Journal Article

  • Unless the sample encompasses a substantial portion of the population, the standard error of an estimator depends on the size of the sample, but not the size of the population. This is a crucial statistical insight that students find very counterintuitive. After trying several ways of convincing students of the validity of this principle, I have finally found a simple memorable activity that convinces students beyond a reasonable doubt. As a bonus, the data generated by this activity can be used to illustrate the central limit theorem, confidence intervals, and hypothesis testing.

  • Statistical thinking is required for good statistical analysis. Among other things, statistical thinking involves identifying sources of variation. Students in introductory statistics courses seldom recognize that one of the largest sources of variation may come in the collection and recording of the data. This paper presents some simple exercises that can be incorporated into any course (not just statistics) to help students understand some of the sources of variation in data collection. Primary attention is paid to operational definitions used in the data collection process.

  • This study investigated the knowledge base necessary for choosing appropriate statistical techniques in applied research. In this study, we compared knowledge used by six experts and six novices in two types of statistical tasks. The tasks were: 1) comparing research scenarios from the perspective of choosing a statistical technique, and 2) direct comparison of statistical techniques. The framework was based on expert knowledge in inferential statistics using the repertory grid technique for data collection. A qualitative analysis of data showed that of the three types of expert knowledge, research design knowledge comprised the biggest portion, with theoretical and procedural knowledge comprising relatively smaller parts. Little difference was observed between experts and novices in extensiveness of knowledge use, although experts' knowledge use was found to be more integrated than novices'. Finally, two implications were drawn regarding how to better teach selection skills in statistics education: (1) statistical techniques should be taught in relation to relevant research designs, and (2) conceptual connections between statistical techniques should be explicitly taught.

  • In this article, we focus primarily on what we have learned more recently from research about how younger students reason about data, concentrating on ideas that begin developing in early elementary school. We therefore do not review the literature related to statistical inference. One reason for not reviewing that literature here is that a reasonable treatment would require us to review as well the development of probabilistic thinking (see Shaughnessy's review, this volume). But more importantly, there are core ideas in reasoning about data that tend to get shoved to the wings as soon as statistical inference takes the stage. The issues we discuss here, though basic, are still critical to statistical reasoning in the upper grades.

  • As part of the University of Newcastle's Total Quality Management (TQM) course, students study Experimental Design (ED) and Statistical Process Control (SPC) within the framework of the scientific approach to process improvement. A sufficient balance of theory and application is required to keep Business and Management students, most with a largely non-quantitative background, interested and aware of the need and method to correctly implement ED and SPC in industry. Tools to facilitate a basic understanding of the importance of the 3Rs, namely, Randomization, Replication, and Blocking, as well as highlighting the potential for mistakes or inefficient calibration techniques are essential in the learning process. This paper describes the use of a particular tool, called the "Ballistat," to illustrate TQM concepts, which enables students to obtain the hands-on experience needed to control processes in industry.

  • Several examples are presented to demonstrate how Venn diagramming can be used to help students visualize multiple regression concepts such as the coefficient of determination, the multiple partial correlation, and the Type I and Type II sums of squares. In addition, it is suggested that Venn diagramming can aid in the interpretation of a measure of variable importance obtained by average stepwise selection. Finally, we report findings of an experiment that compared outcomes of two instructional methods for multiple regression, one using Venn diagrams and one not.

  • Percentage of body fat, age, weight, height, and ten body circumference measurements (e.g., abdomen) are recorded for 252 men. Body fat, one measure of health, has been accurately estimated by an underwater weighing technique. Fitting body fat to the other measurements using multiple regression provides a convenient way of estimating body fat for men using only a scale and a measuring tape. This dataset can be used to show students the utility of multiple regression and to provide practice in model building.

  • While written comments are a popular and potentially effective method of student exam feedback, these comments are often overshadowed by students' focus on their grades. In this paper I discuss the additional use of orally recorded exam feedback in introductory statistics classes of 40 or fewer students. While grading and writing comments on a student's exam solution, I create a personalized sound file of detailed oral feedback for each question. The student can then securely access this file. The oral feedback in combination with written comments is more understandable for and motivating to the students, and accommodates a broader range of student learning styles. In support of this new feedback method, I provide and discuss classroom data collected from my students. Furthermore, I make suggestions for the use of orally recording feedback when time and resources are scarce.

  • The probability unit in a first statistics course is difficult to teach because there is not much time, the concepts and mechanics are difficult, and the students do not see the relevance of learning it. Research by Cosmides and Tooby (1996) supports our findings that instructors should avoid fractions and decimals and capitalize on students' affinity for counting things. In addition, we avoid the use of normal tables at the beginning of our discussion of continuous random variables by using uniform and triangular distributions. These ideas may be used in traditionally structured classes or in group-based and activity-based classes.

  • A Venn diagram capable of expositing results relating to bias and variance of coefficient estimates in multiple regression analysis is presented, along with suggestions for how it can be used in teaching. In contrast to similar Venn diagrams used for portraying results associated with the coefficient of determination, its pedagogical value is not compromised in the presence of suppressor variables.

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