We consider the effect on estimation of simultaneous variable centering and interaction effects in linear regression. We technically define, review, and amplify many of the statistical issues for interaction models with centering in order to create a useful and compact reference for teachers, students, and applied researchers. In addition, we…

A course disk in either CD or DVD format can be very beneficial to online, hybrid, or distance courses in statistics as well as traditional on-campus courses, augmenting existing technologies like course management systems. A typical course disk may include the syllabus and course outline, calendar, instructions, lecture notes and lecture…

Students learn to examine the distributional assumptions implicit in the usual t-tests and associated confidence intervals, but are rarely shown what to do when those assumptions are grossly violated. Three data sets are presented. Each data set involves a different distributional anomaly and each illustrates the use of a different nonparametric…

Null distributions of permutation tests for two-sample, paired, and block designs are simulated using the R statistical programming language. For each design and type of data, permutation tests are compared with standard normal-theory and nonparametric tests. These examples (often using real data) provide for classroom discussion use of metrics…

Confidence interval estimation is a fundamental technique in statistical inference. Margin of error is used to delimit the error in estimation. Dispelling misinterpretations that teachers and students give to these terms is important. In this note, we give examples of the confusion that can arise in regard to confidence interval estimation and…

Two improvements in teaching linear regression are suggested. The first is to include the population regression model at the beginning of the topic. The second is to use a geometric approach: to interpret the regression estimate as an orthogonal projection and the estimation error as the distance (which is minimized by the projection). Linear…

This article looks at a process of integrating real-life data investigation in a course on descriptive statistics. Referring to constructivist perspectives, this article suggests a look at the potential of inculcating alternative teaching methods that encourage students to take a more active role in their own learning and participate in the…

The use of a real data set has the potential to increase engagement and learning in students who enrol in a statistics course at university. The present report describes the development of an approach that uses a real data set, but one that is collected from the students. The questions are designed so that the data set can be used throughout the…

Language and the telling of data stories have fundamental roles in advancing the GAISE agenda of shifting the emphasis in statistics education from the operation of sets of procedures towards conceptual understanding and communication. In this paper we discuss some of the major issues surrounding story telling in statistics, challenge current…

This research shows that active learning is not universally effective and, in fact, may inhibit learning for certain types of students. The results of this study show that as increased levels of active learning are utilized, student test scores decrease for those with a high grade point average. In contrast, test scores increase as active learning…

This paper describes three spreadsheet exercises demonstrating the nature and frequency of type I errors using random number generation. The exercises are designed specifically to address issues related to testing multiple relations using correlation (Demonstration I), t tests varying in sample size (Demonstration II) and multiple comparisons…

For many students meeting, say, the gamma distribution for the first time, it may well turn out to be a rather fruitless encounter unless they are immediately able to see an application of this probability model to some real-life situation. With this in mind, we pose here an appealing problem that can be used as the basis for a workshop activity…

This paper proposes an argument framework for the teaching of null hypothesis statistical testing and its application in support of research. Elements of the Toulmin (1958) model of argument are used to illustrate the use of p values and Type I and Type II error rates in support of claims about statistical parameters and subject matter research…

On the 2009 AP[c] Statistics Exam, students were asked to create a statistic to measure skewness in a distribution. This paper explores several of the most popular student responses and evaluates which statistic performs best when sampling from various skewed populations. (Contains 8 figures, 3 tables, and 4 footnotes.)

Inferential reasoning is a central component of statistics. Researchers have suggested that students should develop an informal understanding of the ideas that underlie inference before learning the concepts formally. This paper presents a hands-on activity that is designed to help students in an introductory statistics course draw informal…