George W. Cobb

Mathematics, statistics, and teaching

How does statistical thinking differ from mathematical thinking? What is the role of mathematics in statistics? If you purge statistics of its mathematical content, what intellectual substance rema...

Reconsidering Statistics Education: A National Science Foundation Conference

1 Recent survey data demonstrate an acute need for curricular resources in statistics. The first half of this paper summarizes and compares a dozen current or recent NSF projects, most of which are developing such resources. (As an aid to interested instructors, an appendix gives more detail on the individual projects, along with a list of available files that provide even more detail.) Nearly all these projects involve activities for statistical laboratories, at least implicitly, although the labs are used in a variety of ways: for analysis of archival data sets, for hands-on production of data for analysis, and for simulation-based learning. These three kinds of labs are compared in terms of their complementary sets of advantages.2 This paper grows out of a small conference which brought together NSF Program Officers, Principal Investigators and Co-PIs of the projects, and a half-dozen other teachers of statistics. The second half of the paper develops four themes from the conference: (1) Questioning st...

Understanding conditional probabilities

Abstract In two experiments, subjects were asked to judge whether the probability of A given B was greater than, equal to, or less than the probability of B given A for various events A and B. In addition, in Experiment 2, subjects were asked to estimate the conditional probabilities and also to calculate conditional probabilities from contingency data. For problems in which one conditional probability was objectively larger than the other, performance ranged from about 25–80% correct, depending on the nature of A and B. Changes in the wording of problems also affected performance, although less dramatically. Patterns of responses consistent with the existence of a causal bias in judging probabilities were observed with one of the wordings used but not with the other. Several features of the data suggest that a major source of error was the confusion between conditional and joint probabilities.

Statistics Education Fin de Siecle

Abstract Higher education faces an environment of financial constraints, changing customer demands, and loss of public confidence. Technological advances may at last bring widespread change to college teaching. The movement for education reform also urges widespread change. What will be the state of statistics teaching at the university level at the end of the century? This article attempts to imagine plausible futures as stimuli to discussion. It takes the form of provocations by the first author, with responses from the others on three themes: the impact of technology, the reform of teaching, and challenges to the internal culture of higher education.

Mere Renovation is Too Little Too Late: We Need to Rethink our Undergraduate Curriculum from the Ground Up

The last half-dozen years have seen The American Statistician publish well-argued and provocative calls to change our thinking about statistics and how we teach it, among them Brown and Kass, Nolan and Temple-Lang, and Legler et al. Within this past year, the ASA has issued a new and comprehensive set of guidelines for undergraduate programs (ASA, Curriculum Guidelines for Undergraduate Programs in Statistical Science). Accepting (and applauding) all this as background, the current article argues the need to rethink our curriculum from the ground up, and offers five principles and two caveats intended to help us along the path toward a new synthesis. These principles and caveats rest on my sense of three parallel evolutions: the convergence of trends in the roles of mathematics, computation, and context within statistics education. These ongoing changes, together with the articles cited above and the seminal provocation by Leo Breiman call for a deep rethinking of what we teach to undergraduates. In particular, following Brown and Kass, we should put priority on two goals, to make “fundamental concepts accessible” and to “minimize prerequisites to research.” [Received December 2014. Revised July 2015]

Rethinking Assessment of Student Learning in Statistics Courses

Although much attention has been paid to issues around student assessment, for most introductory statistics courses few changes have taken place in the ways students are assessed. The assessment literature describes three foundational elements—cognition, observation, and interpretation—that comprise an “assessment triangle” underlying all assessments. However, most instructors focus primarily on the second component: tasks that are used to produce grades. This article focuses on three sections written by leading statistics educators who describe some innovative and even provocative approaches to rethinking student assessment in statistics classes.

Curriculum Guidelines for Bachelor of Arts Degrees in Statistical Science

Curriculum guidelines for a bachelor of arts degree in statistical science are proposed. These guidelines are intended for liberal arts colleges, and other institutions where statistics is taught in departments of mathematics. A flexible curriculum is described consisting of three main parts: mathematics, core statistical topics and a substantive area of study. The curriculum guidelines permit and actively encourage the rethinking of traditional courses and the development of new courses. Guidelines for a minor in statistical science are also proposed. The guidelines are the result of an Undergraduate Statistics Education Initiative workshop held in Alexandria, Virginia in April 2000.

Combating Anti-Statistical Thinking Using Simulation-Based Methods Throughout the Undergraduate Curriculum

The use of simulation-based methods for introducing inferen-ce is growing in popularity for the Stat 101 course, due in part to increasing evidence of the methods ability to improve studen-ts’ statistical thinking. This impact comes from simulation-based methods (a) clearly presenting the overarching logic of inference, (b) strengthening ties between statistics and probability/mathematical concepts, (c) encouraging a focus on the entire research process, (d) facilitating student thinking about advanced statistical concepts, (e) allowing more time to explore, do, and talk about real research and messy data, and (f) acting as a firm-er foundation on which to build statistical intuition. Thus, we argue that simulation-based inference should be an entry point to an undergraduate statistics program for all students, and that simulation-based inference should be used throughout all under-graduate statistics courses. To achieve this goal and fully recognize the benefits of simulation-based inference on the undergraduate statistics program, we will need to break free of historical forces tying undergraduate statistics curricula to mathematics, consider radical and innovative new pedagogical approaches in our courses, fully implement assessment-driven content innovations, and embrace computation throughout the curriculum. [Received December 2014. Revised July 2015]

What Might a Twenty-Year Old Conference Tell us About the Future of Our Profession?

The 1993 inaugural issue of the Journal of Statistics Education (JSE) published an article about a small conference for Principal Investigators (PIs) and co-PIs of twelve projects in statistics education funded by the National Science Foundation (NSF). This twenty-year retrospective (1) offers some personal memories related to the founding of JSE, (2) offers some thoughts about the legacies of the twelve funded projects, (3) sets out a sense of how the conference themes have fared over the last twenty years, and (4) indicates what this might suggest about the future of our profession. In conclusion, I argue (briefly) that at this moment in its history, statistics education faces the biggest opportunity and challenge of its last 40 years.

An Algorithmic Approach to Elementary ANOVA

Abstract An elementary approach to the analysis of variance for balanced designs is sketched and illustrated with an analysis of a repeated measures design. The approach is based on a conceptually simple algorithm that computes the usual linear decomposition of the data by repeatedly calculating and removing averages for groups of observations corresponding to the sources of variation in the design. An interactive computer program, written in Applesoft Basic, is available for use in teaching the algorithm.