Journal Article

  • 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.

  • This paper discusses a set of programs written in the statistical package Stata that is designed to support interactive student tutorials. The tutorial package has several desirable features, including customized tutorials, full student interaction, checking of student answers, repetition of practice problems using randomly chosen values, and a simple way to gauge student comprehension even when students run the tutorials at home. As an example, a tutorial used in an undergraduate econometrics class is discussed. The example illustrates Monte Carlo experiments on the linear regression model that allow students to demonstrate the validity of various formulas for the sampling distribution of ordinary least squares estimators.

  • This paper presents a data set based on an industrial case study using design of experiments. The data set is pedagogically rich because it has a rather large total sample size from an industrial setting that naturally yields a large third order interaction term. The experiment is a 23 design and is initially presented with no replications. The sample size of the data is then doubled and the analysis repeated, comparing these results with previous results. The process is repeated until eight replications are available for each combination of factors and all parameters are estimated. With eight replications, the analysis shows all main effects and all interactions are statistically significant at the a = 0.05 level. With smaller sample sizes, various main effects and interactions are not found to be statistically significant. Through this presentation the instructor can lead students in discussions about the effect of increased sample sizes, power, statistical significance (or insignificance), interaction terms, Type I and Type II errors as well as the importance and the role of the error term. In addition, students can manipulate the data set in a computer laboratory setting to illustrate many of the concepts inherent in the design of experiments and analysis of variance.

  • This paper discusses reasons for using humor in the statistics classroom. Humor strengthens the relationship between student and teacher, reduces stress, makes a course more interesting, and, if relevant to the subject, may even enhance recall of the material. The authors provide examples of humorous material for teaching students such topics as descriptive statistics, probability and independence, sampling, confidence intervals, hypothesis testing, and regression and forecasting. Also, some references, summarized strategies, and suggestions for becoming more humorous in the classroom are provided.

Pages

register