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1、作业&多因素方差分析data0806-height是从三个样方中测量的八种草的高度，问高度在三个取样地点，以及八 种草之间有无差异？具体怎么差异的？打开 spss 软件，打开 data0806-height 数据，点击 An alyze-Ge neral Lin ear Model-Un ivariate 打开：把 plot 和 species 送入 Fixed Factor(s),把 height 送入 Dependent Variable，点击 Model打开：选择 Full factorial , Type III Sum of squares, Include intercept in
2、 model (即全部默认选项) 点击Con ti nue回到Uni variate主对话框，对其他选项卡不做任何选择，结果输出:Univariate Analysis of VarianceBetweefl-Siibjecis FactorsNweed species 123457eplot12333333333993r ests or BeiMeen-siihiects trrecisDependent Variable weed height (cm)ScmmaType ill Sum of SquareorMan SouaneFSig.Corrected Model7e.898a233
3、.4301Intercept3234 06213234.0B3seeder33.10574 73fiplot24.261上12.130species* plot21.472n1.534Error.000IITotal3312.96D24Corretted Total79.99923a. R Squared = 1.0011 Rusted R Squared = J因无法计算？?Tor ,即无法分开？?i ntercept和?error ,无法检测in teraction的影响,无法进行方差分析，重新 An alyze-Ge neral Lin ear Model-Uni variate 打开：
4、选择好 Dependent Variable 和 Fixed Factor(s)，点击 Model 打开:点击Custom，把主效应变量 species和plot送入Model框，点击Co nti nue回到Uni variate主 对话框，点击Plots:把 date 送入 Horizontal Axis,把 depth 送入 Separate Lines,点击 Add，点击 Continue 回到 Uni variate 对话框，点击 Opti ons:把 OVERALL,species, plo送入 Display Means for 框，选择 Compare main effects
5、, Bonferroni ,点击Continue回到Univariate对话框,果:Tests of H el ween-Subjects EffectsDependent Vanable weed height (cm)SourceType III Sumf Squra-sdfMean SquareFSig.Corrected Model57.4261g6 3814160l009intencapt3234.00213234.082210B.611肿species33 165747383.009.034plot24201212.13D7 9090Q5Error21.472141.534Tota
6、l3312.98024C Drra eta d Total78.89923a. R Squared = .728 Rusted R Squared = .553可以看到：SSspecies=33.165 , dfspecies=7 , MSspecies=4.738 ； SSplot =33.165 , dfplot =7 , MSplot=4.738 ； Serror =21.472, dferror =14, MSerror=1.534 ；Fspecies=3.089, p=0.0340.05;Fplot=12.130,p=0.0050.01;所以故认为在5%的置信水平上，不同样地，不同物
7、种之间的草高度是存在差异的。Estimated Marginal Means1. Grand MennDependent Variable: w&ed height (cm)Std. Error95% Confidence IntervalLower BoundUpper Bound11.603.25311J66121512. weed speciesEslimatesDependent Variable: weed height cm)weed speciesMeanStd. Error95% ( knfidente IntervalLower BoundUpper Bound110.933
8、.7159.40012.467212.367.7151083313.900311.3677159.83312.90049.967.715843311.500514 167.71512.63315.700610.9337159.30012.367711.967.71510.33313.400e11.367J159.83312.900Uniwiriate TestsDependent Variable: weed height (cm)Sum ofSquaresdfSquareFSigContrast33165747363.069.034Error21.472141.534The F tests
9、the effect of weed species. This test is based on the linearly independent pairwise comparisons among the estimated marginal means.dferror=14 ,该表说明：SSspecies=33.165, dfspecies=7 , MSspecies=4.738 ； SSerror=21.472 ,MSerror=1.534 ； Fspecies=3.089, p=0.0340.05;物种间存在差异：3. plotr stiiiMtesDependent Variab
10、le: weed heiglrt(cm)plotMeanStd. Error95% Confidence fntervaiLower BoundUpper Bound110.3B34399.44911J211.538.4391D.64S1 2527312.850.43911.9111 3789Pairwise ComparisonsDependent Vaiiable: weed height (cm)(0 plot(J) platMeanDifference (I- J)Std. EnorSig b95% Confidence Interval for in$tencebLower Boun
11、dUpper Bound121.200.619.219-2.6B3.4933-2.462.619.004-4.145-.7S0211.200.619.219,4日32.8833-1.262.619.1S2-2.945.420312.462r619.004.7804.14521.262.61 a.102-.4202.945Based on estimated marginal means*. The moan difference Is significant at th a .D5 levelUnrvariate TestsDependentvariable: weed heigfit(cm)
12、Sum of SquaresdfMean SquareFSig.Contra stError24.26121.47221412.1301.5347.909.005The F tests the effect of plot This test is based on the linearly independent pairwise comparisons among the estimated marginal meansSSplot=33.165, dfplot=7 , MSplot=4.738 ； SSerror=21.472, dferror=14 , MSerror=1.534 ；F
13、plot=12.130,p=0.0050.01;不同的物种间在差异：i:o-Eabmaua MarginaltMWtfld hklght 1111,1Profi le Plats由边际分布图可知：类似结论：草的高度在不同样地的条件之间有差异(Fplot=12.130,p=0.0050.01)，具体是，样地一和样地三之间存在的差异最大；八种不同草 的高度也存在差异(Fspecies=3.089, p=0.034Ge neral Linear Model- Uni variate :把 species 送入 Fixed Factor(s),把 high 送入 Depe ndent Variable
14、，点击 Plots：把 species 送入 Horizontal Axis，点击 Add，点击 Continue 回到 Univariate，点击 Post Hoc （因为我 们已经知道species效应显著）：把 species 送入 Post Hoc Tests for 框，选择 Tukey,dewTianstarm Anaize DredlMarhebng Graphs UEiinH；曲 rxEr IHelpdat fi.UVIlS-hLht-jav Dal k2iet 1 - IB!占FF生 St htutici Dt a Edit or蓟箫:fln释眉visible: DataVw
15、 VaflablelEiHSRSSSialisies Picceaw is；桂狛UniccidtOJ输出结果:Tests of Between-Subjects EffectsDependent Variable： weed height (cm)SourceType III Sum (SquaresdfMean SquareFSi 3-Corrected Model31165*74.7391.656.190Intercept3234.08213234.0821131,457.000species33 15574.7361 658.190Error45.733162.050Total3312.
16、99024Corrected Total7S.S9S23a. R Squared = .40 (Adjusted R Squared - .167)Homogeneous Subsetsweevl hiEiight Icm)TukerH9DFbweed sp eciesNSubfBHl1439.9675310.33313mg”3311 357e311J677311.8672312.367531J.16TSiC.107MeaD5dogmupw in hDmageneDiJ5 ubshi are displaced.Qad on Qb9.ryd m$an$The error term 15 M&a
17、n SquareCErnir) =s.ma. U$ Harmoflic Man Sample So# =3.DDD.b. Alphas .05.各组均值从小到大向下排列。最大的是第五组，最小的是第四组，其中有些种类草的高度存在差异，有些不存在。Profile Plats再次检验不同样地草的高度差异：过程和上相似：结果如下SourceEroe III Sunnof SquaresOfMean SquareFconfecied Model24.261*212J304.62Intercept3234 06213234 0S212*3.02Ge neral Lin ear Model-Un ivari
18、ate 实现，把因变量height 送入 Dependent Variable 栏，把因素变量 temperature 和口 attitude 送入 Fixed Factor(s)栏点击 Model 选项卡，打开：选着full factorial , type 3，点击）In elude in tercept in model占八、击 Plots 对话框，打开：可选择 attitude 到 Horizontal Axis，然后选择 temperature 到 HorizontalAxis，再选择 attitude 至U Separate Lines， Plots 框显示 attitude, t
19、emperature, attitude *temperature，Estimated Marginal Means选择OVERALL产生边际均值的均值Display框选择要输岀的统计量，Descriptive statistics 描述统计量，Homogeneity tests 方差齐性检验。结果输出:Univariate Analysis of VarianceBetween-Subjects FactorsValue Label忖altitude132Q0m4423400 m43temperature level 1T1472T240主效应各因素各水平以及样本量,Descriplvve
20、StalislicsDependentVaHable: height (mm) to floweraltitude lemperature levelM&anStd. DeviationN32 DO m T1146.7193 065127T2135.053870417Total142 2116 2431443400 m T1137 5505 357820T2134.4612 487623Total135 89S4.31 3543TotalT1142.S176.177647T2134.7131.957940Total139.0916.217387各水平的均值和标准差。Levenes Test o
21、f Equality of Error Variances aDependent Variable: height (mm) to flowerFdfldf2Sig.9.529383.000Tests the null hypothesis that the error variance of the dependentvariable is equal across groups.a. Design: Intercept + altitude + temperature +altitude * temperature把样本分为四组，进行方差齐性检验，方差不一致。Tests of Betwee
22、rv Subjects EffectsDpendent Variable： height (mm) to flowerSourceType HI Sum of SquaresdrMean SquareFSig.Corrected Model23BB.605-379620270.622.000Intercept1619714.623i1619714.6281 43667.239.ODDaltitude5D3.1671503.16744.630.ODOtemperature1149.79811149.798101.996.ODDaltitude- temperature369.48613B8.4B
23、634.458.ODDError935.7498311.274Total1686446.27087Corrected Total3324.35386a. R Squared = .719 (Adjusted R Squared = 708J可以看到：SSaltitude=503.167, dfaltitude=1 , MSaltitude=503.167 ; SStemperature=1149.798 , dftemperature=1 ， MStemperature=1149.798 ； SSinteraction=338.486 ， dfinteraction=1 ， MSinterac
24、tion=338.486 ； SSerror=935.748，dferror=83， MSerror=935.748 ； Faltitude=44.63， p=0.0340.001;Ftemperature=101.986,p=0.0050.001;Ftemperature=101.986,0.001;Finteraction=34.458 ， pson$Dependent variable: height (mm) to flowerI) altitude(J) altitudeMeanDHference (1J)Std. ErrorSig?95% Confidence Interval f
25、or Difference11Lower BoundUpper Bound200 m3400 i4.731.0003.4276.3333400 m320Q m-4.88Dr.731.000-6.333-3.427on estimated marginal means* The mean difference is significant at the .05 level.b. Adjuslment for multiple comparisons: Leasl Significant DlfTerence (equkalent to no adjuslments).aititude各水平的边际
26、均值的多重比较，在本试验中，事实上？Q 平均aititude （3200）=aititude （ 3400）；但是平均 aititude （ 3200）花高度一平均 aititude （ 3400）花高度，在 95%置信区间为3.427到6.333.故均值存在差异。Univariate TestsDependent Variable: height (Him) to flowerSum of SquaresdfMean SquareFSig.ContrastError503.167935.746183503.16711 27444.630.000The f tests the effect o
27、r altitude. This test is based on the linearly independent pairwise comparisons among the sstimated marginal means.SSaltitude=503.167, dfaltitude=1 ， MSaltitude=503.167 ；SSerror=935.748, dferror=83 ,MSerror=935.748 ; Faltitude=44.63 , Psan SquareFSigContrastError114D7DB535 748183114979011.274101.986
28、00QTTie F tests the effect of temperature leve.This test Is tised on the lin&arlyindependent pairwise comparisons among the estimated rnarinal means.SStemperature=1149.798 , dftemperature=1 , MStemperature=1149.798 ； SSerror=935.748, dferror=83，MSerror=935.748 ； Ftemperature=101.986,p0.001;不同温度下， 花的
29、高度存 在差异。4. aAlflud 円 temperafLire levelDependlent Va ri a ble: heighl (mm) Io fl ower95% Confidenc-e InleiYalattitu 血te rnpe-rafiu re 哦也MeanSid. ErrorLower BoundUpper Bound3200 m T114B 719,646145.(33148 004T2135.D53.814133.433136 6733400 m T1137 550751136.057139 043T2134 481.700133.06135.65 3在温度为 之间
30、。在温度为 之间。在温度为 之间。在温度为 之间。T1,海拔3200米处，在95%的置信区间,T2处，海拔3200米处在95%的置信区间,T1处，海拔3400米处，在95%的置信区间,T2处，海拔3400米处，在95%的置信区间,花的平均高度范围为花的平均高度范围为花的平均高度范围为花的平均高度范围为Profiile Plots5UEVS-C*E?!FSpEEgi5lu不同海拔下的的边际均值图Estimated Marginal Means of height (ee) tc flowerlemi1-10.0=1375-ipersnureT1FT2145.433 到133.433 到136.0
31、57 到133.068 到148.004136.673139.043135.853t35.O=altitude两个因素的边际均值交互效应图，该图直线相互交叉(即斜率不一样)表明有交互效应。结论如下：某种草的开花初期高度在两种温度之间有差异(Ftemperature=101.986,p0.001;)， T1时草的开花初期高度高于T2时草的开花初期高度.某种草的开花初期高度在两种海拔之间有差异(Faltitude=44.63，P0.001.)，海拔3200时草的开花初期高度高于海拔3400时草的开花初期高度.，p0.001) 。温度和海拔对草的开花初期高度的影响存在交互效应 (Finteraction=34.458