双因素完全随机设计的方差分析

两因素完全随机试验设计的方差分析2008-10-21.iT.ixjT...Tjx...x海拔高度/m植被类型原生林次生乔木林次生灌木林500~100069382613344.331000~1500104794222575.001500~2000216165115496165.332000~2500128542821070.005173362111064()129.2584.0052.7588.67()表3-2-24林麝种群数量统计表22AbK22Aa22Ab22BaK22Ba22BaK222变异因素dfSSMSEMS固定模型随机模型A随机B固定Aa-1SSAMSABb-1SSBMSB误差（e）(a-1)(b-1)SSeMSe总变异ab-1SST表3-2-27双因素无重复试验方差分析模式表3-2-28麝种群分布方差分析表F变异来源dfSSMSF5%1%海拔（A）325135.348378.4531.81**4.799.78植被间（B）211835.175917.5922.47**5.1410.92误差（e）61580.16263.36总变异1138550.67表3-2-30海拔高度、植被类型的差异显著性（SSR法）因素平均数显著性5%1%AA3165.33aAA275.00bBA470.00bBA144.33bBBB1129.25aAB284.00bBB352.75cBp234SSR0.053.463.583.64ALSR0.0532.4233.5434.11BLSR0.0528.0629.0329.52SSR0.015.245.515.65ALSR0.0149.1051.6352.94BLSR0.0142.5044.6945.8237.9336.263bMSSeEA11.8436.263aMSSeEB..iT..ix..jT...T..jx...xABB1对照B2(N)B3(N+K)B4(N+P)xi1kxi2kxi3kxi4kA1（砂土）31353045434776717560646263953.259632135452227418662A2（砂土）50525461636588909274757083469.5015652189632709021973A3（粘土）40454455525686848470716975663.001294316354.3325486.67210703814877466152229()42.3354.1182.8968.3361.92()表3-2-25不同土质、施肥条件下苗床高资料表（单位：cm）22AbrK22BarK22BArK2222ABAbrr222BBAarr22BAr2222ABAbrKr22Bar22BAr2变异来源自由度df平方和SS均方MSEMS固定模型随机模型A固定B随机ABA×B误差（e）a-1b-1(a-1)(b-1)ab(r-1)SSASSBSSA×BSSeMSAMSBMSA×BMSe总变异abr-1SST表3-2-26两因素等重复试验的方差分析模式表3-2-31不同土质、施肥条件下的苗高方差分析（固定模型）F变异来源DFSSMSF土壤间（A）21605.50802.75176.04**F0.01(2,24)=5.61施肥间（B）38328.972776.32608.84**F0.01(3,24)=4.72交互作用（A×B）674.9512.492.74*F0.05(6,24)=2.51误差（e）24109.334.56F0.01(6,24)=3.67总变异3510118.75因素与处理平均数显著性5%1%A壤土（A2）69.50aA粘土（A3）63.00bB砂土（A1）53.25cCBN+K(B3)82.89aAN+P(B4)68.33bBN(B2)54.11cCCK(B1)42.33dDAB（处理）A2B390.00aAA3B384.67bBA1B374.00cCA2B473.00cdCA3B470.00dCA2B263.00eDA1B462.00eDA3B254.33fEA2B152.00fEA1B245.00gFA3B143.00gFA1B132.00hGp23456789101112SSR0.052.923.073.153.223.283.313.343.373.383.403.41ALSR0.051.801.891.941.982.022.042.062.082.082.092.10BLSR0.052.082.192.242.292.332.362.382.402.412.422.43ABLSR0.053.603.793.883.974.044.084.124.154.174.194.20SSR0.013.964.144.244.334.394.444.494.534.574.604.62ALSR0.012.442.552.612.702.712.742.772.792.822.842.85BLSR0.012.822.953.023.083.123.163.203.223.253.273.29ABLSR0.014.885.105.235.345.415.475.545.595.635.675.70表3-2-32例1中A、B和AB的SSRα与LSRα6164.01256.4brMSSeEA7118.0956.4arMSSeEB2329.1356.4rMSSeEAB单因素随机区组设计的方差分析MadebyLidexiao10-22-2008回顾：随机区组设计区组的概念不局限于田间试验，可以认为只要将性质近似的试验材料（如同一窝动物，同年龄，同身长，同体重的个体等）或大致相同的环境条件安排在同一组群中，该组群则可称为区组．随机区组设计也称为随机单位组设计，它是以划分区组的方法使区组内部条件尽可能一致，以达到局部控制的目的．在进行随机区组设计时，关键是掌握区组内的环境变异要尽可能小，而区组间允许存在一定的环境变异．将环境均匀性的控制范围从整个试验缩小的一个个区组，区组间的差异可以通过方差分析使其与误差分离．因而，随机区组设计既能保持完全随机设计的优点，又能克服完全随机设计的缺点减少试验误差．随机区组设计要点在田间的区组设置中，应考虑到试验精确度与工作便利等方面，并以前者为主．为此，必须使区组间有最大的土壤差异，区组内的各个小区间变异最小．一般来讲，方形区组的差异大，狭长形小区变异小，常用的是狭长形小区．当土壤肥力有方向性递减时，区组设置应与此方向垂直，区组内小区长边应与此方向平行；当区组内小区多时，可分为两排，当然还必须有四周的保护行，观察道路等．ⅠⅡⅢⅣ74211317368548732164524887566532肥力梯度ⅠⅡⅢ38110715149613416112125（b）16个品种3个重复的随机区组（小区布置成两排）a）8个品种4个重复的随机区组排列单因素随机区组的方差分析实质是两因素无重复（只有单个观察值）的方差分析方法..ˆ,..ˆ..,ˆˆ,ˆ,..ˆ........xxxxxxxxxxxjiijijjjiijjiiijjiijx表3-3-3小麦品比试验的产量结果（单位：kg）.iT.ix2·iTjijx2jT.2.iTijijx2jx...x2.jT2.jT区组BB1B2B3品种AA110.911.312.234.411.51183.36395.29A210.812.314.037.112.41376.41463.93A311.112.510.534.111.41162.81389.71A49.110.711.130.910.3954.81320.51A511.813.914.840.513.51640.25551.49A610.110.611.832.510.81056.25393.61A710.011.514.135.611.91267.36431.04A89.310.412.432.110.71030.41348.4183.193.2100.9277.2T..9671.663253.9910.411.712.611.66905.618686.2410180.8125772.6622AbK22Aa22Ab22BaK22Ba22BaK222变异因素dfSSMSEMS固定模型随机模型A随机B固定Aa-1SSAMSABb-1SSBMSB误差（e）(a-1)(b-1)SSeMSe总变异ab-1SST表3-2-27双因素无重复试验方差分析模式**将B因素视为区组，区组数为r,代换相应的b.即成为单因素随机区组的方差分析表表3-3-9例3-3-2的方差分析51.6)14,2(01.0F28.4)14,7(01.0F变异来源dfSSMSFFα区组间（B）219.929.9613.644**品种间（A）722.233.164.356**误差（e）1410.250.73总变异2352.4.ix.6.()ixxCK品种A5A2A7A1A3A6A8A413.5012.3711.8711.4711.3710.8310.7010.302.67**1.54*1.040.640.540－0.13－0.53表3-3-10参试品种与对照品种产量的差异显著性6962.0373.022..rMSSekxix49.1145.26962.0)14(6962.005.005.0tLSD07.2977.2696.0)14(6962.001.001.0tLSD