E-Book Overview
Lack of ability to think probabilistically makes one prone to a variety of irrational fears and vulnerable to scams designed to exploit probabilistic naivet?, impairs decision making under uncertainty, facilitates the misinterpretation of statistical information, and precludes critical evaluation of likelihood claims. Cognition and Chance presents an overview of the information needed to avoid such pitfalls and to assess and respond to probabilistic situations in a rational way. Dr. Nickerson investigates such questions as how good individuals are at thinking probabilistically and how consistent their reasoning under uncertainty is with principles of mathematical statistics and probability theory. He reviews evidence that has been produced in researchers' attempts to investigate these and similar types of questions. Seven conceptual chapters address such topics as probability, chance, randomness, coincidences, inverse probability, paradoxes, dilemmas, and statistics. The remaining five chapters focus on empirical studies of individuals' abilities and limitations as probabilistic thinkers. Topics include estimation and prediction, perception of covariation, choice under uncertainty, and people as intuitive probabilists. Cognition and Chance is intended to appeal to researchers and students in the areas of probability, statistics, psychology, business, economics, decision theory, and social dilemmas.
E-Book Content
Cognition ana Chance The Psychology 01 Probabilistic Reasoning
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Cognition and Chance The Psychology 01 Probabilistic Reasoning
Raymond S. Nickerson Tufts University
2004
LAWRENCE ERLBAUM ASSOCIATES, PUBLISHERS Mahwah, New Jersey London
Copyright © 2004 by Lawrence Erlbaum Associates, Inc. All rights reserved. No part of this book may be reproduced in any form, by photostat, microform, retrieval system, or any other means, without prior written permission of the publisher. Lawrence Erlbaum Associates, Inc., Publishers 10 Industrial Avenue Mahwah, New Jersey 07430 Cover design by Kathryn Houghtaling Lacey Library of Congress Cataloging-in-Publication Data
p. cm. Includes bibliographical references and index. ISBN 0-8058-4898-3 (cloth : alk. Paper) ISBN 0-8058-4899-1 (pbk.: alk. paper)
2003 —dc22
2003000000 CIP
Books published by Lawrence Erlbaum Associates are printed on acid-free paper, and their bindings are chosen for strength and durability. Printed in the United States of America 10 9 8 7 6 5 4 3 2 1
To the fond memory of Carlton Gregory and A. Douglas Glanville exceptional teachers who honored their students by making them think
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Contents
Preface
ise
1.
Probability and Cbance
1
2.
Randomness
54
3.
Coincidences
82
4.
Inverse Probability and tbe Reverend Tnomas Bayes 1O9
5.
Some Instructive Problems
144
6.
Some Probability Paradoxes and Dilemmas
181
7.
Statistics
232
8.
Estimation and Prediction
283
9.
Perception of Covariation and Contingency
332
10.
Cboice under Uncertainty
355
11.
People as Intuitive Probabilists
398
12.
Concluding Comments
436
Vll
vm
References
439
Author Index
489
Subject Index
5O5
Pre£ace everybody thinks probabilistically, whether knowingly or not. We judge the likelihood that the barking dog will bite, that the rumor that the company is about to have a big layoff is true, that bottled water is purer than wha