Journal Article

Recent years have witnessed a strong movement away from what might be termed classical statistics to a more empirical, data-oriented approach to statistics, sometimes termed exploratory data analysis, or EDA. This movement has been active among professional statisticians for twenty or twenty-five years but has begun permeating the area of statistical education for non-statisticians only in the past five to ten years. At this point, there seems to be little doubt that EDA approaches to applied statistics will gain support over classical approaches in the years to come. That is not to say that classical statistics will disappear. The two approaches begin with different assumptions and have different objectives, but both are important. These differences will be outlined in this article.

Psychologists interested in such diverse areas as scientific reasoning, attribution theory, depression, and judgment have central to their theories the ability of people to judge the degree of covariation between two variables. We performed seven experiments to help determine what heuristics people use in estimating the contingency between two dichotomous variables. Assume that the two variables are Factor 1 and Factor 2, each of which may be present or absent. In Experiment 1 we hypothesized that people assess contingency solely based on the number of instances in which both Factor 1 and Factor 2 are present. By manipulating column and row tables of a 2x2 matrix, we were able to place various values in this "present-present" cell, also called Cell A. If subjects do base their contingency estimate on Cell A, we would expect a monotonic relation between Cell A frequency and the contingency estimate. This test of the Cell A heuristic led us to conclude that it could not represent a complete explanation of contingency estimation. Although Experiment 2 resulted in a rejection of one possible explanation of the results of Experiment 1, Experiment 2 and 3 together provided us with an essential finding: Very low cell frequencies are greatly overestimated. In Experiment 4 participants in a contingency estimation task involving no memory demands used rather complex heuristics in judging contingency. When the memory demands were increased in Experiment 5, the comparatively simple Cell A heuristic emerged as the modal strategy. Two factors, the use of simple heuristics by most subjects and the overestimation of small cell frequencies, combined to explain the results of Experiments 2 and 3. In Experiment 6 we showed that in a contingency estimation task, salience can augment the impact of one type of data but not another. In Experiment 7 we learned that the versus at the end of the data stream, can influence the final estimate. From this group of experiments we concluded that the "framing" of the task affects the contingency estimate; a number of factors that bear no logical relation to the contingency between two factors nevertheless influence one's perception of the contingency. Finally, we related our findings to a variety of analogous findings in the research areas of memory, attribution theory, clinical judgment, and depression.

The classroom activity described here is a structured problem series developed for students to discover concepts themselves. Among psychology students, introductory statistics is a course which often is less appealing than other courses. As a result, one of the major challenges in teaching it to undergraduates is making the material both interesting and relevant to the student's personal experience. This is particularly true in relation to other courses in the major, where the self-referential nature of the content insures at least some degree of relevance. During the past three years, I have taught introductory statistics courses to classes which included not only psychology majors but also education and biology students. The students of these courses and feedback from students has convinced me that a few key features of the course structure and manner of presentation of the material are primarily responsible for making the courses effective and enjoyable. These features all relate the material to the direct experience of the students. This approach has a strong justification of both educational theory (e.g., Dewey, 1938) and from psychological research (e.g., Craik & Lockhart, 1972); material made meaningful in this way is more likely to be assimilated and retained. In particular, the aspect of individual experience to which the statistical material is conceptually related is the manner in which knowledge is gained. This will be elaborated later in the article; the justification of this approach can be made in terms of the nature of the discipline as well as pedagogically. Statistical inference is directly concerned with specifying principles by which scientific knowledge is gained; be relating the content of statistics to one's own experience of gaining knowledge, one sees more clearly the core of the discipline. This paper first describes the classroom activities which have been features of this approach; it then reviews the manner in which statistical principles have been conceptually related to the students' experience of gaining knowledge.

Explaining abstract, theoretical distributions to beginning students is sometimes difficult. This article describes a demonstration that helps to make the central limit theorem for generating sampling distributions concrete and understandable.