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100 Statistical Tests (3rd ed.), Third Edition
Gopal K. Kanji
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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.
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British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British
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:
Typeset by Newgen Imaging Systems (P) Ltd, Chennai, India.
List of Common Symbols
Introduction to the Book
Introduction to Statistical Testing
Examples of Test Procedures
List of Tests
Classification of Tests
List of Tables
The author and publishers wish to thank the following for permission to use
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.
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.
Each test or method may have its own terminology and symbols but the
following are commonly used by all statisticians.
number of observations (sample size)
number of samples (each having n
level of significance
degrees of freedom
standard deviation (population)
standard deviation (sample)
population correlation coefficient
sample correlation coefficient
standard normal deviate