spss-多因素方差分析例子

1、作业&多因素方差分析1, 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 Analyze-General Linear Model-Univariate 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 m

2、odel (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 VarianceBetwen-Su FactorsN234567Bglut1233333J339aBTests of Sctffeeii-SubKtis Effectsendenl Varlablweed nmight (cm)sourt&ryps ll Sum of SousesafMean 3uartFCcrTected Mode)FS四旷-nIrtACApI32 3 4.08 J1323,08277381plot24

3、261212.130EpKiet * pin2f .4?1 634LError.0000Total3312 9B024Corrected Total7S.B&S23. F? Smdied = 1.030 谄djj*ud F Squalid =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：选择好 Dependent Variable 和 Fixed Factor(s)，点击 Model 打开:点击Custom，

4、把主效应变量 species和plot送入Model框，点击Con ti nue回到Uni variate主 对话框，点击Plots:-suoKounWH nu_coo ppseun 9eedes )depsSX_2UONOH 101 mD i-i霽i把 OVERALL,species, plo送入 Display Means for 框，选择 Compare main effects , Bonferroni ,点击Continue回到Univariate对话框,果:epndnl v+iablaheight (tmoSO LI IICSTyae III Sum of Squsroa0fMoa

5、n SquareFSig.Corracte j IM odel57426*gBJ81.16DIntercept3Z34.0B213234 03221CBJC11.00033.1 B674.739?joeg.03Jplot2DI212130r09.005trrar214721d1.531Tolal3312.9B024orrarted Totsl23a R Squared = 77F (Mjiisrqd R squarp(l=可以看到：SSspecies=33.165 , dfspecies=7 , MSspecies=4.738 ； SSplot =33.165 , dfplot =7 , MS

6、plot=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，不同物种之间的草高度是存在差异的。Estimated Marginal Means1, Grand MeanDependant Variable: wesd he ight (cm)Mean8W Error95% CorrTidence IntervalLower BoundUpper Bound11.60S25311.06612 151

7、2 weed speciesEstimatesDep endent Vsri able: wec height (cm)atpAri speripqMg anstd. Error95% Confidence IntervalLcrtref BoundUpper Bojnd110 9337159 40012 407212.317.7151083313 9OD311 367.7159fl3312.30049.9 G7,71 SR43311印0514 157715126331570C610 6337153 30012 367111 B677151D33313 4(10m11 3577159 8331

8、2.900Univariate TestsDependent Variable: waedtiaight (cm)Sum of SquaresdfMean SquareFSigContrast3316574.7383.089.034Error21 472141.53+The F tasts the effect of weed species. Thisl&st is ba$9d orttis linearly indp$nd&ntpairvise marisons among tls estimated marginal nnn.dferror=14 ,该表说明：SSspecies=33.1

9、65, 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, plotEtttnatesDependent Variable: weed height (cm|plotStd Enor95% Confid8nc& InternalLower BcundUpper Biund110.396439S.US11.327211-53643310.&4312,527312.S5D43911.&1113 789Pairwise ConiparieonsDs

10、pndsmtVariable; wood hoight(erm(DPotWplDtMean r)ifltr#nrt (k J)ErrorSig?95% Coni de nee Interval farDiffrntshLowqt BoundUpper Bound11*1 200-3JH34R33-2.46 /.Bly.004-4.145-7B0211200.619.219-.4032叭3-1 262fiig.102-2945420312 4C2.019.0D4.7004.14521 J62.E1S162-.420294503s?don esimate5 level.Univariate Tes

11、tsDependent Vanablei weed height (cm)Sum of SquaresIfMan SquareFSig.Contrast24.2512121307.9C9.005Error21472141.534The F tests the effed of plot This test is based on the linearly indepen deni pairwise comparisors among the estimated marginal means.SSplot=33.165， dfplot=7， MSplot=4.738 ； SSerror=21.4

12、72， dferror=14， MSerror=1.534 ；Fplot=12.130,p=0.0050.01;不同的物种间在差异：ProTi le PlotsEvtmaM hlariglnal Mtans nf wkD height 杞网由边际分布图可知：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)

13、,把 high 送入 Depe ndent Variable，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）：Fl heEA View 口豳 TwMNni Analyze Pired UarfceingLnilUie Md-tfis之HI吕闵r f再雋棗E n尊圜SpKIBS11213142占262738393fO4n412413f11 1155佃6IT6ie619724?1L6VJsibk adSVan.jMwIIIJHDfita

14、 Viewiou SPSSProttas&ris您站卩LMICOtl# OM羽箫嚅 *列閣黑乜厨 肩把 species 送入 Post Hoc Tests for 框，选择 Tukey,hvicJhfl.输出结果:Tests of Beiweeti-Subjects EffectsDependentvariatde: weed height (cm)SourceType III Sum of SquaresdfMean BquareFSig.Corrected Model33.1 65*74 7361.658.190Intercept3534 00213234.0&21131.457000sp

15、ecies33.16514.7361.656.190Error45 733162.858Tata II3312 90024Corrected Total7S 89823a. R Squared = .450 Adjusted R Squared = .1 7?Homogeneous Subsetswe Ml heMitri |cm)TUk刖 H5Di JIJl43曲前4)1lQ.31)1H.33)11 3TQ1IWT3ii ee?J12J675)14.1Sig1(17呼4 is-f.illuucitm r# 3itpic. 曰移詞n时輯mtingFir 咛rwi tsm is wgn 吕刖.骑

16、肌Evcin 2B9Ba U*出* Harwp 呻 哄2厲 Sawpit 8ijj =1 ODQ.b.Wiv-.K.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。rpofll* Flot再次检验不同样地草的高度差异：过程和上相似：结果如下n-S4ifect UTectsDepsndenfVQri3t|$- wed heigit(cmguicTps II Sum of SquaresdfFSi acorRCT-sdoiii24.2612111304JI62.021kitefeept32340B213：34(JB21243JD24.000pio

17、i34J11212.1304JIH.021Fiim40382T2.BD2Total3312.9 BO24Double cl cklo.: nrrrtdTotl78 8833Gn F? 3quarsd- 07 (Adjux1id F? Squalid = ?42)Post Hoc TestsHomogeneous Subsetsueed heigit(cm)Tuktiy HSDplotNSubsei12191D.3BB2611.50711.50731：.05DSir?s317.292MeiiisftJi giciLpE ir liomogenticus subsets are onpiayd.B

18、asaa on ot)served means.Tne errorterm isluien Square(ErTur1 = 2.50J.a Usgs Harmnic Moan Sampls Sizo - 6.000.b. Alpha - .05.3样地的草高度最高，且三组之间都存不同样地的草高度存在差异，其中一样地的草高度最短,在差异。Profile Plots2, data0807-flower，某种草的开花初期高度在两种温度和两个海拔之间有无差异？具体怎么差 异的？多因素单因变量方差分析通过An alyze-Ge neral Lin ear Model-Un ivariate 实现，把因变

19、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 Horizontal Axis，再选择 attitude 至U Separate Lines， Plots 框显示 attitude, temperatu

20、re, 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 VarianceBetweert-Subjeds FedorsValue LabelNaltitude3200 m4434D0 m43temperature leveii 1T1472T240主效应各因素各水平以及样本量,epencendVsriabla:Desc

21、ript h/c statisacs he gh: (rrm) to lowtrititudetemueratureiiMe 日 ii3id Dniattin忖3200 mT1ue.7133D651271213S.053070+17Tolal142.2116 2431234D0 IT1T1137.550Bijsri2GT2124 4B12 467&nTo：al135.8984 313543TolaT1142 617ei77&47T2134 7131 957 &4aToiai139 0916 2173S7各水平的均值和标准差。Leuen es Test cf E(|ualitv or Error

22、 Variances aDependent Variable: heighl (mm) to flow&rFdndf3Sig.S.520 1385r .woT e sts the null hypdlhesis th ft the e rror variance of trie dependent variable is equal across groups.a D&sig Intercept 4 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 Bet ween-Subjects Ef

23、fectsOopondant Variable, hoijht (mm) to flowrSourceTyps III Sum of SquiresdfMari SquareFSl-J.Ooirsctod Modol2360.3766.20270.622003ntercepi1919714.6281161 9714 620143667.239003ilULide503.10715C3.I6744.03D000lerr pu dlLiiti1149.79811149.7981DT9B6ODOaitiun lernperaiure3ee.4B613te,4063M59QOQError935.740

24、B311.27Total166644.27007SoirectedTolal3324.353晡a R Squared = .719 (Miusted R Sqjared = .708)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 ， MSinteraction=338.486 ； SSerror=935.7

25、48，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 ， p0.001;所以故认为在0.1%的置信水平上，不同温度，不同海拔之间的草高度是存在差异的。Estimated Marginal Means1f Grand |H eanDependent Variable: h 已 ight (nim) to flowerM3nStd Error9f% Confidenc

26、e IntivalLcwer BoundUpper Bound138.4463C5137710139 1722、altitudeEstimatesDe pendent Variable height (mni) to flows raltitudeMsanStd. Error95% Confidence IntervalLower BoundUpper Bound3200 m140.686.52013S.6521d1.9203400 m136.005.513134,985137.026在海拔为3200米处，在95%的置信区间，花的平均高度范围为 139.852到141.920之间。在海拔为34

27、00米处，在95%的置信区间，花的平均高度范围为 134.985到137.036之间。Pairwise ConwrisonsDependent Variable: heiqht mm) to flower(l) slttude(J) altitudeMeanDifTeRnct (I-J)Std. ErrorSigb95% Confidence Interval for unrererice11Lower BoundUpper Hound32D0m3400 m4 680t73 I000)42TC 333340C m3200 m-j.eeo71000-6.333工贮7Basd on eslmat&

28、d margina means* The mean difference iw sigiificant at the .05 level.b. Adj u slm ent far mu tip 柜 comparisons: Least Significantir&rence (equivale rtto no adjustments aititude各水平的边际均值的多重比较，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

29、.333.故均值存在差异。Univariate TestsDependent Variable: height (mm to flowerSun ofSquaresdfMean SquareFSig一ContrastError503.1 67935748163503,1711.27444,530The F tests the effect of altitude. This test is basd on 1he linearly independent pairwise corridarisons among the estimated marginal nneans.SSaltitude=

30、503.167, dfaltitude=1 ， MSaltitude=503.167 ；SSerror=935.748, dferror=83 ,MSerror=935.748 ; Faltitude=44.63 , P0.001.不同海拔的花高度不存在差异的的概率v 0.001.3. temperature levelEstimatesDependent Variable: height (mm) to flowerlemperatur已 levelMean8U. Error95% Confidence intervalLower SoundUpper BoundT1143.134495141.149143 119T2134.757.537133 589135.325在温度为T1处，在95%的置信区间，花的平均高度范围为141.149到143.119之间。在温度为T2处，在95%的置信区间，花的平均高度范围为133.689到135.825之间。lOh5D333n da it Varian ： hGighiflaAer1 tamp 9 rat Lire IgvI(J) tswipraLUira IhyrIMean DiffeiencE il-J)StJ E tor斷弔intPiwai TrrILcwhi BoundUpper BuuncTIT21377J3