Table Of ContentData Driven Statistical Methods
CHAPMAN & HALL TEXTS IN STATISTICAL SCIENCE SERIES
Editors:
Dr Chris Chatfield Professor Jim V. Zidek
Reader in Statistics Department of Statistics
School of Mathematical Sciences University of British Columbia
University of Bath, UK Canada
The Analysis of Time Series - An Modelling Binary Data
introduction Fifth edition D. Collett
C. Chatfield Modelling Survival Data in Medical
Applied Bayesian Forecasting and Time Research
Series Analysis D. Collett
A. Pole, M. West and J. Harrison Multivariate Analysis of Variance and
Applied Non-parametric Statistical Repeated Measures
Methods Second edition D. J. Hand and C. C. Taylor
P. Sprent Multivariate Statistics - A practical
Applied Statistics - A handbook of approach
BMDP analyses B. Flury and H. Riedwyl
E. J. Snell Practical Longitudinal Data Analysis
Applied Statistics - Principles and D.J. Hand and M. Crowder
Examples Practical Statistics for Medical Research
D. R. Cox and E.J. Snell D. G. Altman
Bayesian Data Analysis Probability - Methods and measurement
A. Gelman, J. Carlin, H. Stern and D. A. O'Hagan
Rubin Problem Solving - A statistician's guide
Decision Analysis - A Bayesian approach Second edition
J.Q. Smith C. Chatfield
Elementary Applications of Probability Randomization , Bootstrap and Monte
Theory Second edition Carlo Methods in Biology
H.C. Tuckwell Second edition
Elements of Simulation B. F. J. Manly
B. J.T. Morgan Readings in Decision Analysis
Essential Statistics S. French
Third edition Statistical Analysis of Reliability Data
D.G. Rees M. J. Crowder, A. C. Kimber, T. J.
Interpreting Data Sweeting and R. L. Smith
A. J. B. Anderson Statistical Methods for SPC and TQM
An Introduction to Generalized Linear D. Bissell
Models Second edition Statistical Methods in Agriculture and
A. J. Dobson Experimental Biology Second edition
Introduction to Multivariate Analysis R. Mead, R. N. Curnow and A. M. Hasted
C. Chatfield and A. J. Collins Statistical Process control - Theory and
Introduction to Optimization Methods practice Third edition
and their Applications in Statistics G. B. Wetherill and D. W. Brown
B. S. Everitt Statistical Theory Fourth edition
Large Sample Methods in Statistics B.W. Lindgren
P.K. Sen and J. da Motta Singer Statistics for Accountants
Markov Chain Monte Carlo - Stochastic S. Letchford
simulation for Bayesian inference Statistics in Engineering - A practical
D. Gamerman approach
Modeling and Analysis of Stochastic AV. Metcalfe
Systems The Theory of Linear Models
V. Kulkarni B. Jorgensen
Full information on the complete range of Chapman & Hall statistics books is available from the
publisher.
Data Driven Statistical Methods
P. Sprent
Emeritus Professor of Statistics
University of Dundee
Scotland
Boca Raton London New York
CRC Press is an imprint of the
Taylor & Francis Group, an informa business
A CHAPMAN & HALL BOOK
First edition 1998
Published 1998 by Chapman & Hall/CRC Press
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© 1998 by Taylor & Francis Group, LLC
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ISBN 13: 978-0-412-79540-4 (hbk)
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Contents
Preface ix
i Data-driven inference 1
i.i Data-driven or model-driven 1
1.2 Some data-driven methods 4
1.3 The approach 6
1.4 Different kinds and sources of data 7
1.5 Randomization and permutation tests 9
1.6 A basic permutation test 10
1.7 More about tests 15
1.8 Confidence intervals 21
1.9 Asymptotic results 25
1.10 Computer software 26
Exercises 28
2 The bootstrap 29
2.1 Basic concepts 29
2.2 The bootstrap concept 32
2.3 The bootstrap sampling distribution 34
2.4 Using bootstrap samples 37
2.5 Bias and the jackknife 42
2.6 Bootstrap confidence intervals 45
2.7 The two-sample bootstrap 50
2.8 Bootstraps in a broader context 54
2.9 Cross-validation 55
Exercises 56
3 Outliers contamination and robustness 57
3.1 Models and data 57
3.2 Outliers and contamination 57
3.3 Diagnostic tests for outliers 61
3.4 Accommodating outliers 64
3.5 Some robust estimators 68
Exercises 76
vi Contents
4 Location tests for two independent samples 77
4.1 The Fisher-Pitman test robustness and ranks 77
4.2 Ranks 81
4.3 Validity of inferences 84
4.4 An alternative form of the rank sum test 85
4.5 Transformation of ranks 92
4.6 Using minimum data - the median test 93
4.7 Analysis of survival data 101
4.8 Modified WMW tests 103
4.9 Improved tests for survival data 109
Exercises 116
5 Location tests for single and paired samples 119
5.1 The single sample location problem 119
5.2 The single sample permutation test 119
5.3 The signed-rank test 124
5.4 Transformation of ranks 129
5.5 Location tests for asymmetric distributions 130
5.6 Paired sample data 13 2
5.7 Observational data 137
Exercises 139
6 More one- and two-sample tests 141
6.1 Some further considerations 141
6.2 Generalizations of the sign test 142
6.3 McNemar’s test 144
6.4 A sign test for trend 145
6.5 Tests for dispersion 147
6.6 Gastwirth scores 153
6.7 Goodness of fit tests 156
6.8 Comparing two distributions 167
6.9 Run tests 171
6.10 A case study 175
Exercises 178
7 Three or more independent samples 180
7.1 Some extensions and some differences 180
7.2 Permutation analysis for ¿-samples or treatments 181
7.3 Rank related location tests 185
7.4 The median test 187
Contents vii
7.5 Permutation tests for ordered location shifts 188
7.6 Factorial treatment structures 193
7.7 Stratified samples 203
7.8 Tests for specific effects 205
7.9 Differences in dispersion and other characteristics 207
Exercises 207
8 Designed experiments 210
8.1 Randomized block experiments 210
8.2 Tests based on ranks 213
8.3 Specified comparisons 217
8.4 Binary responses 219
8.5 Using individuals as blocks 220
Exercises 222
9 Correlation and concordance 225
9.1 Measures of bivariate association 225
9.2 Two important rank correlation coefficients 231
9.3 Some asymptotic results 240
9.4 Some other measures of correlation 241
9.5 The bootstrap and correlation 243
9.6 Partial correlation 250
9.7 Concordance 254
Exercises 257
10 Bivariate regression 260
10.1 Bivariate straight line regression 260
10.2 Permutation test least squares 262
10.3 Regression associated with Spearman’s rho 266
10.4 Regression associated with Kendall’s tau 269
10.5 Some alternative approaches 271
10.6 Joint estimation of slope and intercept 276
10.7 Some general considerations 281
10.8 The bootstrap in regression 283
Exercises 288
11 Other regression models and diagnostics 290
11.1 Multiple regression and the general linear model 290
11.2 Permutation tests in multiple regression 291
11.3 Regression diagnostics 298
vüi Contents
11.4 A/-estimators in regression 310
11.5 Penalty functions in regression 312
11.6 A case study 317
Exercises 323
12 Categorical data analysis 326
12.1 Types of categorical data 326
12.2 Inferences in 2x2 tables 335
12.3 Association in r*c tables 341
12.4 Linear-by-linear association 346
12.5 Stratified 2x2 tables 349
12.6 Multiway tables 359
Exercises 361
13 Further categorical data analysis 363
13.1 Partitioning of chi-squared statistics 363
13.2 A new look at location and dispersion 365
13.3 More thought for food 368
13.4 Matched pair data and repeated responses 371
13.5 Trends in contingency tables 374
13.6 Statistics and the law 375
Exercises 379
14 Data-driven or model-driven? 381
14.1 A merging of approaches 381
14.2 Logistic regression 385
14.3 Estimation of logistic regression parameters 386
14.4 Generalized linear models 389
Exercises 391
References 392
Index 402
Preface
This book is designed both as a textbook to highlight practical aspects of data
analysis and statistical inference for students with a preliminary grounding in the
subject and also as a reference manual for research workers, scientists, engineers,
industrialists, technologists or managers in any field who have a basic knowledge
of statistics such as that imparted in a service or introductory course, but who
want to know more about possible ways to handle data analytic problems they
meet in their work. I deal with methods stimulated by the data rather than those
based upon abstract models.
Statistical methods are developing rapidly so a book at this level can only cover
selected applications. I try to capture the spirit of the subject by considering a
range of techniques in a way that brings together modem developments,
especially those made possible by computing power now at our fingertips, but
undreamt of 50 or even 20 years ago.
Many undergraduate courses now include computationally feasible methods
such as permutation based inference, bootstrapping and diagnostic tests for
outliers and influential observations and also introduce powerful tools like
generalized linear models. Specialist textbooks on any one of these and other
modern developments, admirable as many are, often do not, at least at the
elementary level, draw attention to relationships between topics. One result is
that many tools are not exploited to maximum advantage.
In this elementary treatment I emphasize breadth rather than depth. This lets
me illustrate many relationships between topics and techniques. Despite giving
priority to breadth, I could not in 400 pages include even brief accounts of many
important methods and applications, but I hope the diversity in my approach will
encourage instructors to use the book as a class text that can be supplemented
with material from their own fields of interest or from areas particularly relevant
to their students. Many teachers will want to develop some topics in more detail,
and may regard others as worth less coverage than I have given them. I make no
apology for this, for one of my aims is to encourage further exploration. I urge
students, research workers, industrialists and others with statistical problems to
look beyond this book when they need more information. I give numerous
enthusiastic references to specialist books on the main topics (highlighting these
by asterisks in the list of references). Because my treatment is elementary a
reader wanting to use the methods I describe in any but simple applications
should consult a relevant specialist text.
