Teaching

  • 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.

  • 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.

  • This article demonstrates the use of two datasets as an aid in teaching polynomial and nonlinear regression. The data were gathered by Galileo during his studies of falling bodies and projectiles. In analyzing and discussing these data, students are challenged to give thought to parsimony, independent and dependent variables, and the importance of understanding the scientific nature of the experiment. The opportunities for class discussion are especially rich in this understandable and real experiment, particularly when coupled with graphical analysis.

  • Many students doubt that statistical distributions are of practical value. Simulation makes it possible for students to tackle challenging, understandable projects that illustrate how distributions can be used to answer "what-if" questions of the type often posed by analysts. Course materials that have been developed over two years of classroom trials will be shared, including (1) overviews of distributions and simulation; (2) basic capabilities of @RISK software; (3) simulation spreadsheets suitable for analysis by teams; and (4) exercises to guide the teams. These revisable materials could also be used as in-class demonstrations. Concepts illustrated include expected value, k-tiles (e.g., quartiles), empirical distributions, distribution parameters, and the law of large numbers. For those who don't have @Risk, spreadsheets are provided which demonstrate elementary risk-modeling concepts using only Excel. All materials can be downloaded from www.sba.oakland.edu/Faculty/DOANE/downloads.htm.

  • The estimation of proportions is a subject which cannot be circumvented in a first survey sampling course. Estimating the proportion of voters in favour of a political party, based on a political opinion survey, is just one concrete example of this procedure. However, another important issue in survey sampling concerns the proper use of auxiliary information, which typically comes from external sources, such as administrative records or past surveys. Very often, an efficient insertion of the auxiliary information available will improve the precision of the estimations of the mean or the total when a regression estimator is used. Conceptually, it is difficult to justify using a regression estimator for estimating proportions. A student might want to know how the estimation of proportions can be improved when auxiliary information is available. In this article, I present estimators for a proportion which use the logistic regression estimator. Based on logistic models, this estimator efficiently facilitates a good modelling of survey data. The paper's second objective is to estimate a proportion using various sampling plans (such as a Bernoulli sampling and stratified designs). In survey sampling, each sample possesses its own probability and for a given unit, the inclusion probability denotes the probability that the sample will contain that particular unit. Bernoulli sampling may have an important pedagogical value, because students often have trouble with the concept of the inclusion probability. Stratified sampling plans may provide more insight and more precision. Some empirical results derived from applying four sampling plans to a real data base show that estimators of proportions may be made more efficient by the proper use of auxiliary information and that choosing a more satisfactory model may give additional precision. The paper also contains computer code written in S-Plus and a number of exercises.

  • The baby boom dataset contains the time of birth, sex, and birth weight for 44 babies born in one 24-hour period at a hospital in Brisbane, Australia. The data can be used to demonstrate that some common distributions -- the normal, binomial, geometric, Poisson, and exponential -- can be used to model real situations. Because the dataset is small and easily understood, it provides a useful classroom example for discussing these distributions.

  • In elementary statistics courses, students often have difficulty understanding the principles of hypothesis testing. This paper discusses a simple yet effective demonstration using playing cards. The demonstration has been very useful in teaching basic concepts of hypothesis testing, including formulation of a null hypothesis, using data as evidence against the null hypothesis, and determining the strength of the evidence against the null hypothesis, i.e., the p-value.

  • Many undergraduate students are introduced to frequentist or classical methods of parameter estimation such as maximum likelihood estimation, uniformly minimum variance unbiased estimation, and minimum mean square error estimation in a reliability, probability, or mathematical statistics course. Rossman, Short, and Parks (1998) present some thought provoking insights on the relationship between Bayesian and classical estimation using the continuous uniform distribution. Our aim is to explore these relationships using the exponential distribution. We show how the classical estimators can be obtained from various choices made within a Bayesian framework.

  • The dice game HOG has been used successfully in a variety of educational situations as an activity that not only introduces students to concepts in probability, statistics, and simulation but also fosters student interest in these concepts. This article presents several areas in the statistics curriculum where important concepts can be dealt with in a hands-on way. These areas include probability as decision making, experimental versus theoretical probability, expected value, and optimization.<br>This article explains the rules for HOG, gives examples of students' understanding, develops the probability theory, and identifies a "best" strategy for playing the game. This "best" strategy is developed in the context of fair six-sided dice and then generalized to fair s-sided dice.

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