Journal Article

  • An important step in the statistical problem-solving process is the selection of the appropriate statistical procedure for the real-world situation under analysis. A decision-tree term project has been found to be an effective teaching device to help MBA students understand this step. The project requires the students to construct a decision-tree structure, which, through a series of questions and responses, will lead from the statement of a statistical question to the appropriate sampling distribution to use in addressing the question.

  • This paper discusses the Illinois procedure for teaching the Monte Carlo method. Where there is limited time, or where students will not be able to grasp conventional methods firmly, we advocate teaching the Monte Carlo approach, and perhaps that only. Where there is more time, and where students will be able to well learn conventional methods, we advocate (a) teaching Monte Carlo methods at the very beginning as an introduction to statistical thinking and practice; and (b) afterwards teaching the Monte Carlo method with the conventional method as alternatives to the same problems, to help students learn analytic methods and to give them an alternative tools for their use.

  • Strong movements in both education research and education reform are emphasizing that teaching should encourage student activity rather than simply aim knowledge in the general direction of a student audience. Yet video, at least in its traditional technological forms, is passive. How can teachers make effective use of an apparently in effective medium? What role can video best play in new multimedia instructional systems? This article reviews research on learning through television in order to make practical suggestions. Specific examples are two widely distributed series, Against All Odds: Inside Statistics and Statistics: Decisions Through Data.

  • We present a critique showing the flawed logical structure of statistical significance tests. We then attempt to analyze, why, in spite of this faulty reasoning the use of significance tests persists. We identify the illusion of probabilistic proof by contradiction as a central stumbling block, because it is based on a misleading generalization of reasoning from logic to inference under uncertainty. We present new data from a student sample and examples from the psychological literature showing the strength and prevalence of this illusion. We identify some intrinsic cognitive mechanisms (similarity to modus tollens reasoning; verbal ambiguity in describing the meaning of significance tests; and the need to rule out chance findings) and extrinsic social pressures which help to maintain the illusion. We conclude by mentioning some alternative methods for presenting and analyzing psychological data, none of which can be considered the ultimate method.

  • This article presents a critique of the concept of randomness as it occurs in the psychological literature. The first section of our article outlines the significance of a concept of randomness to the process of induction; we need to distinguish random and non-random events in order to perceive lawful regularities and formulate theories concerning events in the world. Next we evaluate the psychological research that has suggested that human concepts of randomness are not normative. We argue that, because the tasks set to experimental subjects are logically problematic, observed biases may be an artifact of the experimental situations and that even if such biases do generalise they may not have pejorative implications for induction in the real world. Thirdly we investigate the statistical methodology utilised in tests for randomness and find it riddled with paradox. In a fourth section we find various branches of scientific endeavour that are stymied by the problems posed by randomness. Finally we briefly mention the social significance of randomness and conclude by arguing that such a fundamental concept merits and requires more serious considerations.

  • This interview was conducted for JSE at the Harvard Department of Statistics on December 18, 1992. The topics discussed include the history and future of statistics education, the use of video and computers in teaching statistics, the role of data analysis in statistics textbooks, innovation in the classroom, and graduate education.

  • 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. The second half of the paper develops four themes from the conference.

  • Many high school and college statistics courses, however, do not teach statistical reasoning effectively. Rather than helping students understand how to interpret the statistical statements they encounter, these courses focus upon statistical formulas and tests. We believe that the conventional approach not only leaves students confused about fundamental statistical concepts, but also makes the mathematics involved in statistics more rather than less obscure.

  • We explore challenges in achieving authentic inquiry with data in classrooms from the fifth through the eighth grade. We present the Tabletop, a prototype computer-based data analysis tool based on animated visual representations, and reports on clinical and classroom trials of this tool. Vignettes from clinical sessions illustrate students' understanding of the software interface as well as interacting subtleties of data creation and data analysis. One year of classroom trials is summarized in terms of three important categories of conceptual and cultural prerequisites for successful implementation: a) reasoning about the aggregate, b) the objectification of knowledge, and c) the pragmatic structure of classroom projects.

  • The familiar sampling procedures of statistical inference can be recast within a purely set-theoretic (ST) framework, without resorting to probabilistic prerequisites. This article is an introduction to the ST approach of statistical inference, with emphasis on its attractiveness for teaching. The main points treated are unsophisticated ST significance testing and ST inference for a relative frequency (proportion).