生物统计习题及答案-4.pdf

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1、生物统计与试验设计生物统计与试验设计--作业四彭继光3090100060植物保护Problem2：Inafieldexperiment,therearegvarieties,ddifferentplantdensitiesandldifferentplantlocations,theobservationvaluecanbeexpressedbyfollowingmodel:?ℎ??=μ+?ℎ+??+??+??ℎ?+??ℎ?+????+?ℎ??Where,μisthepopulationmean；?ℎistheeffectduetoh’thvariety，fixede

2、ffect；??istheeffectduetoi’thdensity，?~N(0，?2)；?istheeffectduetoj’thlocation，????~N(0，?2)；??istherandominteractioneffectbetweenvarietyandplant??ℎ?density，??~N(0，?2)，??istherandominteractioneffectbetweenvarietyandℎ???ℎ?location，??~N(0，?2)，??istheinteractioneffectbetweenplantdensityandℎ???

3、??location，randomeffect，??~N(0，?2)，?istheresidualeffect，?~N(0，?2)。????ℎ??ℎ???(1)Accordingtothedesignofexperiment,writeoutthedistributionofobservation；?~N(μ+?，?2+?2+?2+?2+?2+?2)ℎ????????????(2)Writeouttheformulaofcalculatingsumofsquaresforeacheffect；SSG=∑∑∑(?̅ℎ∙∙−?̅∙∙∙)2=??∑(?̅ℎ∙∙−?̅∙∙∙)

4、2ℎ??ℎSSD=∑∑∑(?̅∙?∙−?̅∙∙∙)2=??∑(?̅∙?∙−?̅∙∙∙)2ℎ???SSL=∑∑∑(?̅∙∙?−?̅∙∙∙)2=??∑(?̅∙∙?−?̅∙∙∙)2ℎ???SSGD=∑∑∑(?̅ℎ?∙−?̅ℎ∙∙−?̅∙?∙+?̅∙∙∙)2=l∑∑(?̅ℎ?∙−?̅ℎ∙∙−?̅∙?∙+?̅∙∙∙)2ℎ??ℎ?SSGL=∑∑∑(?̅ℎ∙?−?̅ℎ∙∙−?̅∙∙?+?̅∙∙∙)2=d∑∑(?̅ℎ∙?−?̅ℎ∙∙−?̅∙∙?+?̅∙∙∙)2ℎ??ℎ?SSDL=∑∑∑(?̅∙??−?̅∙?∙−?̅∙∙?+?̅∙∙∙)2=g∑∑(?̅∙??−?̅∙?∙−?̅∙∙?+?

5、̅∙∙∙)2ℎ??ℎ?SSTO=SSG+SSD+SSL+SSGD+SSGL+SSDL+SSE=∑∑∑(?−?̅)2ℎ??∙∙∙ℎ??pengjiguang@ZJU生物统计与试验设计(3)Writeoutthemeanexpectationofeachsumsquaresforeacheffect；??E(MSG)=?2+l?2+d?2+∑?2?????ℎ?−1ℎE(MSD)=?2+gl?2+??2????E(MSL)=?2+gd?2+??2????E(MSGD)=?2+??2???E(MSGL)=?2+d?2???E(MSDL)=?2+??2???E(MSE)=??2

6、(4)Howtotestthesignificanceduetovarietyeffect？?:∑?2=00???:∑?2>01??∗???当原假设成立时，?=~?(?−1,??)????+????−???(????+????−???)2??=????2????2???2++(g−1)(d−1)(?−1)(?−1)(?−1)(?−1)(?−1)(5)Howtotestthesignificanceduetotheinteractioneffectofvarietyandlocation？?:?2=00???:?2>01??∗????当原假设成立时，?=~?((g−1)

7、(l−1)，(g−1)(d−1)(l−1))???pengjiguang@ZJU