes skeptical of reported results. Often, no matter how large a sample size researchers use in their studies, people believe that the sample size is too small to make broad generalizations. The tasks presented in this article use simulations of repeated…