Statistics for Terrified Biologists

361 Pages·2008·1.7 MB·English

by  Helmut van Emden

Statistics for Terrified Biologists
VanEmden: “C000” — 2008/1/31 — 16:18 — PAGE i — #1
VanEmden: “C000” — 2008/1/31 — 16:18 — PAGE ii — #2
Statistics for Terrified
Biologists
HelmutF.vanEmden
EmeritusProfessorof Horticulture
Schoolof BiologicalSciences
Universityof Reading,UK
VanEmden: “C000” — 2008/1/31 — 16:18 — PAGE iii — #3
©HelmutF.vanEmden2008
BLACKWELLPUBLISHING
350MainStreet,Malden,MA02148-5020,USA
9600GarsingtonRoad,OxfordOX42DQ,UK
550SwanstonStreet,Carlton,Victoria3053,Australia
TherightofHelmutF.vanEmdentobeidentifiedastheauthoroftheeditorialmaterialinthis
workhasbeenassertedinaccordancewiththeUKCopyright,Designs,andPatentsAct1988.
Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,or
transmitted,inanyformorbyanymeans,electronic,mechanical,photocopying,recordingor
otherwise,exceptaspermittedbytheUKCopyright,Designs,andPatentsAct1988,withoutthe
priorpermissionofthepublisher.
Designationsusedbycompaniestodistinguishtheirproductsareoftenclaimedastrademarks.All
brandnamesandproductnamesusedinthisbookaretradenames,servicemarks,trademarks,
orregisteredtrademarksoftheirrespectiveowners.Thepublisherisnotassociatedwithany
productorvendormentionedinthisbook.
Thispublicationisdesignedtoprovideaccurateandauthoritativeinformationinregardtothe
subjectmattercovered.Itissoldontheunderstandingthatthepublisherisnotengagedin
renderingprofessionalservices.Ifprofessionaladviceorotherexpertassistanceisrequired,the
servicesofacompetentprofessionalshouldbesought.
Firstpublished2008byBlackwellPublishingLtd
12008
LibraryofCongressCataloging-in-PublicationData
VanEmden,HelmutFritz.
Statisticsforterrifiedbiologists/HelmutF.vanEmden.
p.cm.
Includesbibliographicalreferencesandindex.
ISBN978-1-4051-4956-3(pbk.:alk.paper)
1.Biometry–Textbooks.I.Title.
QH323.5.V332008
(cid:1)
570.15195–dc22
2007038533
AcataloguerecordforthistitleisavailablefromtheBritishLibrary.
Setin10.5/12.5ptPhotina
byNewgenImagingSystems(P)Ltd.,Chennai,India
PrintedandboundinSingapore
byFabulousPrintersPteLtd
Thepublisher’spolicyistousepermanentpaperfrommillsthatoperateasustainableforestry
policy,andwhichhasbeenmanufacturedfrompulpprocessedusingacid-freeandelementary
chlorine-freepractices.Furthermore,thepublisherensuresthatthetextpaperandcoverboard
usedhavemetacceptableenvironmentalaccreditationstandards.
ForfurtherinformationonBlackwellPublishing,visitourwebsiteat
www.blackwellpublishing.com
VanEmden: “C000” — 2008/1/31 — 16:18 — PAGE iv — #4
Contents
Preface xiii
1 Howtousethisbook 1
Introduction 1
Thetextof thechapters 1
Whatshouldyoudoif yourunintotrouble? 2
Elephants 3
Thenumericalexamplesinthetext 3
Boxes 3
Spare-timeactivities 4
Executivesummaries 4
Whygotoallthatbother? 4
Thebibliography 6
2 Introduction 8
Whatarestatistics? 8
Notation 8
Notationforcalculatingthemean 10
3 Summarizingvariation 12
Introduction 12
Differentsummariesof variation 13
Range 13
Totaldeviation 13
Meandeviation 13
Variance 14
Whyn−1? 16
Whythesquareddeviations? 17
Thestandarddeviation 18
Thenextchapter 20
Spare-timeactivities 20
VanEmden: “C000” — 2008/1/31 — 16:18 — PAGE v — #5
vi Contents
4 Whenaresumsof squaresNOTsumsof squares? 21
Introduction 21
Calculatingmachinesofferaquickermethodof calculating
sumsof squares 21
Addedsquares 21
Thecorrectionfactor 22
Avoidbeingconfusedbytheterm“sumof squares” 22
Summaryof thecalculatormethodof calculatingdownto
standarddeviation 23
Spare-timeactivities 24
5 Thenormaldistribution 25
Introduction 25
Frequencydistributions 25
Thenormaldistribution 26
Whatpercentisastandarddeviationworth? 27
Arethepercentagesalwaysthesameasthese? 29
Othersimilarscalesineverydaylife 30
Thestandarddeviationasanestimateof thefrequency
of anumberoccurringinasample 31
Frompercenttoprobability 31
Executivesummary1–Thestandarddeviation 33
6 Therelevanceof thenormaldistributionto
biologicaldata 35
Torecap 35
Isourobserveddistributionnormal? 36
Checkingfornormality 37
Whatcanwedoaboutadistributionthatclearlyisnotnormal? 38
Transformation 38
Groupingsamples 40
Doingnothing! 40
Howmanysamplesareneeded? 40
Factorsaffectinghowmanysamplesweshouldtake 41
Calculatinghowmanysamplesareneeded 41
7 Furthercalculationsfromthenormaldistribution 42
Introduction 42
Is“A”biggerthan“B”? 42
Theyardstickfordeciding 43
Derivationof thestandarderrorof adifferencebetween
twomeans 45
Step1–fromvarianceof singledatatovarianceof means 45
VanEmden: “C000” — 2008/1/31 — 16:18 — PAGE vi — #6
Contents vii
Step2–fromvarianceof singledatato“varianceof
differences” 48
Step3–thecombinationof Steps1and2;thestandard
errorof differencebetweenmeans(s.e.d.m.) 49
Recapof thecalculationof s.e.d.m.fromthevariance
calculatedfromtheindividualvalues 51
Theimportanceof thestandarderrorof differencesbetween
means 52
Summaryof thischapter 52
Executivesummary2–Standarderrorof adifference
betweentwomeans 56
Spare-timeactivities 57
8 Thet-test 58
Introduction 58
Theprincipleof thet-test 58
Thet-testinstatisticalterms 59
Whyt? 60
Tablesof thet-distribution 61
Thestandardt-test 64
Theprocedure 64
Theactualt-test 69
t-testformeansassociatedwithunequalvariances 69
Thes.e.d.m.whenvariancesareunequal 70
Aworkedexampleof thet-testformeansassociated
withunequalvariances 73
Thepairedt-test 75
Pairwhenpossible 78
Executivesummary3–Thet-test 80
Spare-timeactivities 82
9 Onetailortwo? 83
Introduction 83
Whyistheanalysisof varianceF-testone-tailed? 83
Thetwo-tailedF-test 84
Howmanytailshasthet-test? 86
Thefinalconclusiononnumberof tails 87
10 Analysisof variance–Whatisit?Howdoesitwork? 88
Introduction 88
Sumsof squaresintheanalysisof variance 89
Some“made-up”variationtoanalyzebyAnova 89
Thesumof squarestable 91
VanEmden: “C000” — 2008/1/31 — 16:18 — PAGE vii — #7
viii Contents
UsingAnovatosortoutthevariationinTableC 91
Phase1 91
Phase2 92
SqADS–animportantacronym 93
Backtothesumof squarestable 96
Howwelldoestheanalysisreflecttheinput? 96
EndPhase 97
Degreesof freedominAnova 97
Thecompletionof theEndPhase 99
Thevarianceratio 100
Therelationshipbetween“t”and“F” 101
Constraintsontheanalysisof variance 103
Adequatesizeof experiment 103
Equalityof variancebetweentreatments 103
Testingthehomogeneityof variance 104
Theelementof chance:randomization 104
Comparisonbetweentreatmentmeansintheanalysisof
variance 107
Theleastsignificantdifference 108
AcaveataboutusingtheLSD 110
Executivesummary4–Theprincipleof theanalysisof variance 111
11 Experimentaldesignsforanalysisof variance 115
Introduction 115
Fullyrandomized 116
Dataforanalysisof afullyrandomizedexperiment 117
Prelims 117
Phase1 118
Phase2 118
EndPhase 120
Randomizedblocks 121
Dataforanalysisof arandomizedblockexperiment 123
Prelims 123
Phase1 125
Phase2 126
EndPhase 127
Incompleteblocks 127
Latinsquare 130
Datafortheanalysisof aLatinsquare 131
Prelims 132
Phase1 134
Phase2 134
VanEmden: “C000” — 2008/1/31 — 16:18 — PAGE viii — #8
Contents ix
EndPhase 135
FurthercommentsontheLatinsquaredesign 136
Splitplot 137
Executivesummary5–Analysisof arandomizedblock
experiment 139
Spare-timeactivities 141
12 Introductiontofactorialexperiments 143
Whatisafactorialexperiment? 143
Interaction 145
If thereisnointeraction 145
Whatif thereisinteraction? 147
Howaboutabiologicalexample? 148
Measuringanyinteractionbetweenfactorsisoftenthe
main/onlypurposeof anexperiment 148
Howdoesafactorialexperimentchangetheformof the
analysisof variance? 150
Degreesof freedomforinteractions 150
Thesimilaritybetweenthe“residual”inPhase2and
the“interaction”inPhase3 151
Sumsof squaresforinteractions 152
13 2-Factorfactorialexperiments 154
Introduction 154
Anexampleof a2-factorexperiment 154
Analysisof the2-factorexperiment 155
Prelims 155
Phase1 156
Phase2 156
EndPhase(of Phase2) 157
Phase3 158
EndPhase(of Phase3) 162
Twoimportantthingstorememberaboutfactorialsbefore
tacklingthenextchapter 163
Analysisof factorialexperimentswithunequalreplication 163
Executivesummary6–Analysisof a2-factorrandomized
blockexperiment 166
Spare-timeactivity 169
14 Factorialexperimentswithmorethantwofactors 170
Introduction 170
Different“orders”of interaction 171
VanEmden: “C000” — 2008/1/31 — 16:18 — PAGE ix — #9