Determination
Decemrl999JournalofNortheastAgriculturalUnlversityVol6?No2l58？160
;DeterminationofEvenDegreeof
;AnimalPopulation
;SongRen—xue,YangYun—qing
;(North*eastAgricu|tura|University.Harbinl5OO3OPRC)
;ABSTRACT
;Theevendegreeofanimalpopulationisgenerlaymeasuredbythecoefficientofvariationofmajoreco- ;nom~ccharacters.Facingthecoefficientofvariation?astatisticwithe~mplexpropertiesachievedindirectly
;thedeterminationofconfidenceintervalforevendegreeofananimalpopu[ationbyanalysingthereciprocalof
;thestatistic.Thesamplesizewhichissuitabletothedeterminationoftheevendegreeofananimalpopulation
;wasprobedintowithintheextentofpermissiveestimationerror.
;KEYWORDS:evendegree;coefficient0{variation;determination;samplesize ;Inproductionofmodernanimalhusbandry,especiallyinindustrialpigfarmingandpoul—
;tryfarming,theproductionflowofwholeinandwholeOUtrequireshighlevelevendegree ;ofananimalpopulation(LiuZhenyi1981).Therefore,apartfromeconomiccharacters.even ;degreehasbecomeanimportantindextOmeasurebreedsperfomanceandraisingeffect.The ;evendegreeofananimalpopulationisusuallyreflectedbythecoefficientofvariationofma—
;jOreconomiccharacters.CoefficientofVariationC.V.iSequaltOstandarddeviationofob—
;servedcharactersSdividedbythemeanvalue,andisintheformofpetcentage:CV=S/至
;×100.Theindexvarieswiththestagesofgrowing.SOitisneededthattheindexisoh—
;servedregularlyattheraisingOrbreedingsite.BecausethehighCOSTSoftheobserving,the ;charactersofeachindividualofapopulationcannotbeobtainedateachtimeofobservlng. ;Therefore,thecoefficientofvariationofapopulationcanonlybeiMeredfromthecoefficient ;ofvariationofthesample.Determinationofevendegreeofananimalpopulationcanbeper—
;formedbymeansofstatistics.
;1Determinationofevendegree
;Let,betherandomvariabledefinedonaprobabilityspace(Q,F,P),and
;e(?)?,)?砒,(>O),??Q
;Thenwehave:
;(m(m)<m)=(m:)<音<)
;Hence
;SupportedhyHeilengihtaaScienceandTechnologyCommittee
;Manuacriptrecevivedl999一一l8
;
;No.2JournalofNoz~eaB~A~dculturalUniverslty?159?
;P(}<.<一P(<吉<)
;Where0isaconstant.Theaboveequalitywillbeusedinthefollowing. ;Letpand口bethemeanvalueandstandarddeviationofaneconomiccharacterofanani- ;realpopulation,respectively.LetandSbethecorrespondentstatisticsofthesamplefrom ;thep.pulation,respectively-Because.f詈？N[詈,],the1一ac.nfidenceintervalforthe
;parameter詈is:詈一u{吾?导?詈+u考1.If一u詈s>o(thisc.nditi.ncanbe
;metinpractice),letSreplaced,takethereciprocalsatthetwosidesoftheaboveinequality, ;hencethe1一ac.nfidenceintervalf.rtheparameter詈,thec.effic|ent.fVa血ti.n.fthe
;population,canbeobtained.
;:?导?—:旦(1)/+u一一一U1S…
;Example1.Sixtyoflayersatfirstlayingaretakenfromapopulationrandomlytomeasure ;theirweights.andS@recalculated:j=1430.6g,S一142.4g.Basedonthesedata,compute
;the95confidenceintervalfortheevendegreeoftheweight.
;Whenais0.05,U=1.96.Puttheknowndataintotheinequality(1)andcalculate: ;Theupperconfidencelimit
;Thelowerconfidencelimit
;Hencethe95confidence
;EO.0971,0.1021].
;10.21g~,6O×1430
;.
;6—1.96×142.4
;_一一9.71V6
;0×1430.6+1.96×142.4
;intervalsfortheevendegreeofthelayers’weightsis
;2Estimationofsamplesize
;Inpreviouspartsofthispaper,theestimationofconfidenceintervalfortheevendegree ;ofaoanimalpopulationwasfulfilledindirectlybyanalysingthereciprocalofthec.efficient ;ofvariation-Fromthesethesamplesizewhichisusedinmeasurementofc0efficient0fvarla—
;tionca?beestimated.
;UndertheconditionsofgivenmeasurementerrorLof/SandCOnfidencederee1一a,
;thesamplesizenusedindeterminationofcoefficientofvariationsatisfiestheappr.ximat ;e
;?for
;mula[u/L]z,thecauseI詈一导l?—一L.
;Example2-Determinatingtheweightevendegreeof20weeksoldmeathenp0pu1ati.n0fpar ;entgeneratlon-AccordingtOtheexpectationvalued/=9.9(YangShah1995),ifweh.De ;thatthemeasurementerrorofthecorrespondencecoefficientofvariationisnot ;greaterthan
;，！ ”七hme丑.remnterr0r七heeciprocal.fthec?
;V?is:L一百一1
;
;?16O?JournalofNorthe~tAgricuLturaLUniversityVolS
;=0.200.Ifwetaked一0.05,thenU=1.96.thereforebytheapproximate[ormula,thesam- ;plesizec.msp0ndingt.the9S%c0nfidenc:n一(]一96.
;3Discussionsandconclusion