Theory

• The psychology of inference and the teaching of probability and statistics: Two sides of the same coin?

In this paper we explore the interrelationships of research in judgment and decision making with research in mathematical education on the learning of probability concepts. The psychological literature demonstrates that people are subject to heuristic and biases when making inferences or probabilistic estimates. The literature of mathematics education indicates that many people are statistically illiterate. Thus, central motivating questions for the paper are: Can research in the learning and teaching of probability and statistics help the statistically naive judge? Can research in the psychology of inference help the naive statistician? How can research from both these disciplines aid the teacher of probability and statistics? The paper consists of three main parts. Part one investigates obstacles to the use of statistics when making judgments or inferences. Part two discusses some suggestions from psychologists and from mathematics educators for increasing people's reliance upon statistics when making inferences. In part three, suggestions for further research are discussed. It is suggested that cooperative research efforts between psychologists and mathematics educators be conducted in order to further investigate these questions.

• The statistician and the pedagogical monster: Characteristics of effective instructors of large statistics classes

This paper offers suggestions in the areas of enthusiasm, organization and clarity, one-to-one skills, one-to-group skills, and an analytic/synthetic approach to teaching.

• Misconceptions of statistical significance

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.

• The perception of randomness

This paper discusses the concept of chance.

• Heuristics and biases

This article described three heuristics that are employed in making judgments under uncertainty: (i) representativeness, which is usually employed when people are asked to judge the probability that an object or event A belongs to class or process B; (ii) availability of instances or scenarios, which is often employed when people are asked to assess the frequency of a class or the plausibility of a particular development; and (iii) adjustment from an anchor, which is usually employed in numerical prediction when a relevant value is available. These heuristics are highly economical and usually effective, but they lead to systematic and predictable errors. A better understanding of these heuristics and of the biases to which they lead could improve judgments and decisions in situations of uncertainty.

• Causal schemes in judgments under uncertainty

The present paper is concerned with the role of causal reasoning in judgments under uncertainty and with some biases that are associated with this mode of thinking.

• Evidential impact of base rates

Although procedural variables have a considerable effect, the present chapter is confined to the discussion of evidential variables that control the interpretation and the impact of the base-rate data. Specifically, we focus on the distinction between two types of base rates, which we label causal and incidental.

• The availability bias in social perception and interaction

Every day the social perceiver makes numerous, apparently complex social judgments - Predicting another's behavior, attributing responsibility, categorizing an individual, evaluating anothers, estimating the power or influence of a person, or attributing causality. A central task of social psychology has been to determine how the social perceiver makes these judgments. Until recently, research on this topic was marked by a rationalistic bias, the assumption that judgments are made using thorough, optimal strategies (see, for example, Fischhoff, 1976, for discussion of this point). Errors in judgment were attributed to two sources: (a) accidental errors due to problems with information of which the perceiver was presumably unaware; and (b) errors which resulted from the irrational motives and needs of the perceiver. However, over a period of years, a growing body of evidence suggested not only that people's judgments and decisions are less complete and rational than was thought but that not all errors can be traced to motivational factors. Even in the absence of motives, judgments are often made on the basis of scant data, which are seemingly haphazardly combined and influenced by preconceptions (see, e.g., Dawes, 1976). These findings led to a revised view of the cognitive system. People came to be seen as capacity-limited, capable of dealing with only a small amount of data at a time. Rather than being viewed as a naive scientist who optimizes, the person was said to "satisfice" (Simon, 1957) and use shortcuts that would produce decisions and judgments efficiently and accurately.

• Informal covariation assessment: Data-based versus theory-based judgments

The flow of social experience frequently challenges us to recognize empirical covariations. Sometimes, these covariations are merely another test of our powers of observation and are of no immediate practical concern to us. At other times - for example, when those covariations involve early symptoms of problems and late manifestations, or behavioral strategies employed and outcomes obtained, or relatively overt characteristics of people or situations and relatively covert ones - such detection abilities may help to determine our success in adapting to the demands of everyday social life. More generally, covariation detection will play a large role in our continuing struggle as "intuitive scientists" (see Nisbett &amp; Ross, 1980; Ross, 1977, 1978) to evaluate and update the hypotheses we hold about ourselves, our peers, and our society. An obvious question therefore presents itself: How proficient are we, as laypeople, at assessing the empirical covariations presented by experiential evidence.