Statistical Design and Analysis for Intercropping Experiments: Volume II: Three or More Crops

283 Pages·1999·1.538 MB·English

by  Walter T. Federer (auth.)

Springer Series in Statistics
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Walter T. Federer
Statistical Design and Analysis
for Intercropping Experiments
Volume II: Three or More Crops
With 34 Illustrations
1 3
WalterT.Federer
BiometricsUnit
CornellUniversity
Ithaca,NY14853-7801
USA
LibraryofCongressCataloging-in-PublicationData
Federer,WalterTheodore,1915–
Statisticaldesignandanalysisforintercroppingexperimentsby
WalterT.Federer.
p. cm.—(Springerseriesinstatistics)
Includesbibliographicalreferencesandindex.
Contents:v.1.Twocrops
ISBN0-387-98533-6
1.Intercropping—Experiments. 2.Experimentaldesign.
I.Title. II.Series.
S603.5.F43 1993
(cid:1)
631.58—dc20 92-29586
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ISBN0-387-98533-6 Springer-Verlag NewYork Berlin Heidelberg SPIN10659500
To Edna
Preface to Volume II
The comments about Volume II in the Preface to Volume I were overoptimistic.
Inordertoobtainthestatisticaldesignsandanalyses,itwasnecessarytoperform
aninordinateamountofresearchtopreparenewandmorecomplextreatmentand
experiment designs and associated statistical analyses. A considerable amount
of algebraic manipulation was required. Owing to the algebraic complexity, it
wasusefultoemploycomputersoftwaresuchasGAUSS,MATHEMATICA,and
MAPLE. Specific cases were obtained using these packages, which enabled a
generalization.Someoftheprogramsareincludedtoaidthereaderindeveloping
computer programs for other situations. As intercropping research is a complex
andbroadfield,manynewsituations,whichwerenotcontemplatedwhenVolume
IIwaswritten,willarise.Useoftheabovepackagesresultedinsavingaconsider-
ableamountoftimeinarrivingatsolutions.Estimationofothereffectsandtheir
varianceswillbeneededandothergoalswillariseinmeetingtheneedsoffuture
intercroppingresearch.
ThescopeofVolumeIIisgiveninthefirstchapter.Thesimplestcaseofinter-
croppingwiththreeormorecropsisonemaincropwithk supplementarycrops
as discussed in Chapter 12. The statistical analyses are much more complicated
thanwhenthereisonlyonesupplementarycrop.Thecomplexityofthestatistical
designandanalysiscontinuesforallothersituations.Fromastudyoftheliterature
citationsinthebibliographydescribedinChapter20,intercroppingresearchhas
been concerned almost entirely with rather simple intercropping goals, designs,
andanalysis.Withthedesignsandanalysespresentedherein,itwillbepossible
for the researchers to study more complex, meaningful, and practical situations.
Thepaststudies,foralargepart,dealwithonlyonecomponentoftheagricultural
viii PrefacetoVolumeII
cropping system. Analyses given herein allow for a consideration of the entire
systemaswellasitscomponentparts.
Acomparisonofsystemsorprogramsarisesinmanyfieldsbesidesagriculture.
Even in agriculture there are many systems involving mixtures of items which
arenotordinarilythoughtofasintercropping,butinrealityare.Someexamples
arepasture,orchard,lumberplantations,teaandcoffeeplantations,weedcontrol,
rotation,anddoublecroppingstudiesasdescribedinChapter19.Inmedicine,pa-
tientsusemanytypesofdrugmixtures,sometimestakingtenormoreprescription
drugs. Drug “cocktails” are being prescribed. Many of the designs and analyses
presented here may be used in studying the various effects of drug mixtures. In
educationandrecreation,manyprogramsareusedandtheproceduresgivenwill
beusefulinassessingthevariousprograms.Mixturesofitemsappearinengineer-
ing, transportation, nutrition, ecology, etc. studies. Procedures for intercropping
studieshavedirectapplicationinalltheseareas.
WalterT.Federer,1998
Preface to Volume I
Twovolumesarebeingpublishedonthetopicofthetitle.VolumeI,thepresent
one, deals with the statistical design and analysis of intercropping experiments
in which there are mixtures (intercrops) of two crops and/or sole crops. Volume
II will deal with the statistical design and analysis of three or more crops in the
mixture(intercrop),togetherwithsolecropsandpossiblemixturesoftwocrops.
It is necessary to fully comprehend the concepts and analyses for mixtures of
two crops prior to considering three or more crops in the mixture. The utility,
concepts, comprehensions, and application of techniques for two crops are an
orderofmagnitudemoredifficultthanforsolecropsonly.Thedegreeofdifficulty
in these aspects for three or more crops in the mixture is an order of magnitude
greater than when considering only two crops. Hence, the reader is cautioned
to fully comprehend Volume I before proceeding to Volume II. Most published
literaturedealswithtwocropsinamixture.Inpractice,thenumberofcropsinan
intercroppingsystemmaybequitelarge.Mixturesofthreeormorecropsarequite
commoninpractice,e.g.,pastures.ThelastchapterofVolumeIconsidersdesign
conceptsandexperimentdesignsthatmaybeofuseforintercroppingexperiments.
ThelasttwochaptersofVolumeIIwillcontainabibliographyofpublicationson
intercropping,whicharenotcitedattheendofeachchapterinVolumesIandII,
andadiscussionofapplicationsofthematerialforintercroppingexperimentsto
otherareas.Someoftheareasaresurveysampling,chemistry,haycropmixtures,
repeatedblockdesigns,dietarystudies,andrecreationalandeducationalprograms.
Inpresentingthestatisticaldesignandanalysisforintercroppingexperiments,
involvingmixturesoftwocropswithorwithoutsolecrops,wehaveattemptedto
presentthetopicsinorderofincreasingdifficulty.First,thesituationinvolvingone
maincropandonesupplementarycropisconsideredinChapter2.Here,weadd
x PrefacetoVolumeI
littleoverthatappearinginstandardstatisticalmethodsbooks.Then,inChapter
3, we consider both crops to be main crops and analyze the individual crop re-
sponses.Again,littleisaddedonstatisticalmethodologythatisnotstandard.In
Chapter4,bothcropsareconsideredtobemaincropsandacombinedresponse
for the yields of both crops is required. This involves creating variables as in a
multivariateanalysis.Theformsusedwillnotordinarilybethosefromstandard
multivariate analyses. Ratios of yields, prices, or other variables are used. This
is an innovation over other procedures appearing in the literature. We show that
severalanalysesaredesirable,asopposedtoonewhenonlysolecropsareinthe
experiment.Densityofcropsisheldconstantuptohere.InChapter5,densityis
a variable for the two main crops and yield is modeled as a function of density.
In Chapter 6, we model responses in much the same way as they are for diallel
crossingsystemsinbreedinginvestigations,exceptthattheyieldsfrombothcrops
are available. In Chapter 7, we do the same type of modeling for the case when
the individual crop yields are not available. This is closer to the ordinary diallel
crossingsituation.InChapter8,spatialarrangementsoftwocropsarediscussed,
withmanyarrangementsbeingconsidered.IntheninthchapterofVolumeI,anal-
yses of replacement series experiments and a linear programming approach for
consideringtworesponsessimultaneouslyinareplacementseriesarediscussed.
Thelastchaptercontainsadiscussionofdesignconceptsandexperimentdesigns
thatareconsideredtobeofuseinintercroppingexperiments.
Asofthisdate,mostofthetheoreticalworkforVolumeII,Chapters11to20,
hasbeencompleted.Chapters12and13havealreadybeenwrittenandareinthe
process of being put in final form. A search for appropriate examples is being
made.Abibliographyonintercroppingexperiments,Chapter20,hasbeenmade
butwillrequireupdating.
WalterT.Federer,1993
Acknowledgments
ThenameofNancyMilesMcDermottwasinadvertentlyomittedintheacknowl-
edgments to Volume I. Deep appreciation and many thanks are due to her for
her efforts in assuring correctness of the computations and for her enlightening
comments.Itwasajoytoworkwithher.
NormaPhalen’seffortinpreparingthemanuscriptforthisbookinLaTexformat
isgreatlyappreciated.Thanksaredueherforreadingoverthemanuscript,check-
ing for spelling errors, making comments, and especially her patience with the
entireprocess.TheeffortsandsuggestionsoftheSeniorProductionEditor,Les-
leyPoliner,andCopyeditor,BarbaraTomkins,aresincerelyappreciated.Ladies,
Icouldn’thavedoneitwithoutyou.Many,manythanks.
WalterT.Federer,1998