Springer Series in Statistics Advisors: P. Bickel, P. Diggle, S. Fienberg, U. Gather, I. Olkin, S. Zeger Phillip Good Permutation, Parametric and Bootstrap Tests of Hypotheses Third Edition With 22 Illustrations Phillip Good 205 W. Utica Avenue Huntington Beach, CA 92648 USA
[email protected] Library of Congress Cataloging-in-Publication Data Good, Phillip I. Permutation, Parametric and Bootstrap Tests of Hypotheses Phillip Good.— 3rd ed. p. cm. — (Springer series in statistics) Includes bibliographical references and index. ISBN 0-387-20279-X (hardcover : alk. paper) 1. Statistical hypothesis testing. 2. Resampling (Statistics) I. Title. II. Series. QA277.G643 2004 519.5′6—dc22 2004050436 ISBN 0-387-20279-X Printed on acid-free paper. © 1994, 2000, 2005 Springer Science+Business Media, Inc. All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, Inc., 233 Spring St., New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed in the United States of America. 9 8 7 6 5 4 3 2 1 springeronline.com (MVY) SPIN 10952368 Preface to the Third Edition This text is intended to provide a strong theoretical background in testing hypotheses and decision theory for those who will be practicing in the real world or who will be participating in the training of real-world statisticians and biostatisticians. In previous editions of this text, my rhetoric was somewhat tentative. I was saying, in effect, “Gee guys, permutation methods provide a practical real-world alternative to asymptotic parametric approximations. Why not give them a try?” But today, the theory, the software, and the hardware have come together. Distribution-free permutation procedures are the primary method for testing hypotheses. Parametric procedures and the bootstrap are to be reserved for the few situations in which they may be applicable. Four factors have forced this change: 1. Desire by workers in applied fields to use the most powerful statistic for their applications. Such workers may not be aware of the fundamental lemma of Neyman and Pearson, but they know that the statistic they want to use—a complex score or a ratio of scores, does not have an already well-tabulated distribution. 2. Pressure from regulatory agencies for the use of methods that yield exact significance levels, not approximations. 3. A growing recognition that most real-world data are drawn from mixtures of populations. 4. A growing recognition that missing data is inevitable, balanced designs the exception. Thus, it seems natural that the theory of testing hypothesis and the more general decision theory in which it is embedded should be introduced via the permutation tests. On the other hand, certain relatively robust parametric tests such as Student’s t continue to play an essential role in statistical practice. As the present edition is intended to replace rather than supplement existing graduate level texts on testing hypotheses and decision theory, it includes vi Preface to the Third Edition material on parametric methods as well as the permutation tests and the bootstrap. The revised and expanded text