1、作業&多因素方差分析1, data0806-height是從三個樣方中測量的八種草的高度，問高度在三個取樣地點，以及八 種草之間有無差異？具體怎么差異的？翻開 spss軟件，翻開 data0806-height 數據，點擊 Analyze-General Linear Model-Univariate 翻開：把 plot 和 species 送入 Fixed Factor(s),把 height 送入 Dependent Variable，點擊 Model翻開：選擇 Full factorial , Type III Sum of squares, Include intercept in m

2、odel (即全部默認選項) 點擊Con ti nue回到Uni variate主對話框，對其他選項卡不做任何選擇，結果輸出:Univariate Analysis of VarianceBetwen-Su FactorsN234567Bglut1233333J339aBTests of Sctffeeii-SubKtis Effectsendenl Varlablweed nmight (cm)sourt&ryps ll Sum of SousesafMean 3uartFCcrTected Mode)FS四曠-nIrtACApI32 3 4.08 J1323,08277381plot24

3、261212.130EpKiet * pin2f .4?1 634LError.0000Total3312 9B024Corrected Total7S.B&S23. F? Smdied = 1.030 諂djj*ud F Squalid =因無法計算？?Tor ,即無法分開？?i ntercept和?error ,無法檢測in teraction的影響,無法進行方差分析，重新 An alyze-Ge neral Lin ear Model-Uni variate 翻開：選擇好 Dependent Variable 和 Fixed Factor(s)，點擊 Model 翻開:點擊Custom，

4、把主效應變量 species和plot送入Model框，點擊Con ti nue回到Uni variate主 對話框，點擊Plots:-suoKounWH nu_coo ppseun 9eedes )depsSX_2UONOH 101 mD i-i霽i把 OVERALL,species, plo送入 Display Means for 框，選擇 Compare main effects , Bonferroni ,點擊Continue回到Univariate對話框,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;所以故認為在5%的置信水平上，不同樣地，不同物種之間的草高度是存在差異的。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 ,該表說明：SSspecies=33.1

9、65, dfspecies=7 , MSspecies=4.738 ； SSerror=21.472 ,MSerror=1.534 ； Fspecies=3.089, p=0.0340.05;物種間存在差異：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;不同的物種間在差異：ProTi le PlotsEvtmaM hlariglnal Mtans nf wkD height 杞網由邊際分布圖可知：類似結論：草的高度在不同樣地的條件之間有差異(Fplot=12.130,p=0.0050.01)，具體是，樣地一和樣地三之間存在的差異最大；八種不同草 的高度也存在差異(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，點擊 Plots：把 species 送入 Horizontal Axis，點擊 Add，點擊 Continue 回到 Univariate，點擊 Post Hoc 因為我 們已經知道species效應顯著：Fl heEA View 口豳 TwMNni Analyze Pired UarfceingLnilUie Md-tfis之HI呂閔r f再雋棗E n尊圜SpKIBS11213142占262738393fO4n412413f11 1155佃6IT6ie619724?1L6VJsibk adSVan.jMwIIIJHDfita V

14、iewiou SPSSProttas&ris您站卩LMICOtl# OM羽簫嚅 *列閣黑乜廚 肩把 species 送入 Post Hoc Tests for 框，選擇 Tukey,hvicJhfl.輸出結果:Tests of Beiweeti-Subjects EffectsDependentvariatde: weed height (cm)SourceType III Sum of SquaresdfMean BquareFSig.Corrected Model33.1 65*74 7361.658.190Intercept3534 00213234.0&21131.457000spec

15、ies33.16514.7361.656.190Error45 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時輯mtingFir 嚀rwi tsm is wgn 呂刖.騎肌E

16、vcin 2B9Ba U*出* Harwp 呻 哄2厲 Sawpit 8ijj =1 ODQ.b.Wiv-.K.各組均值從小到大向下排列。最大的是第五組，最小的是第四組，其中有些種類草的高度存在差異，有些不存在。rpofll* Flot再次檢驗不同樣地草的高度差異：過程和上相似：結果如下n-S4ifect UTectsDepsndenfVQri3t|$- wed heigit(cmguicTps II Sum of SquaresdfFSi acorRCT-sdoiii24.2612111304JI62.021kitefeept32340B213：34(JB21243JD24.000pioi3

17、4J11212.1304JIH.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.Bas

18、aa on ot)served means.Tne errorterm isluien Square(ErTur1 = 2.50J.a Usgs Harmnic Moan Sampls Sizo - 6.000.b. Alpha - .05.3樣地的草高度最高，且三組之間都存不同樣地的草高度存在差異，其中一樣地的草高度最短,在差異。Profile Plots2, data0807-flower，某種草的開花初期高度在兩種溫度和兩個海拔之間有無差異？具體怎么差 異的？多因素單因變量方差分析通過An alyze-Ge neral Lin ear Model-Un ivariate 實現，把因變量h

19、eight 送入 Dependent Variable 欄，把因素變量 temperature 和口 attitude 送入 Fixed Factor(s) 欄占八、擊 Plots 對話框，翻開：可選擇 attitude 到 Horizontal Axis，然后選擇 temperature 到 Horizontal Axis，再選擇 attitude 至U Separate Lines， Plots 框顯示 attitude, temperature, attitude *temperature，Estimated Marginal Means選擇OVERALL產生邊際均值的均值Display

20、框選擇要輸岀的統計量，Descriptive statistics 描述統計量，Homogeneity tests 方差齊性檢驗。結果輸出：Univariate Analysis of VarianceBetweert-Subjeds FedorsValue LabelNaltitude3200 m4434D0 m43temperature leveii 1T1472T240主效應各因素各水平以及樣本量,epencendVsriabla:Descript h/c statisacs he gh: (rrm) to lowtrititudetemueratureiiMe 日 ii3id Dnia

21、ttin忖3200 mT1ue.7133D651271213S.053070+17Tolal142.2116 2431234D0 IT1T1137.550Bijsri2GT2124 4B12 467&nTo：al135.8984 313543TolaT1142 617ei77&47T2134 7131 957 &4aToiai139 0916 2173S7各水平的均值和標準差。Leuen es Test cf E(|ualitv or Error Variances aDependent Variable: heighl (mm) to flow&rFdndf3Sig.S.520 1385r

22、.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把樣本分為四組，進行方差齊性檢驗，方差不一致。Tests of Bet ween-Subjects EffectsOopondant Variable, hoijht (mm) to flowrSourceTyps III Sum of Squiresdf

23、Mari SquareFSl-J.Ooirsctod Modol2360.3766.20270.622003ntercepi1919714.6281161 9714 620143667.239003ilULide503.10715C3.I6744.03D000lerr pu dlLiiti1149.79811149.7981DT9B6ODOaitiun lernperaiure3ee.4B613te,4063M59QOQError935.740B311.27Total166644.27007SoirectedTolal3324.353晡a R Squared = .719 (Miusted R

24、 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=935.748，dferror=83， MSerror=935.748 ； Faltitude=44.63， p=0.0340.001;Ftemperature=

25、101.986,p=0.0050.001;Ftemperature=101.986,0.001;Finteraction=34.458 ， p0.001;所以故認為在0.1%的置信水平上，不同溫度，不同海拔之間的草高度是存在差異的。Estimated Marginal Means1f Grand |H eanDependent Variable: h 已 ight (nim) to flowerM3nStd Error9f% Confidence IntivalLcwer BoundUpper Bound138.4463C5137710139 1722、altitudeEstimatesDe

26、pendent Variable height (mni) to flows raltitudeMsanStd. Error95% Confidence IntervalLower BoundUpper Bound3200 m140.686.52013S.6521d1.9203400 m136.005.513134,985137.026在海拔為3200米處，在95%的置信區間，花的平均高度范圍為 139.852到141.920之間。 在海拔為3400米處，在95%的置信區間，花的平均高度范圍為 134.985到137.036之間。Pairwise ConwrisonsDependent Var

27、iable: 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工貯7Basd on eslmat&d margina means* The mean difference iw sigiificant at the .05 level.b. Adj

28、 u slm ent far mu tip 柜 comparisons: Least Significantir&rence (equivale rtto no adjustments aititude各水平的邊際均值的多重比擬，在本試驗中，事實上？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%置信區間為3.427到6.333.故均值存在差異。Univariate TestsDependent Variable: height (mm to flowerSun ofSquaresdfMe

29、an 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=503.167, dfaltitude=1 ， MSaltitude=503.167 ；SSerror=935.748, dferror=83 ,MSerror=935.7

30、48 ; Faltitude=44.63 , P0.001.不同海拔的花高度不存在差異的的概率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在溫度為T1處，在95%的置信區間，花的平均高度范圍為141.149到143.119之間。在溫度為T2處，在95%的置信區間，花的平均高度范圍為133.689到135.825之間。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