有交互作用的方差分析

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1、因素A因素B(m个水平)总和Ti..平均Xi..B1B2BmA1X111X121X1m1X112X1m2X11rX1mrT1j.T11.T1m.T1..X1j.X11.X1m.X1..A2X111X121X1m1X112X1m2X11rX1mrT2j.T21.T2m.T1..X2j.X21.X2m.X1..AkX111X121X1m1X112X1m2X11rX1mrTkj.Tk1.T1m.T1..Xkj.X11.X1m.X1..总和T.j.T.1.T.m..T平均X.J.X.1.X.m.X假设H01A1=A2=AKH02B1=B2=BMH03ABkm=0计算步骤求总和与平均见表

2、格数据求平方和dfT=kmr-1dfA=k-1同理求SSBdfB=m-1dfAB=(k-1)(m-1)dfE=dfT-dfA-dfB-dfAB因素A(肥料)因素B(m个水平)土壤总和Ti..平均Xi..B1B2BmA121.419.617.621.218.816.620.116.417.5T1j.62.754.851.7169.2X1j.20.918.317.218.8A212.013.013.314.213.714.012.112.013.9T2j.38.338.741.2118.2X2j.12.812.913.713.1Ak12.814.212.013.813.614.61

3、3.713.714.0Tkj.40.341.140.6122.0Xkj.13.413.713.513.5总和T.j.141.3134.6133.5409.4平均X.J.15.715.714.815.16K=3m=3r=3SST=21.42+21.22+...........14.02.-409.42/3*3*3=219.28dfT=26SSA=(1/9)(169.22+118.22+122.02)-6207.72=179.38dfA=2SSB=(1/9)(141.32+134.62+133.52)-6207.72=3.96dfB=2SS(AB)=(1/3)(62.72+54.8

4、2+…….40.62)-SSA-SSB-6207.72=19.24dfAB=4SSE=SST-SSA-SSB-SS(AB)=16.70dfe=18变异来源平方和自由度均方FF0.01显著性因素A179.38289.6996.446.01**因素B3.9621.982.136.01交互作用19.2444.815.184.58**误差16.70180.93总和219.2826一般来讲对于有交互作用的方程分析，当交互作用显著时，对各因素间均数的显著性讨论与多重比较其意义不大，而多关注的是交互作用的多重比较DUNCAN新复极差法误差自由度P为将各样本平均数的个数SSRa差DUNCAN表

5、格得到α为显著水平Se误差项均方