In Bayesian statistics, the choice of the prior distribution is often controversial. Different rules for selecting priors have been suggested in the literature, which, sometimes, produce priors that are difficult for the students to understand intuitively. In this article, we use a simple heuristic to illustrate to the students the rather counter-intuitive fact that flat priors are not necessarily non-informative; and non-informative priors are not necessarily flat.
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.
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.
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.
A number of programs written for the TI-83 Plus calculator are demonstrated in this article to illustrate this graphing calculator's surprisingly advanced statistical capabilities. Examples include residual plots for analysis of variance, pairwise comparison in one-factor experimental design, statistical inference for simple linear regression and confidence intervals for contrasts used in experimental design. These and a number of other programs are available for download. Advances in graphing calculator statistical programs, such as those described in this article, allow instructors and students in introductory applied graduate level statistics courses to perform sophisticated statistical data diagnostic and inference procedures during class time in an ordinary class room.
An alternative perspective is presented for teaching students the logic and details underlying McNemar's test of the equality of correlated proportions. The new perspective enables straightforward extension to other correlated proportions situations.