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100 Statistical Tests (3rd ed.), Third Edition

Gopal K. Kanji

Pub. date: 2006 | DOI: http://dx.doi.org/10.4135/9781849208499

Print ISBN: 9781412923767 | Online ISBN: 9781849208499

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(b) critical values for a standard normal distribution The normal distribution is symmetrical with respect to μ = 0. Anderson , R.L. ‘Distribution of the serial correlation coefficient’, Annals of Mathematical Statistics (1942), 13: 1–13. Durbin , J. Watson , G.S. ‘Testing for serial correlation in least squares regression II’, Biometrika (1951), 38: 159–78. Hart , B.I. ‘Significance levels for the ratio of the mean square successive difference to the variance’, Annals of Mathematical Statistics (1942), 13: ...

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    • Covers all the most commonly used tests with information on how to calculate and interpret results with simple datasets. Each entry begins with a short summary statement about the tests purpose, and contains details of the test objective, the limitations (or assumptions) involved, a brief outline of the method, a worked example, and the numerical calculation. © Gopal K. Kanji 2006 First edition published 1993, reprinted 1993 Reprinted with corrections 1994 Reprinted 1995, 1997 New edition published 1999 Reprinted 2000, 2001, 2003 and 2005 Third edition published 2006 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, transmitted or utilized in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without permission in writing from the Publishers. SAGE Publications Ltd 1 Oliver's Yard 55 City Road London EC1Y 1SP SAGE Publications Inc. 2455 Teller Road Thousand Oaks, California 91320 SAGE Publications India Pvt Ltd B 1/I 1 Mohan Cooperative Industrial Area Mathura Road, Post Bag 7 New Delhi 110 044 SAGE Publications Asia-Pacific Pte Ltd 33 Pekin Street #02-01 Far East Square Singapore 048763 British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN-10 1 4129 2375 1 ISBN-13 978 1 4129 2375 0 ISBN-10 1 4129 2376 X ISBN-13 978 1 4129 2376 7 (Pbk) Library of Congress catalog card number 98-61738: 2005910188 Typeset by Newgen Imaging Systems (P) Ltd, Chennai, India. Printed in Contents Acknowledgements vi Preface vii List of Common Symbols viii Introduction to the Book 1 Introduction to Statistical Testing 2 Examples of Test Procedures 5 List of Tests 14 Classification of Tests 19 The Tests 21 List of Tables 185 Tables 186 References 240 Index 241 Acknowledgements The author and publishers wish to thank the following for permission to use copyright material: The American Statistical Association for Table 16 adapted from Massey. F.J. Jr (1951) ‘The Kolmogorov-Smirnov test for goodness of fit’, Journal of the American Statistical Association, 4(6). Copyright © 1951 by the American Statistical Association; the Biometrika Trustees for Table 33 from Durbin, J. and Watson, G.S. (1951) ‘Testing for serial correlation in least squares regression II’, Biometrika. 38, pp. 173–5; for Table 36 from Stephens, M.A. (1964) ‘The distribution of the goodness of fit statistic, Un2 II’, Biometrika, 51, pp. 393–7; for Table 3 from Pearson, E.S. and Hartley, H.O. (1970) Biometrika Tables for Statisticians, Vol. I, Cambridge University Press; for Table 12 from Merrington, M. and Thompson, CM. (1946) ‘Tables for testing the homogeneity of a set of estimated variances’, Biometrika, 33, pp. 296–304; and for Table 7 from Geary, R.E. and Pearson, E.S. (n.d.) ‘Tests of normality’; Harcourt Brace Jovanovich Ltd for Tables 38 and 39 from Mardia, K.V. (1972) Statistics of Directional Data, Academic Press; and Tables 35, 36 and 37 from Batschelet, E. (1981) Circular Statistics in Biology, Academic Press; the Institute of Mathematical Statistics for Table 28 from Hart, B.I. (1942) ‘Significance levels for the ratio of the mean square successive difference to the variance’, Annals of Mathematical Statistics, 13, pp. 445–7; and for Table 29 from Anderson, R.L. (1942) ‘Distribution of the serial correlation coefficient’, Annals of Mathematical Statistics, 13, pp. 1–13; Longman Group UK Ltd on behalf of the Literary Executor of the late Sir Ronald A. Fisher, FRS and Dr Frank Yates FRS for Table 2 from Statistical Tables for Biological, Agricultural and Medical Research (6th edition, 1974) Table IV; McGraw-Hill, Inc. for Tables 8, 15, 18 and 31 from Dixon, W.J. and Massey, F.J. Jr (1957) Introduction to Statistical Analysis; Macmillan Publishing Company for Table l(a) from Walpole, R.E. and Myers, R.H. (1989) Probability and Statistics for Engineers and Scientists, 4th edition, Table A.3. Copyright © 1989 by Macmillan Publishing Company; Routledge for Tables 4 and 22 from Neave, H.R. (1978) Statistical Tables, Allen & Unwin; Springer-Verlag GmbH & Co. KG for Tables 9, 10, 14, 19, 23, 26 and 32 from Sachs, L. (1972) Statistiche Auswertungsmethoden, 3rd edition; TNO Institute of Preventive Health Care, Leiden, for Tables 6, 11, 13, 25, 27 and 30 from De Jonge, H. (1963–4) Inleiding tot de Medische Statistiek, 2 vols, 3rd edition, TNO Health Research. Every effort has been made to trace all the copyright holders, but if any have been inadvertently overlooked the publishers will be pleased to make the necessary arrangement at the first opportunity. Preface Some twenty years ago, it was only necessary to know about a dozen statistical tests in order to be a practising statistician, and these were all available in the few statistical textbooks that existed at that time. In recent years the number of tests has grown tremendously and, while modern books carry the more common tests, it is often quite difficult for a practising statistician quickly to turn up a reference to some of the less used but none the less important tests which are now in the literature. Accordingly, we have attempted to collect together information on most commonly used tests which are currently available and present it, together with a guide to further reading, to make a useful reference book for both the applied statistician and the everyday user of statistics. Naturally, any such compilation must omit some tests through oversight, and the author would be very pleased to hear from any reader about tests which they feel ought to have been included. The work is divided into several sections. In the first we define a number of terms used in carrying out statistical tests, we define the thinking behind statistical testing and indicate how some of the tests can be linked together in an investigation. In the second section we give examples of test procedures and in the third we provide a list of all the 100 Statistical Tests (3rd ed.). The fourth section classifies the tests under a variety of headings. This became necessary when we tried to arrange the tests in some logical sequence. Many such logical sequences are available and, to meet the possible needs of the reader, these cross-reference lists have been provided. The main part of the work describes most commonly used tests currently available to the working statistician. No attempts at proof are given, but an elementary knowledge of statistics should be sufficient to allow the reader to carry out the test. In every case the appropriate formulae are given and where possible we have used schematic diagrams to preclude any ambiguities in notation. Where there has been a conflict of notation between existing textbooks, we have endeavoured to use the most commonly accepted symbols. The next section provides a list of the statistical tables required for the tests followed by the tables themselves, and the last section provides references for further information. Because we have brought together material which is spread over a large number of sources, we feel that this work will provide a handy reference source, not only for practising statisticians but also for teachers and students of statistics. We feel that no one can remember details of all the tests described here. We have tried to provide not only a memory jogger but also a first reference point for anyone coming across a particular test with which he or she is unfamiliar. Lucidity of style and simplicity of expression have been our twin objectives, and every effort has been made to avoid errors. Constructive criticism and suggestions will help us in improving the book. Common Symbols Each test or method may have its own terminology and symbols but the following are commonly used by all statisticians. n number of observations (sample size) K number of samples (each having n elements) α level of significance v degrees of freedom σ standard deviation (population) S standard deviation (sample) μ population mean sample mean ρ population correlation coefficient r sample correlation coefficient Z standard normal deviate

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