Fundamentals of Modern Statistical Methods Substantially Improving P
Conventional statistical methods have a very serious flaw. They routinely miss differences among groups or associations among variables that are detected by more modern techniques, even under very small departures from normality. Hundreds of journal artic
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Rand R. Wilcox X
Fundamentals of Modern Statistical Methods Substantially Improving Power and Accuracy
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Fundamentals of Modern Statistical Methods
Rand R. Wilcox
Fundamentals of Modern Statistical Methods Substantially Improving Power and Accuracy Second Edition
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Rand R. Wilcox Department of Psychology University of Southern California College of Letters, Arts & Sciences 3620 S. McClintock Ave. Los Angeles, CA 90089-1061 SGM 501 USA [email protected]
ISBN 978-1-4419-5524-1 e-ISBN 978-1-4419-5525-8 DOI 10.1007/978-1-4419-5525-8 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2010922890 c Springer Science+Business Media, LLC 2010 ° 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, LLC, 233 Spring Street, 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 on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
PREFACE TO THE SECOND EDITION Since the publication of the first edition, there have been a number of advances and insights that are relevant to the basic principles covered in this book. Some of these advances are outlined here. One has to do with inferences based on the usual sample median. When tied values can occur, it is now known that a wide range of estimators of the standard error of the median can be highly inaccurate, even with large sample sizes. Indeed, no estimator has been found that is completely satisfactory. A consequence is that any method for comparing medians, based in part on an estimate of the standard error, can be highly unsatisfactory regardless of which estimate of the standard error is used. A related issue is that with tied values, the central limit theorem can fail, as is now illustrated. A simple method for dealing with this problem, when comparing the medians of two groups, is now included. Another general area where there has been substantial progress is regression. When dealing with least squares regression, many new results and methods are now discussed regarding how to deal with heteroscedasticity. This second edition also expands on robust and more flexible methods for measuring the strength of an association. For example, measures of association based on a robust smoother are discussed using in part robust measures of scatter. In practical terms, there are new strategies for robustly measuring the strength of an association when dealing with outliers, nonnormality, and curvature
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