Literature Index

Numerous writers have argued quite forcefully that users of statistics in the behavioral sciences have been guilty of misunderstanding and misapplying even the most rudimentary concepts and procedures of applied statistics. Why is this the case when almost rudimentary concepts and procedures of applied statistics. Why is this the case when almost every university and college in America has several departments teaching applied statistics courses in the behavioral sciences? We are quick to hold researchers responsible for statistical abuses, but it may well be that researchers are only parroting what they have read or been taught. Since the most common element in almost all teaching of behavioral statistics is the textbook, could it not be that the textbook is a source of statistical "myths and misconceptions" so often denounced as misleading and inappropriate? A conceivable source of statistical misconceptions and errors occurring in the published literature, theses, and dissertations is the behavioral statistics textbook. To illustrate the nature and extent of myths and misconceptions found in some of the best-selling introductory behavioral statistics textbooks is the purpose of this paper.

One of the most common misconceptions about probability is the belief that successive outcomes of a random process are not independent. This belief has been dubbed the "gambler's fallacy". The belief that non-normative expectations such as the gambler's fallacy are widely held has inspired probability and statistics instruction that attempts to counter such beliefs. This study presents an investigation of student performance pre and post instruction on problems dealing with these kinds of statistical misconceptions. Instruction consisted of 10 laboratory sessions, 1.5 hours each, delivered to 16 high school students attending a summer mathematics program at Mount Holyoke College (Massachusetts). The instruction included computer simulations that were intended to provide students with sufficient data to refute expectations based on the representativeness heuristic, as well as other misconceptions about chance. Student performance suggests that a belief in representativeness may not be as widespread as thought, and that curriculum development aimed at countering this belief should proceed cautiously. In addition, student who apparently do not have a well-developed understanding of independence in random sampling may nevertheless answer such problems correctly based on reasoning that is fundamentally non-probabilistic. Thus, many items currently being used to assess conceptual development may be insensitive to certain misconceptions about probability. Student misconceptions about probability need to be better understood if more appropirate mathematics instruction is to be achieved. (KR)

This paper presents a cognitive analysis of subjective probability judgments and proposes that these are assessments of belief-processing activities. The analysis is motivated by an investigation of the concepts of belief, knowledge, and uncertainty.

In Experiment 1, subjects estimated a) the mean of a random sample of ten scores consisting of nine unknown scores and a known score that was divergent from the population mean; and b) the mean of the nine unknown scores. The modal answer (about 40% of the responses) for both sample means was the population mean. The results extend the work of Tversky and Kahneman by demonstrating that subjects hold a passive, descriptive view of random sampling rather than an active balancing model. This result was explored further in in-depth interviews, wherein subjects solved the problem while explaining their reasoning. The interview data replicated Experiment 1 and further showed (a) that subjects' solutions were fairly stable-- when presented with alternative solutions including the correct one, few subjects changed their answer; (b) little evidence of a balancing mechanism; and (c) that acceptance of both means as 400 is largely a result of the perceived unpredictability of "random samples."