Literature Index

The authors present and test a new method of teaching Bayesian reasoning, something about which previous teaching studies reported little success. Based on G. Gigerenzer and U. Hoffrage's (1995) ecological frameword, the authors wrote a computerized tutorial program to train people to construct frequency representations (representation training) rather than to insert probabilities into Bayes's rule (rule training). Bayesian computations are simpler to perform with natural freqencies than with probabilites, and there are evolutionary reasons for assumingg that cognitive algorithms have been developed to deal with natural frequencies. In 2 studies, the authors compared representation training with rule training: the criteria were an immediate learning effect, transfer to new problems, and long-term temporal stability. Rule training was as good in transfer as representation training, but representation training had a higher immediate learning effect and greater temporal stability.

At the present time, frequentist ideas dominate most statistics undergraduate programs, and the exposure to Bayesian ideas in undergraduate statistics is very limited. There are historical reasons for this frequentist dominance. Efron (1986) concluded that frequentists had captured the high ground of objectivity (p. 4). Bayesian methods have superior performance, often even outperforming frequentist procedures when evaluated under frequentist criteria. In the past, Bayesian methods were of limited practical use, since analytic solutions for the Bayesian posterior distributions were only possible in a few cases, and the numerical calculation of the posterior often was not feasible because of lack of computer power. Recent developments in computing power, and the development of Markov chain methods for sampling from the posterior have made Bayesian methods possible, even in very complicated models. It is clearly unsatisfactory for our profession that most of our students are not being introduced to the best methods available. In this paper I make a proposal for how our profession should deal with this challenge, by giving my answers to the journalistic "who, what, where, when, why, and how" questions about the place of Bayesian Statistics in undergraduate statistical education.

The computer's potential to improve the teaching of data analysis is now a well-known litany (Jones, 1997; Snell & Peterson, 1992; Velleman & Moore, 1998). It includes its power to illuminate key concepts through simulations and multiple-linked representations. It also includes its ability to free students up, at the appropriate time, from time-intensive tasks - from what NCTM's (1989) Standards referred to as the "narrow aspects of statistics" (p. 113). This potentially allows instruction to focus more attention on the processes of data analysis - exploring substantive questions of interest, searching for and interpreting patterns and trends in data, and communicating findings.

Confidence intervals are pedagogically important but often misinterpreted. This article describes Java applets designed to help students understand two interpretations of confidence intervals.