Journal Article

  • This paper discusses the Hot Hand as a cognitive illusion.

  • There is no adequate survey of ancient writing on chance, much less of its possible influences on writers in the last few centuries, and I am not the scholar to make good the deficiency. But it occurred to me that in the playful, albeit serious, spirit of Renyi's Letters, I could try to show some parallels between ideas central to my own recent work with probability models and discussions I've happened across in my recreational reading of the classics. I will refer particularly to Plutarch, who lived about A.D. 40-120 and whose surviving work is voluminous by comparison with that of almost any other ancient writer with equally broad interests. First, I note a number of general and recurring themes in Plutarch's Moralia and Lives (the two large collections of essays and biographies comprising his oeuvre) that seem to anticipate some of the topics dealt with by writers on probability in the scientific age; and then I mention in detail some specific passages in Plutarch that could be used in a didactic presentation of the probabilistic Rasch measurement model, on which my own research has been focused for the last several years. Allow me to follow Plutarch's own practice of quoting extensively from the sources.

  • Whether the sexes of children born in the same family are independent or whether they are positively or negatively correlated, is an important biological problem, that is interesting also for statisticians.

  • Subjects judged whether binary strings had been generated by a random or a nonrandom process.

  • The present study investigated a model used by non-mathematically oriented students in solving problems in descriptive statistics. Analyses show that college students mistakenly assume that a set of means together with simple mean computation constitutes a mathematical group satisfying the four axioms of closure, associativity, identity, and inverse. this set of misconceptions is so deeply ingrained in a students' underlying knowledge base that mere exposure to a more advanced course in statistics is not sufficient to overcome those misconceptions. However, results of an experiment indicated that most students were able to acquire the appropriate schema of statistical concepts by engaging in diagnostic activities embedded within a feedback-corrective procedure.

  • Behavioral decision theory can contribute in many ways to the management and regulation of risk. In recent years, empirical and theoretical research on decision making under risk has produced a body of knowledge that should be of value to those who seek to understand and improve societal decisions. This paper describes several components of this research, which is guided by the assumption that all those involved with high-risk technologies as promoters, regulators, politicians, or citizens need to understand how they and the others think about risk. Without such understanding, well-intended policies may be ineffective, perhaps even counterproductive.

  • In two experiments, subjects were asked to judge whether the probability of A give B was greater than, equal to, or less than the probability of B given A for various events A and B. In addition, in Experiment 2, subjects were asked to estimate the conditional probabilities and also to calculate conditional probabilities from contingency data. For problems in which one conditional probability was objectively larger than the other, performance ranged from about 25-80% correct, depending on the nature of A and B. Changes in the wording of problems also affected performance, although less dramatically. Patterns of responses consistent with the existence of a causal bias in judging probabilities were observed with one of the wordings used but not with the other. Several features of the data suggest that a major source of error was the confusion between conditional and joint probabilities.

  • These results support the hypothesis that one major cause of inappropriate closure among young children is the confusion of possibility with probability

  • A number of theoretical positions in psychology - including variants of case-based reasoning, instance-based analogy, and connectionist models - maintain that abstract rules are not involved in human reasoning, or at best play a minor role. Other views hold that the use of abstract rules is a core aspect of human reasoning. We propose eight criteria for determining whether or not people use abstract rules in reasoning, and examine evidence relevant to each criterion for several rule systems. We argue that there is substantial evidence that several different inferential rules, including modus ponens, contractual rules, causal rules, and the law of large numbers, are used in solving everyday problems. We discuss the implications for various theoretical positions and consider hybrid mechanisms that combine aspects of instance and rule models.

  • This paper explores a heuristic - representativeness - according to which the subjective probability of an event, or a sample, is determined by the degree to which it: i) is similar in essential characteristics to its parent population; and ii) reflects the salient features of the process by which it is generated.