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Statistical Methods in Agriculture and Experimental Biology PDF

421 Pages·1993·9.57 MB·English
by  R. Mead
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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 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the UK Copyright Designs and Patents Act, 1988, this publication may not be reproduced, stored, or transmitted, in any form or by any means, without the prior permission in writing of the publishers, or in the case of reprographic reproduction only in accordance with the terms of the licences issued by the Copyright Licensing Agency in the UK, or in accordance with the terms of licences issued by the appropriate Reproduction Rights Organization outside the UK. Enquiries concerning reproduction outside the terms stated here should be sent to the publishers at the London address printed on this page. The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made. A catalogue record for this book is available from the British Library 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

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