Statistical Methods in Agriculture and Experimental Biology

421 Pages·1993·9.57 MB·English

by  R. Mead

Statistical Methods in
Agriculture and
Experimental Biology
OTHER STATISTICS TEXTS FROM CHAPMAN & HALL
Practical Statistics for Medical Probability Methods and Measurement
Research Anthony O'Hagan
Douglas Altman Essential Statistics
The Analysis of Time Series - An D. G. Rees
Introduction Foundations of Statistics
C. Chatfield D. G. Ress
Problem Solving: A Statistician's Guide Decision Analysis: A Bayesian Approach
C. Chatfield J. Q. Smith
Statistics for Technology Applied Statistics: A Handbook ofBMDP
C. Chatfield Analyses
Indroduction to Multivariate Analysis E. J. Snell
C. Chatfield and A. J. Collins Applied Statistics: A Handbook of
Applied Statistics: Principles and GENSTA T Analyses
Examples E. J. Snell and H. R. Simpson
D. R. Cox and E. J. Snell Elementary Applications of Probability
An Introduction to Statistical Modelling Theory
A. J. Dobson H. C. Tuckwell
Introduction to Optimization Methods Intermediate Statistical Methods
and their Applications in Statistics G. B. Wetherill
B. S. Everitt Statistical Process Control: Theory and
Multivariate Statistics - A Practical practice
Approach G. B. Wetherill and D. W. Brown
B. Flury and H. Riedwyl Statistics in Research and Development
Readings in Decision Analysis Second edition
S. French R. Caulcutt
Multivariate Analysis of Variance and Modelling Binary Data
Repeated Measures D. Collett
D. J. Hand and C. C. Taylor Statistical Analysis of Reliability Data
Multivariate Statistical Methods - a M. J. Crowder, A. C. Kimber, T. J.
primer Sweeting and R. L. Smith
Bryan F. Manly
Elements of Simulation
B. J. T. Morgan
Further i'lformation of the complete range of Chapman and Hall statistics books is
available from the publishers.
Statistical Methods in
Agriculture and
Experimental Biology
SECOND EDITION
R. Mead
Professor, Department of Applied Statistics
University of Reading, UK
R.N. Curnow
Professor, Department of Applied Statistics
University of Reading, UK
and
A.M. Hasted
Q I Statistics Ruscombe
Reading, UK
u!l l
I
SPRINGER-SCIENCE' BUSINESS MEDIA. B.V
First edition 1983
Reprinted 1986
Second edition 1993
© 1993 Springer Science+Business Media Dordrecht
Originally published by Chapman & Hall in 1993
Typeset in I0/12pt Times by Thomson Press (India) Ltd, New Delhi
ISBN 978-0-412-35480-9 ISBN 978-1-4899-6928-6 (eBook)
DOI 10.1007/978-1-4899-6928-6
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or review, as permitted under the UK Copyright Designs and Patents Act, 1988, this
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accuracy of the information contained in this book and cannot accept any legal
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Library of Congress Cataloging-in-Publication data available
oo Printed on permanent acid-free text paper, manufactured in accordance with the
proposed ANSI(NISO Z 39.48-199X and ANSI Z 39.48-1984
Contents
Preface ix
1 Introduction 1
1.1 The need for statistics 1
1.2 The use of computers in statistics 5
2 Probability and distributions 9
2.1 Probability 9
2.2 Populations and samples 12
2.3 Means and variances 15
2.4 The Normal distribution 18
2.5 Sampling distributions 21
3 Estimation and hypothesis testing 27
3.1 Estimation of the population mean 27
3.2 Testing hypotheses about the population mean 28
3.3 Population variance unknown 32
3.4 Comparison of samples 35
3.5 A pooled estimate of variance 37
4 A simple experiment 41
4.1 Randomization and replication 41
4.2 Analysis of a completely randomized design with two treatments 43
4.3 A completely randomized design with several treatments 46
4.4 Testing overall variation between the treatments 49
4.5 Analysis using a statistical package 55
5 Control of random variation by blocking 59
5.1 Local control of variation 59
5.2 Analysis of a randomized block design 61
5.3 Meaning of the error mean square 66
5.4 Latin square designs 70
5.5 Analysis of structured experimental data using a computer package 74
5.6 Multiple Latin squares designs 76
5.7 The benefit of blocking and the use of natural blocks 79
vi Contents
6 Particular questions about treatments 89
6.1 Treatment structure 89
6.2 Treatment contrasts 94
6.3 Factorial treatment structure 97
6.4 Main effects and interactions 99
6.5 Analysis of variance for a two-factor experiment 102
6.6 Computer analysis of factorials 109
7 More on factorial treatment structure 111
7.1 More than two factors 111
7.2 Factors with two levels 112
7.3 The double benefit of factorial structure 118
7.4 Many factors and small blocks 120
7.5 The analysis of confounded experiments 125
7.6 Split plot experiments 128
7.7 Analysis of a split plot experiment 130
8 The assumptions behind the analysis 137
8.1 Our assumptions 137
8.2 Normality 138
8.3 Variance homogeneity 142
8.4 Additivity 145
8.5 Transformations of data for theoretical reasons 147
8.6 A more general form of analysis 151
8.7 Empirical detection of the failure of assumptions
and selection of appropriate transformations 152
8.8 Practice and presentation 158
9 Studying linear relationships 161
9.1 Linear regression 161
9.2 Assessing the regression line 165
9.3 Inferences about the slope of a line 167
9.4 Prediction using a regression line 168
9.5 Correlation 175
9.6 Testing whether the regression is linear 177
9.7 Regression analysis using computer packages 178
10 More complex relationships 183
10.1 Making the crooked straight 183
10.2 Two independent variables 186
10.3 Testing the components of a multiple relationship 193
10.4 Multiple regression 204
10.5 Possible problems in computer multiple regression 211
Contents Vll
11 Linear models 213
11.1 The use of models 213
11.2 Models for factors and variables 214
11.3 Comparison of regressions 220
11.4 Fitting parallel lines 227
11.5 Covariance analysis 233
11.6 Regression in the analysis of treatment variation 240
12 Non-linear models 247
12.1 Advantages of linear and non-linear models 247
12.2 Fitting non-linear models to data 252
12.3 Inferences about non-linear parameters 258
12.4 Exponential models 262
12.5 Inverse polynomial models 267
12.6 Logistic models for growth curves 274
13 The analysis of proportions 277
13.1 Data in the form of frequencies 277
13.2 The 2 x 2 contingency table 278
13.3 More than two situations or more than two outcomes 280
13.4 General contingency tables 284
13.5 Estimation of proportions 289
13.6 Sample sizes for estimating proportions 294
14 Models and distributions for frequency data 299
14.1 Models for frequency data 299
14.2 Testing the agreement of frequency data with simple models 300
14.3 Investigating more complex models 302
14.4 The binomial distribution 309
14.5 The Poisson distribution 316
14.6 Generalized models for analysing experimental data 323
14.7 Log-linear models 329
14.8 Probit analysis 336
15 Making and analysing many experimental measurements 341
15.1 Different measurements on the same units 341
15.2 Interdependence of different variables 342
15.3 Repeated measurements 346
15.4 Joint (bivariate) analysis 356
15.5 Investigating relationships with experimental data 367
16 Choosing the most appropriate experimental design 373
16.1 The components of design; units and treatments 373
viii Contents
16.2 Replication and precision 374
16.3 Different levels of variation and within-unit replication 377
16.4 Variance components and split plot designs 381
16.5 Randomization 384
16.6 Managing with limited resources 386
16.7 Factors with quantitative levels 387
16.8 Screening and selection 389
17 Sampling finite populations 393
17.1 Experiments and sample surveys 393
17.2 Simple random sampling 394
17.3 Stratified random sampling 397
17.4 Cluster sampling, multistage sampling and
sampling proportional to size 399
17.5 Ratio and regression estimates 400
References 403
Appendix 405
Index 413
Preface
Our aim in this edition, as in the first edition of the book, has been to describe
and explain those statistical ideas which we believe are an essential part of the
intellectual equipment of a scientist working in agriculture or on the experi
mental side of biology. Much of the material in the book has grown out of our
experience as advisory statisticians and from teaching introductory statistics
courses for agricultural students, both undergraduates and postgraduates. The
examples in the early chapters are taken mainly from agricultural experiments
involving field crops or farm animals but later examples are concerned pre
dominantly with laboratory experiments and with biological investigations.
In this second edition we have expanded the scope to include some additional
topics not usually covered in introductory courses or textbooks on statistics.
It is particularly important that, even in an introductory statistics course,
students should develop an appreciation of the breadth of statistical methodo
logy now available. The development of computing facilities, and particularly
of statistical packages, means that there is a very large library of statistical
methods available to any scientist with access to any substantial computing
facilities. Therefore, although some of the topics in this book would not feature
in most introductory courses, we hope that there is a sufficient discussion of
more advanced topics for the student/scientist to have some understanding of
what would be involved in using some of the available advanced methods. Some
students in their first reading of the book may well omit some of the more
advanced chapters or sections.
Experimental scientists should have a clear understanding of the principles
of statistics governing the planning of experiments and the analysis and inter
pretation of experimental data. Therefore, while covering the details of methods
through worked examples, our main aim has been to help our readers understand
why and when the various methods should be used, or not used! We emphasize
the importance of thinking carefully about the purpose of each experiment; of
using the available experimental resources as efficiently as possible; and then
of extracting all the relevant information from the data. We also stress the
importance of checking any assumptions that need to be made about the data
before it can be analysed.
The mathematical knowledge required has been deliberately kept at a low
level even at the cost of omitting mathematical details which would be well