Statistical Methods in Agriculture and Experimental Biology

346 Pages·1983·8.75 MB·English

by  R. Mead

Statistical Methods
in Agriculture
and Experimental
Biology
Statistical Methods
in Agriculture
and Experimental
Biology
R. Mead and
R. N. Curnow
Department0/AppliedStatistics,
University0/Reading
Springer-Science+Business Media, B.Y.
©1983R. MeadandR. N.Cumow
OriginallypublishedbySpringerScience+BusinessMediaDordrechtin1983.
ISBN978-0-412-24240-3 ISBN978-1-4899-2951-8(eBook)
DOI10.1007/978-1-4899-2951-8
Tbis title is available in both hardbound and paperback editions. The paperback
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BritishLibraryCataloguinginPub6cationData
Mead,R.
Statisticalmethodsinagricultureandexperimentalbiology.
1. Agriculture-Statisticalmethods
I. Title 11. Curnow,R.N.
630'.28 S531
Library01CongressCataloginginPub6cationData
Mead,R. (Roger)
Statistical methodsinagricultureandexperimentalbiology.
Bibliography:p.
Includesindex.
1. Agricultural research-Statistical methods. 2. Agriculture-Statistical
methods.3.Biology,Experimental-Statisticalmethods.I.Curnow,R.N.11.Title.
S540.S7M4 1983 630'.72 82-14717
Contents
Preface pageix
Chapter 1 Introduction 1
Chapter2 Probabilityanddistributions 5
2.1 Populations,samples and probability 5
2.2 Meansand variances 10
2.3 Thenormaldistribution 12
2.4 Samplingdistributions 15
Chapter3 Estimationandhypothesistesting 20
3.1 Estimationofthe populationmean 20
3.2 Testinghypothesesaboutthe populationmean 21
3.3 Populationvariance unknown 25
3.4 Comparisonofsampies 27
3.5 A pooledestimateofvariance 29
Chapter4 Asimpleexperiment 33
4.1 Randomizationand replication 33
4.2 Analysis ofacompletelyrandomizeddesignwithtwo
treatments 35
4.3 Acompletelyrandomizeddesignwithseveral treatments 38
4.4 Testingoverall variationbetweenthe treatments 41
Chapter5 Controloftherandomvariation 47
5.1 Local controlofvariation 47
5.2 Analysis ofarandomizedblockdesign 49
5.3 Meaningofthe errormean square 55
5.4 Missingobservationsinarandomizedblockdesign 58
5.5 Latinsquaredesigns 61
5.6 MultipleLatinsquaresdesigns 65
5.7 Replicationoftreatmentswithinblocks 68
v
vi StatisticalMethodsinAgricultureandExperimentalBiology
Chapter6 Particularquestionsabout treatments 71
6.1 Treatmentstructure 71
6.2 Factorialtreatmentstructure 79
6.3 Maineffectsandinteractions 81
6.4 Analysisofvarianceforatwo-factorexperiment 84
6.5 More than twofactors 89
zn
6.6 experiments 90
6.7 Splitplot experiments 96
6.8 Analysisofasplitplotexperiment 98
Chapter7 Theassumptionsbehindtheanalysis 104
7.1 Ourassumptions 104
7.2 Normality . 105
7.3 Homogeneity 109
7.4 Additivity 112
7.5 Transformationsofdata fortheoreticalreasons 113
7.6 Empiricaldetectionofthefailure ofassumptions and selection
ofappropriatetransformations 118
7.7 Practice and presentation 123
Chapter8 Studyinglinearrelationships 125
8.1 Linearregression 125
8.2 Assessingthe regressionline 129
8.3 Inferencesabouttheslopeofaline 130
8.4 Predictionusingaregressionline 131
8.5 Correlation 138
8.6 Testing whetherthe regressionislinear 140
8.7 Regression inthe analysisofexperiments 141
8.8 Covarianceanalysis 145
Chapter9 Morecomplexrelationships 154
9.1 Makingthecrookedstraight 154
9.2 Comparisonofregressions 157
9.3 Fitting parallellines 163
9.4 Twoindependentvariables 169
9.5 Testing the relationship 175
9.6 Multiple regression 183
Chapter10 Non-linearmodels 190
10.1 Advantagesoflinear andnon-linear models 190
10.2 Fitting non-linearmodelstodata 195
10.3 Inferencesaboutnon-linear parameters 200
iO.4 Exponentialmodels 204
10.5 Inverse polynomialmodels 209
10.6 Logisticmodelsforgrowthcurves 215
Contents vii
Chapter11 Theanalysisofproportions 218
11.1 Datainthe formoffrequencies 218
11.2 The2x2contingencytable 219
11.3 Morethan twosituationsormorethan twooutcomes 221
11.4 Generalcontingencytables 225
11.5 Estimationofproportions 230
11.6 Sampiesizesforestimatingproportions 234
Chapter12 Modelsand distributionsforfrequency data 239
12.1 Theuseofmodels 239
12.2 Testingthe agreementoffrequency datawithsimplemodels 240
12.3 Investigatingmore complexmodels 243
12.4 Thebinornial distribution 250
12.5 The Poisson distribution 256
12.6 Log-linearmodels 262
12.7 Probitanalysis 267
Chapter13 Samplingfinitepopulations 274
13.1 Samplingfromfinitepopulations 274
13.2 Simple randomsampling 275
13.3 Stratifiedrandomsampling 277
13.4 Cluster sampling, multistage sampling and sampling propor-
tional tosize 280
13.5 Ratioand regression estimates 281
Chapter14 Choosingagoodexperimentaldesign 284
14.1 Design components,unitsand treatments 284
14.2 Replicationand precision 285
14.3 Differentlevelsofvariation and within-unitreplication 288
14.4 Blocking and the useofnaturalblocks 293
14.5 Randomization 298
14.6 Treatmentstructureand the benefitsoffactorial structure 300
14.7 Many factors inblocked experiments 301
14.8 Factorswithquantitativelevels 304
14.9 Screeningand selection 306
14.10 Practicalproblemsofexperimentation 307
Chapter15 Computersand thestatisticalanalysisofdata 310
15.1 Theimpactofcomputersonstatistics 310
15.2 Storageand processing ofdataoncomputers 311
15.3 Computeranalysisofresultsofdesigned experiments 313
15.4 Multipleregressionanalysisbycomputer 318
15.5 Advantagesanddangersintheincreasinguseofcomputersfor
statisticalanalysis 324
viii StatisticalMethodsinAgricultureandExperimentalBiology
Referencesforfurtherreading 327
Appendix 328
Table A.1 The standardizednormaldistribution 328
Table A.2 The Student'stdistribution 329
Table A.3 The F-distribution: 5%points 329
Table A.4 The F-distribution: 1%points 330
Table A.5 TheF-distribution: 0.1%points 330
Table A.6 The chi-squaredistribution 331
Table A.7 Random numbers 332
Index 333
Preface
Ouraim inthis bookhasbeen to describe and explain those statisticalideas
which we believe are an essential part of the intellectual equipment of a
scientistworking inagriculture oron the experimentalsideofbiology.Much
of the material in the book has grown out of our experience as advisory
statisticiansand from teaching introductorystatisticscoursesfor agricultural
students,bothundergraduatesandpostgraduates.The examples inthe early
chaptersare takenmainlyfromagricultural experimentsinvolvingfieldcrops
orfarm animals but laterexamplesare concemedpredominantlywith labor
atoryexperimentsandwithbiologicalinvestigations.
While writing the book wehave gradually expanded the scope to include
topics not usually covered in an introductory textbook on statistics. This
expansion derives partly from taking ideas to theirlogicalconclusion, partly
from the incitementofoneofthebook'sassessors,andpartlyinrecognitionof
the fact that statistical packages have now made more advanced statistical
methodsmuchmoreavailablethan theywereafewyearsago.Thisexpansion
ofthe bookwillbedetectedbythe readerinthe waythat simpleideas which
canbediscussedintermsofexamplesrequiringonlyasmallpocketcalculator
give way to ideas which can only be implemented with more sophisticated
computationalaids.Somestudentsintheirfirstreadingofthe book mayweIl
omit some of the more advanced chapters or sections; however, we have
decidedagainst anyformallabellingofsectionsasadvanced.
Experimentalscientistsshould haveaclearunderstandingofthe principles
of statistics goveming the planning of experiments and the analysis and
interpretationofexperimentaldata.Therefore,whilecovering the details of
methods through worked examples, our main aim has been to help our
readersunderstandwhyandwhenthevariousmethodsshouldbeused,ornot
used! We emphasize the importanceofthinking carefully aboutthe purpose
of each experiment; of using the available experimental resources as effi
ciently as possible; and then of extracting allthe relevant information from
the data.Wealsostresstheimportanceofcheckinganyassumptionsthatneed
tobe madeaboutthe data before itcanbeanalysed.
Themathematicalknowledge requiredhasbeen deliberatelykeptat alow
level even at the cost of omitting mathematical details whichwould be weIl
ix
x StatisticalMethodsinAgricultureandExperimentalBiology
within the understanding of some undergraduates in biological subjects.
Omission of mathematical details sometimes leads to more lengthy verbal
justificationofthe statistical ideas,but ifthisencourages the readerto think
moredeeply aboutthestatisticalphilosophythiswillbeapositivebenefit.
In mostchapterswepresentworked numerical examplesand exercisesfor
the reader. Although most data are nowanalysedbycomputers,webelieve
thatonlybyworkingthrough atleastoneexampleofeachtypeofanalysisisit
possible to understand fully what is being assumed and how the analysis
providesestimatesoftheaccuracyoftheresultsoftheexperiment.Wewould
expectthatwhere the bookisusedasatextbook foranintroductorycoursein
statistics the lecturer concernedwould relate the philosophy of the book to
the localcomputingfacilities.
Turning to the contents in more detail, the firstsixchapters present the
basic statistical ideas of estimation and hypothesis testing, and givea fairly
conventional development of experimental design ideas and the associated
methods of analysing experimental data. In Chapter 7 we examine the
assumptions of the analytic techniques of the previous chapters and discuss
methods of detecting and dealing with the failures of these assumptions.
Chapters8,9and 10are concerned withrelationships betweentwoor more
variables, starting with simple linear regression, progressing to multiple
regression and concludingwithadiscussionofthe useofnon-linearmodels.
ThelastsectionofChapter9andthewholeofChapter10includesomeofthe
more advancedmaterial.Chapters11and12discusstheanalysisandinterpre
tation of frequency data for discrete variables. The last two sections of
Chapter 12 are on the advanced topics of log-linear models and probit
analysis.Ashortchapteron sampling,arathermore extensive reviewofthe
ideas of experimental design, with some advanced material, and a short
chapteron computers and their impact onusersofstatistical methods, com
pletethe book.
Our examples of data from experiments are drawn from a wide range of
agricultural and biological research and have been garnered over a long
periodoftime.Wehavebeen unabletotracesomeofthesourcesthroughthe
mists of time. We are very grateful to our various colleagues, past and
present, at the Universities ofReading andAberdeen, atthe ARCNational
Vegetable Research Station at Wellesbourne and elsewhere for the use of
theirdata.Wehope that whenthesecolleaguesrecognizetheir data theywill
approve of the way they have been used and accept our apologies for not
acknowledging the useoftheirdata. We have, inallcases, used the units in
which the data were originallymeasured.Thismaybe attributed to laziness
but wepreferto believe that usingthe data astheywere recordedminimizes
possibilitiesofmisinterpretation.To transform alldata intoasinglesystemof
units isa cosmetic operation imposingan unnatural homogeneity upon the
reality.
We have listed only a fewreferences.These are mainlycited in the later
chapters and are intended to provide suggestions for further reading on