Data presented in a newspaper advertisement suggest the use of simple linear regression to relate the prices of diamond rings to the weights of their diamond stones. The intercept of the resulting regression line is negative and significantly different from zero. This finding raises questions about an assumed pricing mechanism and motivates consideration of remedial actions.
Many statistical problems can be satisfactorily resolved within the framework of linear regression. Business students, for example, employ linear regression to uncover interesting insights in the fields of Finance, Marketing, and Human Resources, among others. The purpose of this paper is to demonstrate how several concepts arising in a typical discussion of multiple linear regression can be motivated through the development of a pricing model for diamond stones. Specifically, we use data pertaining to 308 stones listed in an advertisement to construct a model, which educates us on the relative pricing of caratage and the different grades of clarity and colour.
Nonparametric methods form an integral part of many degree programs and concentrations in statistics. In this article a number of useful approaches are suggested to aid the instructor of a nonparametric statistics course. These include ideas for classroom presentations, projects, writing components, student-generated data, and computing. Each suggestion is discussed in the context of nonparametric methods instruction. These techniques help students develop an appreciation for the field of nonparametric statistics and the broad range of its applications in practice. Appendices include a partially annotated bibliography of textbooks and monographs from the field of nonparametric statistics and a collection of Minitab macros.
The dataset "Career Records For All Modern Position Players Eligible For The Major League Baseball Hall of Fame" contains information for the 1340 major league baseball players who had retired prior to the 1993 season and who were eligible for the Major League Baseball Hall of Fame (had played in at least ten seasons). Traditional performance measures included are number of seasons played, games played, official at-bats (AB), runs scored, hits (H), doubles (2B), triples (3B), home runs (HR), runs batted in (RBI), walks (BB), strikeouts (SO), batting average (BA), on base percentage (OBP), slugging percentage (SLG), stolen bases (SB), times caught stealing (CS), fielding average (FA), and primary position played (POS). In addition, the following composite measures are included: adjusted production (AP), batting runs (BR), adjusted batting runs (ABR), runs created (RC), stolen base runs (SBR), fielding runs (FR), and total player rating (TPR). Finally, the dataset includes an indication of whether or not each player has been admitted into the Major League Baseball Hall of Fame and, if so, under what set of rules he was admitted.
The 1969-2000 Major League Baseball Attendance dataset contains Runs Scored, Runs Allowed, Wins, Losses, Number of Games Behind the Division Leader, and Home Game Attendance of each major league franchise for the 1969 through 2000 seasons. Also included for each franchise are its location, league affiliation (National or American), and division affiliation (East, Central, or West). These data have been used in a project-based modeling course to instruct students in basic data management, the use of exploratory data analysis to "clean" data, and construction of regression models. The dataset, which is both cross-sectional and time-series, is of a manageable size and easily understood. Furthermore, it provides a useful, interesting, and realistic classroom example for discussing many important statistical concepts.
A certain dataset, giving population at risk and fatalities for "an unusual episode," has been used for some time in classrooms as an elementary exercise in statistical thinking, the challenge being to deduce the context of the data. Unfortunately, the "solution" has frequently been circulated orally, with few details. Moreover, discrepancies have been found between the dataset and the "solution," which would render the exercise somewhat artificial. This paper investigates the discrepancies and includes a fully-explained version of the dataset for classroom use.
Despite advances in computer technology, quantiles of Student's t (among other distributions) are still calculated using printed tables in most classroom situations. Unfortunately, the structure of the tables found in textbooks (and even in books of tables) is usually better suited to fixed-level hypothesis testing than to the p-value approach that many modern statisticians favor. This article presents a novel arrangement of the table that allows p-values to be determined quite precisely from a table of manageable size.
Similarities and differences in the articles by Rumsey, Garfield and Chance are summarized. An alternative perspective on the distinction between statistical literacy, reasoning, and thinking is presented. Based on this perspective, an example is provided to illustrate how literacy, reasoning and thinking can be promoted within a single topic of instruction. Additional examples of assessment items are offered. I conclude with implications for statistics education research that stem from the incorporation of recommendations made by Rumsey, Garfield and Chance into classroom practice.
Similarities and differences in the articles by Rumsey, Garfield and Chance are summarized. An alternative perspective on the distinction between statistical literacy, reasoning, and thinking is presented. Based on this perspective, an example is provided to illustrate how literacy, reasoning and thinking can be promoted within a single topic of instruction. Additional examples of assessment items are offered. I conclude with implications for statistics education research that stem from the incorporation of recommendations made by Rumsey, Garfield and Chance into classroom practice.
Researchers and educators have found that statistical ideas are often misunderstood by students and professionals. In order to develop better statistical reasoning, students need to first construct a deeper understanding of fundamental concepts. The Sampling Distributions program and ancillary instructional materials were developed to guide student exploration and discovery. The program allows students to specify and change the shape of a population, choose different sample sizes, and simulate sampling distributions by randomly drawing large numbers of samples. The program provides graphical, visual feedback that allows students to construct their own understanding of sampling distribution behavior. To capture changes in students' conceptual understanding we developed diagnostic, graphics-based test items that were administered before and after students used the program. An activity that asked students to test their predictions and confront their misconceptions was found to be more effective than one based on guided discovery. Our findings demonstrate that while software can provide the means for a rich classroom experience, computer simulations alone do not guarantee conceptual change.