This study investigates a range of non-normative ideas that pre-service teachers (PSTs) employ in reasoning about sampling variability. This issue was studied in the context of a content course on statistics and probability for pre-service middle grade teachers at a Midwestern American university. Analysis of seven PSTs' video and screen records…

Introductory statistics courses, which are important in preparing students for their daily lives, generally derive inferential statistics from informal knowledge. In this transition process, sampling distributions have an important place, yet research has shown that students often have difficulties with this concept. In order to increase their…

Value-added models are being implemented in many states in an attempt to measure the contributions of individual teachers and schools toward students' learning. Scores from these models are increasingly used for high-stakes purposes such as setting compensation, hiring or dismissing teachers, awarding tenure, and closing schools. The statistician…

This article reports on a classroom teaching experiment that engaged a group of high school students in designing sampling simulations within a computer microworld. The simulation-design activities aimed to foster students' abilities to conceive of contextual situations as stochastic experiments, and to engage them with the logic of hypothesis…

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…

Repeated sampling approaches to inference that rely on simulations have recently gained prominence in statistics education, and probabilistic concepts are at the core of this approach. In this approach, learners need to develop a mapping among the problem situation, a physical enactment, computer representations, and the underlying randomization…

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 unexpectedness of the birthday problem has long been used by teachers of statistics in discussing basic probability calculation. An activity is described that engages students in understanding probability and sampling using the popular Facebook social networking site. (Contains 2 figures and 1 table.)

The purpose of this study is to define teacher views about the difficulties in learning and teaching middle school statistics subjects. To serve this aim, a number of interviews were conducted with 10 middle school maths teachers in 2011-2012 school year in the province of Trabzon. Of the qualitative descriptive research methods, the…

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 difficulties introductory statistics students have with formal statistical inference are well known in the field of statistics education. "Informal" statistical inference has been studied as a means to introduce inferential reasoning well before and without the formalities of formal statistical inference. This mixed methods study…

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…

Formal inference, which makes theoretical assumptions about distributions and applies hypothesis testing procedures with null and alternative hypotheses, is notoriously difficult for tertiary students to master. The debate about whether this content should appear in Years 11 and 12 of the "Australian Curriculum: Mathematics" has gone on…

Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This third installment of "Explorations in Statistics" investigates confidence intervals. A confidence interval is a range that we expect, with some level of confidence, to include the true value of a population parameter…