Beyond ANOVA: Basics of Applied Statistics (Wiley Series in Probability and Statistics)

330 Pages·1986·20.09 MB·English

by  Rupert G. Miller

BeyondA NOVA,
Basicso f Applied
Statistics
>Ü5 o*alJ
Copyright @ 1986 by John Wiley & Sons, Inc.
All rights reserved. Published simultaneously ín Canada.
Reproduction or translation of any part of this work
beyond that permitted by Section 107 or 108 ofthe
1976 United States Copyright Act without the permission
ofthe copyright owner is unlawful. Requestsf or
permission or further information should be addressedt o
the Permissions Department, John Wiley & Sons, Inc.
Library of Congress Cataloging in Pubücahon Data:
Miller, Rupert G.
Beyond ANOVA, basics of applied statistics.
Bibliography: p.
Includes indexes.
1. Mathematical statistics. I. Title. II. Title:
Beyond A.N.O.V.A., basics of applied statistics.
QA276.M473 1985 519.5 84-19511
ISBN 0-4?1-81922-0
Printed in the United States of America
1098765432r
PREFACE
These are the confessionso f a practicing statistician. They ex'
:r=c to public view what I am likely to do with a set of data- I
nr-r therefore live to regret setting pencil to paper. Yet there does
<
rr:( scrm to be a book that tells ¡ student how to attack a s€t of
:¡: r There are books on the analysis of variance, therc are books :ñ
_¿
:E f,oopüametric statistics, there are books on this and that, but 'o
¡::ü technique should I use on the data? This book attempts to go
(D
:q:nd any specifrcd iscipline and consider the variety of techniques
-(J
úr¡ can be brought to bear on a problem- The statistical problem
r3J
:hc central focus, not a particular theorctical approach.
-- .l3d<
This book is written for M.S. and Ph.D. etudents of statistics J,¡¿<r-)
¡ b b¡ve some knowledge of the analysis of variance, nonparametric <
z.'l-
x¡¡L.tics, etc., but who are still unclear ou what to do when con' C) c)
h:ted with data. It is hoped that this book will be useful as well to
().;¡
:r.:lo6ists. social scientists, and engineers who know some st¡tistics {cl
rcrCr ¡ut to handle their own data analysis. =*
cn
It willbe immediately apparcnt that this book in no way covers o
:ic complete range of statistical problems and ideas. Designs morg
{3
::;rplex than the two-way classifica¡ion (e.t., three-way classifica-
v,
;¡:os and Latin squares)a re not included, uor is multiple regression. É
l5c bope is that the rcader will grasp the basic ideas behind the tl
mpler analyses and thus understand how to cope with the more
¡¡.uplex situations. Unmentioned are problems where the basic ran- =
a
üa rariables are binary valued or categorical. Also, no attempt has
:¡¡n made to incorporate the techniques of multivariate analysis or
iue scries analysis.
Since the statistical techniques based on normal theory have
icn so central to the development ¡nd teaching of statistics, the
Í.octuFe of each chapter (or subchapter) is to fi¡st prcsent the nor'
u.rJ theory methods and then investigate what happens when the
vl Pretace
normality assumptiona nd other assumptionsb reak down. In most
chaptere,t his leadgt o sectionso D nonnonnality, unequal variances,
and dependence.
Exercisesa re included ¿t the eud of each ctrapter. Sone ¡re
theorctical, and others involve data analysis. The lstter weFeE e-
lected for their relevance¡ nd interegtf tom my fileoo f pnojectsa t the
Stanfo¡d Medical Cente¡.
RupertG . Miller,J r.
l,ondon, England
St¡nford, C¿liforni¿
f
a.
*
I
ACKNOWLEDGMENTS
l:: nriting of this book was begun during L972-73w hile I was
: :r::c:ical ieavei n London,E ngland' Peter' {rmitage at the [nu'
: : :.:-::l of Hygienea nd Tropical Medicine and David Cox at the ri
::¡-L loliege of sciencea nd Technologyg raciouslys upplied me co
¡ : :-:e spacea nd accesst o library facilities. A fellowship from E
:. , --- Simon GuggenheimM emorial Foundation provided finan' C
- L : -:::rt for the academic year. Gordon Ray and the staff of -(J:
:É - -:¡en-heinr Foundation were very supportive and generously
:--,i.:l the strpendsf or Fellowsl iving abroad when the u.s. dol- LrJ
L- ¡ Lr ier-aluedi n the middle of the year. From the Statistics and Cr-
: - : r,:...:¡ Program at the National scienceF oundationu uder the
!,J
cf Bob Agins, I receiveds upporüd uring the summer of
-r-,-:.p
,-' '',: ¡ontinuedw ork on the book. ()(
: ::e 197-lm y researchh as been supportedb y a grant fmm the ()
.*c
'u ::r- institute of GeneralM edical Sciences'T he Program Ad'
-- .: i::1::tr for this grant have been Margaret Carlson and Americo
: .-1 ,-'idoubtedly,s ome time spent on this book can be a-scribed o
'--:
-att
_-. I .176t hree chapterso f the book had been written, but they <n
¡.- : _: :n rhe shelf to gather dust at the start of 1977w hen I be- G
L¡J
r-:: r.j :_.ro f the Annalso f sú¿üisticsT. he chaptersw ere removed l
-. : : -: .helf for a one quarter sabbaticall eavei n ttre spring of l98l z,
ir-r -_ - London at Imperial college. unfortunately, by this time =,
:, L-ri¡'written chaptersw ereb adly in needo f revisiont o bring
-: :l date.
:. :':nber of skilled technic¡l typists have worked on this manu'
F-:: :'i: tbe )-ealtsJ-u di Davis,C arolyn Knutsen'G ail Lammond,
r¡: ...-i-!a Thomas all typed parts of the original first ühreec hap
l:: ieviseda nd later chaptersw eret yped by Judi Davis, Karola
l* ¿.: anC \ora Kundo. To Karola Declevefellt he ta.sko f making
vlll Acknowledgmenh
numerous changesa nd conections to produce a final manuscript.
Judi Davis did a superb job of typesetting the finished manu-
script with the T[f, typesetting system on our departmental VAX
computer. Wiley then photographed the pagest o produce this book.
Valuable comments werc received from Bill Brown, Naihua
Duan, Barbara Miller, and Lincoln Moses, who read the original
chapters. The students in Statistics 233A,B, Applied Statistics, at
Stanford University were subjected to the revised chapters as a text
during Autumn and Winter Quarters 1983-81. They found I num-
ber of misprints and suggestedv arious improvements. Particularly
notable in this regard were Jim Cutler, John Willettn and Gary
Williamson.
Barbare Miller provided encouragementa nd assistancet hrough-
out. Especially helpful was her r€scue of the refercncesw hen the Ap
ple computer file in which I was accumulating the refereneesb ecame
so large that ühe word processor started scrambling some of them.
Also, sbe was of great assistancei n helping to proofread and index
the entire book.
To all the aforementionedi ndividuals I exprcss my appreciation
and thanks. I hope that this book is worthy of their support and
efforts.
R. G. M.
CONTENTS
I ONE SAMPLE I
l.l NormalT heory I
1.2 Nonnormality 5
1.2.1 Effect 5
1.2.2 Detection l0
1.2.3 Correction l6
T[ansformations l6
NonparametricT echniques l9
RobustE stimation 28
1.3 l)ependence 32
1.3.1 Effect 34
i.3.2 Detection 35
1.3.3 Correction 36
Exercises 37
2 TWO SAMPLES 40
2.1 NormalT heory 40
2.2 Nonnormality 4l
2.2.1 Effect 4l
2.2.2 Detection 44
2.2.3 Correction 44
Tlausformationg 44
Nonpara metric Techniques 41,
Robust Estimation 54
2.3 UnequalV ariances 56
2.3.1 Effect 56
2.3.2 Detection 58
2.3.3 Correction 58
Thensformations 58
Other Testg 60
2.4 Dependence 63
x Contente
64
Exercises
67
3 ONF-WAY CLASSIFICATION
FIXEDE FFECTS 69
3.1 NormalT heorY 69
3.1.1 Analysiso f Variance( ANOVA) 69
3.1.2 Multiple CornParisons 7l
3.1.3 MonotoneA lternatives . 76
BO
3.2 NonnorrnalitY
3.2.1 Effect 80
3.2.2 Detection 82
3.?.3 Correctiou 82
'fi'r¡nsformations 82
NonparametricT echniquea 82
RobugtE stimation 89
3.3 UnequalV ariances 89
3.3.1 Eflecü 89
3.3.2 Detection : 99
3.3.3 Correction 92
9{
3.4 Depenrlence
RANDOM EFFECTS 95
3.5 NormnlT heory 95
3.5.1 Estimationo f VarianceC omponeuts 96
3.5.2 Testsf or VarianceC ontponents 99
3.5.3 Estimationo f IndividualE flects t0t
3.5.4 Estimationo f the Overall Meur r04
105
3.6 Nonnormality
3.6.1 Effect 105
3.6.2 Detection 107
3.6.3 Correction 108
3.7 UnequalV ariances 109
lt0
3.8 Dependeuce
nl
Exercises
Contente xl
4 TWO.WAY CLASSIFICATION It7
FIXEDE FFECTS ll8
4.1 NcrmaTl heory ll8
4.1.1 Analysiso f Variance( ANOVA) 119
4.1.2 Multiple Comparisons 129
4.1.3 MonotoneA lternatives l3l
4.2 Nonnormality 135
4.2.1 Effect 135
4.2.2 Detection 136
4.2.3 Correction 137
Tbansformatio¡¡s 137
NouparametricT echniques 137
RobustE stimaüion 140
4.3 UnequalV ariances 140
4.3.1 Eflect 140
4.3.2 Detection l4l
4.3.3 Correction l4l
l.tl
4.4 Dependence
MIXED NFFECTS 143
4.5 NormalT heory 143
4.6 Departures fitm AssumPtions 149
RANDOM E}'I.'ECTS 150
4.7 Nor¡nalT treory 150
4.7.1 llstim¡tion of VarianceC omponents l5l
4.7.2 Testsf or VarianceC omponents 155
4.7.3 Estimationo f Individual Effectsa nd Overall
r57
Mean
4.8 Departures fiom AssumPtions 158
Exercises 159
t0{
NEGRDSSION
REGRESSIONM ODEL 168
r68
5.1 NormalL inearM odel
5.1.f One Sample:G eneralI ntercept 168