Journal Article

  • "In reasoning about everyday problems, people use statistical heuristics, that is, judgmental tools that are rough intuitive equivalents of statistical principles. Statistical heuristics improved historically and they improve ontogenetically. Use of statistical heuristics is more likely when (a) the sample space and the sampling process are clear, (b) the orle of chance in producing events is clear, (c) the culture specifies statistical reasoning as normative for the events. Perhaps because statistical procedures are part of people's intuitive equipment to begin with, training in statistics has a marked impact on reasoning. Training increases both the likeli- hood that people will take a statistical approach to a given problem and the quality of the statistical solution. These empirical findings have important normative implications."

  • During the three years 1978-1981 a research project based at Loughborough in the East Midlands region of England investigated probability concepts of 11-16 year olds. A test of twenty-six questions was administered to a stratified sample of 2930 pupils from comprehensive mixed schools. These pupils were also given a test of general reasoning ability. the project's findings have been summarized in a 40 page booklet which includes all the test questions and analyses of responses. Nearly all test items, displayed an improvement in performance with increasing chronological age and with intellectual ability. Items requiring only the comparison of two direct quantities were well done by all ages tested (11 to 16 years), but those requiring comparison of two ratios were very poorly done, especially below the age of 15 years. This contrast is exemplified by the results for the two items. In this article we shall look at the development and test results of just one of the questions used.

  • Recently, one of the compilers of this bibliography published a review of selected publications on the teaching of probability and statistics. A computerized listing of the complete bibliography was made available as a supplement on request. This report is an expanded and updated version of that work. It presents a listing of available literature on the teaching of probability and statistics.

  • Twentieth-century psychologists have been pessimistic about teaching reasoning, prevailing opinion suggesting that people may possess only domain-specific rules, rather than abstract rules; this would mean that training a rule in one domain would not produce generalization to other domains. Alternatively, it was thought that people might possess abstract rules (such as logical ones) but that these are induced developmentally through self-discovery methods and cannot be trained. Research suggests a much more optimistic view: even brief formal training in inferential rules may enhance their use for reasoning about everyday life events. Previous theorists may have been mistaken about trainability, in part because they misidentified the kind of rules that people use naturally.

  • This article presents two major paradoxical examples of one of the simplest statistics, the "average".

  • The purpose of the present paper is to further clarify the misunderstandings concerning the meaning of significant test results, and to reassess the value of this statistical procedure for the teaching of scientific reasoning and for the analysis of research results.

  • This paper discusses the complaints of statistical teaching.

  • This article examines the role of random sampling and random assignment in the interpretation of research results. We discuss the random assignment model, which focuses on causal inference, and recommend that both models be taught in introductory methods and statistics courses.

  • There are two especially useful models of statistical inference, although only one, the normal curve model, is universally taught. The less well known permutation model is contrasted with the normal model and the case made that the permutation model is often more appropriate for the analysis of psychological data. Inappropriate interpretations generated by teaching only the normal model are illustrated. It is recommended that both models be taught so that students and applied workers have a better chance both of understanding the nature of the hypothesis that is being tested, and of correctly discriminating the statistical conditions that support causal inference and generality inference.

  • Probabilistic judgments made by researchers in psychology were investigated in statistical prediction situations. From these situations, it is possible to test the "representativeness hypothesis" (Tversky and Kahneman, 1971), and the "significance hypothesis" (Oakes, 1986). The predictive judgments concerned both an elementary descriptive statistic and a significance test statistic. In the first case, the predictive judgments were generally coherent, and fit comparatively well to Bayesian standard predictive probabilities. In the second case, they were generally incoherent, and fit poorly to Bayesian standard predictive probabilities. As for the two hypotheses tested, our findings are compatible with the significance hypothesis, but go against the representativeness hypothesis.