Paul F. Velleman

Nominal, Ordinal, Interval, and Ratio Typologies are Misleading

Abstract The psychophysicist S.S. Stevens developed a measurement scale typology that has dominated social statistics methodology for almost 50 years. During this period, it has generated considerable controversy among statisticians. Recently, there has been a renaissance in the use of Stevenss scale typology for guiding the design of statistical computer packages. The current use of Stevenss terminology fails to deal with the classical criticisms at the time it was proposed and ignores important developments in data analysis over the last several decades.

BACON: blocked adaptive computationally efficient outlier nominators

Abstract Although it is customary to assume that data are homogeneous, in fact, they often contain outliers or subgroups. Methods for identifying multiple outliers and subgroups must deal with the challenge of establishing a metric that is not itself contaminated by inhomogeneities by which to measure how extraordinary a data point is. For samples of a sufficient size to support sophisticated methods, the computation cost often makes outlier detection unattractive. All multiple outlier detection methods have suffered in the past from a computational cost that escalated rapidly with the sample size. We propose a new general approach, based on the methods of Hadi (1992a,1994) and Hadi and Simonoff (1993) that can be computed quickly — often requiring less than five evaluations of the model being fit to the data, regardless of the sample size. Two cases of this approach are presented in this paper (algorithms for the detection of outliers in multivariate and regression data). The algorithms, however, can be applied more broadly than to these two cases. We show that the proposed methods match the performance of more computationally expensive methods on standard test problems and demonstrate their superior performance on large simulated challenges.

Efficient Computing of Regression Diagnostics

Abstract Multiple regression diagnostic methods have recently been developed to help data analysts identify failures of data to adhere to the assumptions that customarily accompany regression models. However, the mathematical development of regression diagnostics has not generally led to efficient computing formulas. Conflicting terminology and the use of closely related but subtly different statistics has caused confusion. This article attempts to make regression diagnostics more readily available to those who compute regressions with packaged statistics programs. We review regression diagnostic methodology, highlighting ambiguities of terminology and relationships among similar methods. We present new formulas for efficient computing of regression diagnostics. Finally, we offer specific advice on obtaining regression diagnostics from existing statistics programs, with examples drawn from Minitab and SAS.

Definition and Comparison of Robust Nonlinear Data Smoothing Algorithms

Abstract Nonlinear data smoothers provide a practical method of finding smooth traces for data confounded with possibly long-tailed or occasionally spikey noise. They are resistant to the effects of extreme observations that are not part of the local pattern, yet they are able to respond rapidly to well-supported patterns. This article defines a collection of nonlinear smoothers based upon running medians and presents methods for describing and comparing their performance. The characterizations of the smoothers presented here reveal some with excellent low-pass transfer characteristics, negligible Gibbs rebound, and resistance to the effects of non-Gaussian disturbances.

Building Multiple Regression Models Interactively

Automated multiple regression model-building techniques often hide important aspects of data from the data analyst. Such features as nonlinearity, collinearity, outliers, and points with high leverage can profoundly affect automated analyses, yet remain undetected. An alternative technique uses interactive computing and exploratory methods to discover unexpected features of the data. One important advantage of this approach is that the data analyst can use knowledge of the subject matter in the resolution of difficulties. The methods are illustrated with reanalyses of the two data sets used by Hocking (1976, Biometrics 32, 1-44) to illustrate the use of automated regression methods.

Multimedia for Teaching Statistics: Promises and Pitfalls

Abstract In this department The American Statistician publishes articles, reviews, and notes of interest to teachers of the first mathematical statistics course and of applied statistics courses. The department includes the Accent on Teaching Materials section; suitable contents for the section are described under the section heading. Articles and notes for the department, but not intended specifically for the section, should be useful to a substantial number of teachers of the indicated types of courses or should have the potential for fundamentally affecting the way in which a course is taught. This article examines the usefulness of multimedia technology for teaching statistics, with attention to both promises and pitfalls. We suggest some principles for the design and use of multimedia, and we offer opinions on the role of human teachers in a multimedia educational environment.

A Critical Look at Some Analyses of Major League Baseball Salaries

Abstract At a data analysis exposition sponsored by the Section on Statistical Graphics of the ASA in 1988, 15 groups of statisticians analyzed the same data about salaries of major league baseball players. By examining what they did, what worked, and what failed, we can begin to learn about the relative strengths and weaknesses of different approaches to analyzing data. The data are rich in difficulties. They require reexpression, contain errors and outliers, and exhibit nonlinear relationships. They thus pose a realistic challenge to the variety of data analysis techniques used. The analysis groups chose a wide range of model-fitting methods, including regression, principal components, factor analysis, time series, and CART. We thus have an effective framework for comparing these approaches so that we can learn more about them. Our examination shows that approaches commonly identified with Exploratory Data Analysis are substantially more effective at revealing the underlying patterns in the data and at ...

The Resistant Line and Related Regression Methods

Abstract In a bivariate (x, y) scatterplot the three-group resistant line is that line for which the median residual in each outer third of the data (ordered on x) is zero. It was proposed by Tukey as an exploratory method resistant to outliers in x and y and suited to hand calculation. A dual plot representation of the procedure yields a fast, convergent algorithm, nonparametric confidence intervals for the slope, consistency, influence function, and asymptotic normality results. Monte Carlo results show that small sample efficiencies exceed their asymptotic values in important cases. Both breakdown and efficiency are adequate for exploratory work. Replacing medians by other M-estimators of location increases efficiency substantially without affecting breakdown or computational complexity. The method thus combines bounded influence and acceptable efficiency with conceptual and computational simplicity.

Criteria and Considerations in the Evaluation of Statistical Program Packages

Papers describing new algorithms, programs, or statistical packages will not contain listings of the program, although the completely documented program must be available from the author. Review of the paper will always include a running test of the program by the referee. The description of a program or package in this Department should not be construed as an endorsement of it by the American Statistical Association or its Committees, nor is any warranty implied about the validity of the program. The Editorial Committee will be pleased to confer with authors about the appropriateness of topics or drafts of possible articles.

A Randomized Controlled Study of Contrast Baths on Patients with Carpal Tunnel Syndrome

STUDY DESIGN Randomized clinical trial. INTRODUCTION Contrast baths are a treatment modality commonly used in hand clinics. Yet the benefits of contrast baths have been poorly substantiated. Contrast baths have been suggested for the purposes of reducing hand volume, alleviating pain, and decreasing stiffness in affected extremities. PURPOSE OF THE STUDY To determine the effects of specific contrast bath protocols on hand volume in patients diagnosed with Carpal Tunnel Syndrome. METHODS Study participants were randomly assigned to one of three treatment group protocols--contrast baths with exercise, contrast baths without exercise, and an exercise-only control treatment group. Study participants were evaluated with hand volumetry, before and after treatment at two different data collection periods-pre- and postoperatively. RESULTS Data were gathered on 58 participants before Carpal Tunnel Release surgery and on 56 participants after Carpal Tunnel Release surgery, for a total of 114 treatments. The changes in hand volume (the after treatment volume minus the before treatment volume) were analyzed using one-way and multi-way analysis of variance (ANOVA). Although all three treatments resulted in a slight increase in hand volume both pre- and postsurgery, the increase was not clinically significant with regard to hand volumes. Also no significant differences were noted among the three treatments. Specifically, the ANOVA for presurgery differences among treatments had F=0.155 (2 and 55 df), p=0.857. The ANOVA for postsurgery difference among treatments had F=0.544 (2 and 53 df), p=0.584. CONCLUSIONS The use of contrast bath treatment has no significant effect on increase or decrease of hand volume in Carpal Tunnel Syndrome patients, pre- and/or postoperatively. LEVEL OF EVIDENCE 1B.