Statistics as Principled Argument PDF
Preview Statistics as Principled Argument
Statistics as Principled Argument Statistics as Principled Argument Robert P. Abelson Yale University Psychology Press Taylor & Francis Group New York London Psychology Press Psychology Press Taylor & Francis Group Taylor & Francis Group 711 Third Avenue 27 Church Road New York, NY 10017 Hove, East Sussex BN3 2FA © 1995 by Taylor & Francis Group, LLC Originally published by Lawrence Erlbaum Associates Reprinted in 2009 by Psychology Press, an imprint of Taylor & Francis Group Cover design by Mairav Salomon-Dekel International Standard Book Number-13: 978-0-8058-0528-4 (Softcover) Except as permitted by U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging-in-Publication Data Catalog record is available from the Library of Congress Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the Psychology Press Web site at http://www.psypress.com This book is dedicated to Willa Dinwoodie Abelson and to John Wilder Tukey, who in their special ways have encouraged me in seeking wisdom’s direction. Contents Preface xi Abelson’s Laws xv 1 Making Claims With Statistics 1 Misunderstandings of Statistics 1 Claims Made With Statistics: Comparison and Explanation 2 Language and Limitations of Null Hypothesis Tests 8 Persuasive Arguments: The MAGIC Criteria 11 Style and Convention 15 The Bottom Line 16 2 Elementary Arguments and the Role of Chance 17 Random Generating Processes 18 Random Sampling Processes 27 Summary 36 3 Magnitude of Effects 39 Probability Measures 39 Effect Sizes 45 Confidence Limits 52 vii viii CONTENTS 4 Styles of Rhetoric 54 Brash, Stuffy, Liberal, and Conservative Styles 54 One-Tailed, Two-Tailed, and Lopsided Tests 57 Alternative Tests Applied to the Same Data Set 59 Defective Observations 68 Multiple Tests Within the Same Data Set 70 Stating and Interpreting p Values 74 In the Last Analysis 77 5 On Suspecting Fishiness 78 Strange Distributions of Observations 78 The Occurrence of Impossible Scores 88 Strange Test Statistics 89 Inconsistencies Between Parallel Statistics 97 Too Much Consistency in Parallel Statistics 100 A Cautionary Note on the Detection of Fishiness 103 6 Articulation of Results: Ticks and Buts 104 Ticks and Buts 104 Ticks and the Evolution of Knowledge 105 Comparisons of Pairs of Means 108 Refraining Results for Better Articulation 114 Multiple Comparisons 118 Contrasts 125 More Than One Dependent Variable 127 Further Remarks 130 7 Generality of Effects 132 The Nature of Generality 132 Treatment-by-Context Interactions Within Studies 135 Generality Across Studies: Meta-Analysis 149 Generality Across and Within Studies: A Parallel 153 Final Caveat 155 8 Interestingness of Argument 156 Can Statistics Be Interesting? 156 Theoretical Interest 158 Surprisingness 160 Importance 168 CONTENTS ix 9 Credibility of Argument 170 Why Research Claims Are Disbelieved 170 The Structure of Debates on Disbelieved Claims 172 Methodological Artifacts 180 The Influence of Criticism on Methodology 197 References 199 Author Index 212 Subject Index 216
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