Teaching Bayesian Statistics Using Sampling Methods and MINITAB

Bayesian statistics can be hard to teach at an elementary level due to the difficulty in deriving the posterior distribution for interesting nonconjugate problems. One attractive method of summarizing the posterior distribution is to directly simulate from the probability distribution of interest and then explore the simulated sample. We illustrate the use of Rubin's Sampling-Importance-Resampling (SIR) algorithm to simulate posterior distributions for three inference problems. In each example, we focus on the construction of the prior distribution and then use exploratory data analysis techniques to describe the posterior samples and make inferences. The use of MINITAB macros is presented to illustrate the ease of performing this simulation on standard statistical computer programs.     

Phlegon's Stem-and-Leaf Display

The Greek writer Phlegon (80–140 AD) from Tralles in Asia Minor wrote a book entitled On Long-lived Persons that contains a long list of people over a hundred years old. He collected data from the Roman censuses. With respect to the history of statistics, Phlegon's book is the earliest surviving text to use the Stem-and-Leaf display of collected data.     

We Must Preach what is Practiced

Much of what we teach in statistics is seldom used in practice. Much of what students need we do not teach.     

The Blind Paper Cutter: Teaching about Variation,Bias, Stability,and Process Control

The intention of this article is to provide teachers with a student activity to help reinforce learning about variation, bias, stability, and other statistical quality control concepts. Blind paper cutting is an effective way of generating tangible sequences of a product, which students can use to address many levels of questions. No special apparatus is required.     

The Extent of Gross Errors Eliminated by Robust Multiple Linear Regressions

Robust estimation methods can effectively eliminate the influence of gross errors on parameter estimation. However, the extent of gross errors eliminated (EGEE) by robust estimation methods is far-reaching. This article presents a new approach to determine EGEE by robust estimation method. Taking multiple linear regressions (2–5) as examples, simulation experiments were conducted to compare the EGEE of 14 frequently used robust estimation methods. This article confirms several additional efficient robust estimation methods for dealing with multiple linear regressions, as well as the minimum number of observations needed to eliminate gross errors in certain ranges completely.     

Number of predictors and multicollinearity: What are their effects on error and bias in regression?

The present Monte Carlo simulation study adds to the literature by analyzing parameter bias, rates of Type I and Type II error, and variance inflation factor (VIF) values produced under various multicollinearity conditions by multiple regressions with two, four, and six predictors. Findings indicate multicollinearity is unrelated to Type I error, but increases Type II error. Investigation of bias suggests that multicollinearity increases the variability in parameter bias, while leading to overall underestimation of parameters. Collinearity also increases VIF. In the case of all diagnostics however, increasing the number of predictors interacts with multicollinearity to compound observed problems.     

A Survey of the Teaching of Statistics in M.B.A. Programs

A survey of business schools was conducted to obtain information about the current state of the teaching of business statistics to students enrolled in M.B.A. degree programs. The survey was undertaken for and presented at a June 1986 conference on “Making Statistics More Effective in Schools of Business,” held at the University of Chicago's Graduate School of Business. Information was elicited concerning both the required statistics sequence and elective statistics courses for M.B.A. students, as well as computer usage in these courses. This article summarizes the information obtained from the survey.     

Deriving the Normal and Exponential Densities Using EDA Techniques

This paper shows how students in an introductory statistics course discover mathematical expressions for the normal and exponential density functions. Techniques of exploratory data analysis (EDA) are applied to large data sets, the key idea being a straight-line fit to an appropriate reexpression of the histogram.     

Letters to the Editor

Quantitative graphics have been central to the development of science, and statistical graphics date from the earliest attempts to analyze data. Many familiar forms, including bivariate plots, statistical maps, bar charts, and coordinate paper, were used in the 18th century. Statistical graphics developed through attention to four problems: spatial organization (17th and 18th centuries), discrete comparison (18th and early 19th centuries), continuous distribution (19th century), and multivariate distribution and correlation (late 19th and early 20th centuries). Today, statistical graphics appear to be reemerging as an important analytic tool, with recent innovations exploiting computer graphics and related technologies.     

The Racing Car Problem

An approach to teaching linear regression with unbalanced data is outlined that emphasizes its role as a method of adjustment for associated regressors. The method is introduced via direct standardization, a simple form of regression for categorical regressors. Properties of regression in the presence of association and interaction are emphasized. Least squares is introduced as a more efficient way of calculating adjusted effects for which exact decompositions of the variance are possible. Interval-scaled regressors are initially grouped and treated as categorical; polynomial regression and analysis of covariance can be introduced later as alternative methods.     

Some Uses for Distribution-Fitting Software in Teaching Statistics

Statistics courses now make extensive use of menu-driven, interactive computer software. This article presents some insight as to how a new class of PC-based statistical software, called “distribution-fitting” software, can be used in teaching various courses in statistics.     

Will the ASA's Efforts to Improve Statistical Practice be Successful? Some Evidence to the Contrary

ABSTRACT

Recent efforts by the American Statistical Association to improve statistical practice, especially in countering the misuse and abuse of null hypothesis significance testing (NHST) and p-values, are to be welcomed. But will they be successful? The present study offers compelling evidence that this will be an extraordinarily difficult task. Dramatic citation-count data on 25 articles and books severely critical of NHST's negative impact on good science, underlining that this issue was/is well known, did nothing to stem its usage over the period 1960–2007. On the contrary, employment of NHST increased during this time. To be successful in this endeavor, as well as restoring the relevance of the statistics profession to the scientific community in the 21st century, the ASA must be prepared to dispense detailed advice. This includes specifying those situations, if they can be identified, in which the p-value plays a clearly valuable role in data analysis and interpretation. The ASA might also consider a statement that recommends abandoning the use of p-values.     

Forecasting spring flow time series

Summary The paper deals with a statistical analysis, carried out to define the underlying reason of some of the damage observed in many buildings of a southern Italian town. Engineering considerations, substantiated by specific measurements, attributed them to the lowering of the groundwater table in the area below the building locations. Due to two coinciding events which occurred in the preceding years, i.e. a persistent drought and the start up of a system of wells, it was not possible to define the cause of the former phenomenon. As shutting down the wells could generate additional problems, an accurate picture of the whole situation was necessary, before taking any action. By taking advantage of some fragmentary data belonging to the flow of a spring located in the area and on the basis of the knowledge of the rainfall data recorded in the Italian hydrographic service directory, two models have been developed which reproduce the spring flow time series in relation to the rainfall recorded in the surrounding area. By comparing the spring flow predictions with the actual data it has been possible to highlight the main role played by the wells.     

A nonparametric statistical procedure for the detection of marine pollution

This paper is devoted to the estimation of the derivative of the regression function in fixed-design nonparametric regression. We establish the almost sure convergence as well as the asymptotic normality of our estimate. We also provide concentration inequalities which are useful for small sample sizes. Numerical experiments on simulated data show that our nonparametric statistical procedure performs very well. We also illustrate our approach on high-frequency environmental data for the study of marine pollution.     

A Non-Typical Least-Squares Solution to an Engineering Problem

In preposterior analysis, Bayesians use an Expected-Net-Gain chart to identify the optimal sample size. This kind of chart, it turns out, is also an excellent educational vehicle for illustrating many of the reasons given for preferring sampling from a population over taking a census, preferring one type of sampling over another (e.g., stratified sampling rather than simple random sampling), or allocating part of a fixed budget to reduce systematic error rather than using it all to reduce sampling errors. The use of such a chart in a basic statistics course is described.     

The joint distribution and moments of an extreme of the dependent variable and the concomitant of an extreme of the independent varible

We shall in the present paper deal with the basic problem indicated in the title which we encounter when performing regression analysis with order statistics and concomitants. Numerical results of the product-moments will also be presented.     

Some approaches to statistical analysis of a weather modification experiment

Data from a weather modification experiment are examined and a number of statistical analyses reported. The validity of earlier inferences is studied as are the utilities of various statistical methods. The experiment is described. The original analysis of North American Weather Consultants, who conducted the experiment, is reviewed. Data summarization is reported. A major approach to analysis is through the use of cloud-physics covari-ates in regression analyses. Finally, a multivariate analysis is discussed. It appears that the covariates may have been affected by treatment (cloud seeding) and that their use is invalid, not only reducing error variances but removing treatment effect. Some recommendations for improved design of similar future experiments are given in a concluding section, including preliminary trial use of blocking by storms.     

Exploring Cook's Statistic Graphically

An index plot of Cook's statistic is frequently used to highlight influential observations. In this article we illustrate how enhanced higher dimensional plots of Cook's statistic can provide further useful information about sets of influential observations. We provide examples using normal and generalized linear models.     

The Many Facets of Statistics Education: 175 Years of Common Themes

The American Statistical Association's primary founder, Lemuel Shattuck, was driven by a passion for collecting and disseminating accurate information on vital statistics, public health, and other statistically related concerns. The 175th anniversary provides an opportunity to reflect on the education-related reasons ASA was founded and what it has done in education since its founding, especially in the past 25 years since the 150th anniversary. An examination of early and more recent issues of the ASA's journals reveals some common themes that have recurred over the past 175 years. We discuss what those themes are and what the ASA is doing to address them currently, and then conclude by discussing what ASA members can do to help.     

A computational understanding of partial and part determination coefficients

A computational understanding of partial and part determination coefficients brings additional insight concerning their interpretations in regression. It also enables one to easily identify synergistic combinations. Benefits from the practical interpretation of synergism have yet to be fully explored and exploited. Hence, this study provides a new dimension in the analysis of data.