Multivariate Analysis of Variance and Repeated Measures: A practical approach for behavioural scientists

270 Pages·1987·8.319 MB·English

by  D. J. Hand, C. C. Taylor (auth.)

Multivariate Analysis
of Variance and
Repeated Measures
A practical approach for
behavioural scientists
Multivariate Analysis
of Variance and
Repeated Measures
A practical approach for
behavioural scientists
D. J. HAND and C. C. TAYLOR
The Institute of Psychiatry
De Crespigny Park
London
London New York
CHAPMAN AND HALL
First published in 1987 by
Chapman and Hall Ltd
11 New Fetter Lane, London EC4P 4EE
Published in the USA by
Chapman and Hall
29 West 35th Street, New Yorl<, NY 10001
© 1987 D. J. Hand and C. C. Taylor
Softcover reprint of the hardcover 1s t edition 1987
Output from SPSS-X procedures is printed with permission of SPSS Inc.,
Chicago, Illinois 60611.
Output from SAS procedures is printed with permission of SAS Institute Inc.,
Cary, NC 27511-8000, Copyright© 1982.
Output from BMDP procedures is reproduced with permission of BMDP
Statistical Software, Los Angeles, California 90025.
ISBN-13: 978-94-010-7913-6 e-ISBN-13: 978-94-009-3143-5
DOl: 10.1007/978-94-009-3143-5
This title is available in both hardbound and paperback editions. The paperback edition is
sold subject to the condition that it shall not, by way of trade or otherwise, be lent, resold,
hired out, or otherwise circulated without the publisher's prior consent in any form of
binding or cover other than that in which it is published and without a similar condition
including this condition being imposed on the subsequent purchaser.
All rights reserved. No part of this book may be reprinted, or reproduced or utilized in any
form or by any electronic, mechanical or other means, now known or hereafter invented,
including photocopying and recording, or in any information storage and retrieval system,
without permiSSion in writing from the publisher.
British Library Cataloguing in Publication Data
Hand, D. J.
Multivariate analysis of variance and repeated measures.
1. Psychology-Statistical methods
2. Analysis of variance
I. Title II. Taylor, C. C.
519.5'352'0243 BF39
Library of Congress Cataloging-in-Publication Data
Hand, D.J.
Multivariate analysis of variance and repeated measures.
Bibliography: p.
Includes index.
1. Multivariate analysis. 2. Social sciences-Statistical methods.
3. Analysis of variance.
I. Taylor, C. C., 1943- . II. Title.
QA278.H345 1987 519.5'35 86-28421
To Rachel and Emily
Contents - - - - - - - -
Preface xi
PART 1 THE THEORY
1 Introduction 3
1.1 What it is about 3
1.2 Before we start 4
1.3 Further reading 7
2 Between-subjects analysis 9
2.1 Introduction 9
2.2 One-factor designs 10
2.3 Comparisons on a single factor 13
2.4 Estimating the sizes of patterns of differences 17
2.5 A special case 20
2.6 Testing single contrasts 24
2.7 Testing comparisons 27
2.8 Random effects models 29
2.9 The overall mean level 30
2.10 Multi-factor designs 30
2.11 Contrasts in multi-factor designs 33
2.12 Estimation in multi-factor designs 35
2.13 Testing in multi-factor designs 40
2.14 Nested designs 42
2.15 Some important comparisons 42
2.16 Further reading 44
3 Within-subjects analysis 45
3.1 Introduction 45
3.2 Types of question 46
3.3 Multiple univariate studies 48
3.4 Structured multivariate studies: a simple example 48
3.5 Repeated-measures structures: trend analysis 52
3.6 Repeated measures by univariate methods 56
3.7 Factorial structures 57
3.8 Controlling for other variables 62
3.9 Intrinsically multivariate studies: two groups 65
vii
Contents
3.10 intrinsically multivariate studies: several groups 68
3.11 Further reading 71
4 Multivariate tests 72
4.1 Introduction 72
4.2 Towards multivariate tests 73
4.3 Multivariate test statistics 74
4.4 Choice of test statistic 76
4.5 Exploring noncentrality structures 77
4.6 Complications: the hypothesis matrix 78
4.7 Complications: the error matrix 79
4.8 Tests on multivariate analysis of variance
assumptions 79
4.9 Tests on multivariate analysis of covariance
assumptions 80
4.10 Further reading 80
5 Sequential and simultaneous test procedures 81
5.1 Resolution of general questions 81
5.2 Error inflation 81
5.3 Some basic ideas 83
5.4 Sequential tests 84
5.5 Gabriel's method 86
5.6 McKay's method 89
5.7 More on choice of test statistic 90
5.8 Variable selection 91
5.9 Confidence intervals 92
5. to Further reading 93
PART 2 THE PRACTICE 95
Study A Alcohol relapse 97
Data contributed by Dr G. K. Litman (Addiction Research
Unit) and Dr A. N. Oppenheim (London School of
Economics)
Study B Salsolinol excretion 117
Data contributed by Dr Anne Topham
(Addiction Research Unit)
Study C Slimming clinics 126
Data contributed by Professor R. Hodgson and Professor
H. Rankin (Whitchurch Hospital, Cardiff)
viii
Contents
Study 0 Neuropeptides and psychiatric illness 151
Data contributed by Dr J. Coid (Maudsley Hospital),
Dr B. Allolio and Professor L. Rees (St Bartholomew's
Hospital)
Study E Headache 157
Data contributed by C. Philips and M. Jahanshahi
(Institute of Psychiatry)
Study F Smoking styles 167
Data contributed by Dr S. R. Sutton (Addiction
Research Unit)
Study G Alzheimer's disease 182
Data contributed by Professor R. Levy, A. Little and
Dr Paz Chuaqui (Institute of Psychiatry)
Study H Psychophysiological responses 191
Data contributed by Dr John Brown (Institute of
Psychiatry)
ReferenCes 208
Appendix Computer listings 211
Listing 1-SAS System 213
A three group between subjects design (comprising
one factor) with three variables in the within subjects
design (unstructured).
Listing2-BMDP 221
A three group between subjects design (comprising
one factor) with three variables in the within subjects
design (unstructured).
Listing 3 - BMDP 227
A three group between subjects design (comprising
one factor) with a three variable within subjects design
(comprising one factor).
Listing 4 - SPSSX 235
A three group between subjects design (comprising
one factor) with three variables in the within subjects
design (unstructured).
ix
Contents
Listing 5 - SPSSX 247
A three group between subjects design (comprising
one factor) with a three variable within subjects design
(comprising one factor).
Index 253
x
Preface--------
Although there are many excellent books on multivariate statistics available,
none of them is aimed at the mathematically naive. This is not surprising since
statistics is an inherently mathematical subject. To obtain a really effective grasp
of statistics, and multivariate statistics in particular, one requires a good under
standing of the mathematical languages needed to manipulate multidimensional
concepts. A facility with matrix algebra, especially, is needed.
This poses a serious problem for the researcher. He or she may be an expert
perhaps even an internationally renowned expert - in some other domain of
science but may not have the mathematical background to be able to acquire or
understand the mathematics quickly and easily. From the point of view of such
an expert the statistical concepts may be an extra burden to be learned - a burden
because they are not his or her primary interest. And yet the concepts must be
learnt if the researcher is to be able to formulate the multivariate questions or, at
least, to be able to communicate in mutually intelligible terms with a statistician.
Worse is to come. Multivariate statistics is not practicable by hand. Its
increasingly widespread use is very much a development of the computer age.
Computers are essential for its use. This means that the researcher, having
formulated a research question in the language of his or her own science, having
learnt and reformulated it in the language of multivariate statistics, now has to
learn to use one of the computer packages for tackling such analyses - not to
mention the job control language needed to get the computer to accept the
program.
The process has become a sequence of stages, each leading one step further
from the researcher's primary interest, each requiring an investment of time and
intellectual energy which the researcher may be unwilling to make.
This book aims to ease the difficulty at least for one particular multivariate
technique, the use of which is growing dramatically. We mean, of course,
multivariate analysis of variance.
When planning this book we had two distinct and to a certain extent conflicting
aims in mind. The first was that we wanted to present a connected non
mathematical account of the concepts of multivariate analysis of variance which
would be readily comprehensible to researchers in the behavioural sciences.
The second was that we wanted to show such researchers how actually to do a
multivariate analysis of variance. These aims conflict in that embedding
numerical examples in the text can be disruptive to the flow of development of
ideas and can sometimes be offputting to the sort of readers we had in mind. We
xi