SPSS新手簡(jiǎn)明教程6

1、第六章 方差分析第一節(jié) Simple Factorial過(guò)程6.1.1 主要功能6.1.2 實(shí)例操作第二節(jié) General Factorial過(guò)程6.2.1 主要功能6.2.2 實(shí)例操作第三節(jié) Multivarite過(guò)程6.3.1 主要功能6.3.2 實(shí)例操作 方差分析是R.A.Fister發(fā)明的，用于兩個(gè)及兩個(gè)以上樣本均數(shù)差別的顯著性檢驗(yàn)。由于各種因素的影響，研究所得的數(shù)據(jù)呈現(xiàn)波動(dòng)狀，造成波動(dòng)的原因可分成兩類，一是不可控的隨機(jī)因素，另一是研究中施加的對(duì)結(jié)果形成影響的可控因素。方差分析的基本思想是：通過(guò)分析研究中不同來(lái)源的變異對(duì)總變異的貢獻(xiàn)大小，從而確定可控因素對(duì)研究結(jié)果影響力的大小

2、。方差分析主要用于：1、均數(shù)差別的顯著性檢驗(yàn)，2、分離各有關(guān)因素并估計(jì)其對(duì)總變異的作用，3、分析因素間的交互作用，4、方差齊性檢驗(yàn)。 第一節(jié) Simple Factorial過(guò)程  主要功能調(diào)用此過(guò)程可對(duì)資料進(jìn)行方差分析或協(xié)方差分析。在方差分析中可按用戶需要作單因素方差分析（其結(jié)果將與第五章第四節(jié)相同）或多因素方差分析（包括醫(yī)學(xué)中常用的配伍組方差分析）；當(dāng)觀察因素中存在有很難或無(wú)法人為控制的因素時(shí)，則可對(duì)之加以指定以便進(jìn)行協(xié)方差分析。 返回目錄 返回全書(shū)目錄 實(shí)例操作例6-1下表為運(yùn)動(dòng)員與大學(xué)生的身高（cm）與肺活量（cm3）的數(shù)據(jù)，考慮到身高與肺活量有關(guān)，而一般

3、運(yùn)動(dòng)員的身高高于大學(xué)生，為進(jìn)一步分析肺活量的差異是否由于體育鍛煉所致，試作控制身高變量的協(xié)方差分析。 運(yùn) 動(dòng) 員大 學(xué) 生身高肺活量身高肺活量184.9167.9171.0171.0188.0179.0177.0179.5187.0187.0169.0188.0176.7179.0183.0180.5179.0178.0164.0174.043003850410043004800400054004000480048004500478037005250425048005000370036004050168.7170.8165.0169.7171.5166.5165.0165.0173.

4、0169.0173.8174.0170.5176.0169.5176.3163.0172.5177.0173.034504100380033003450325036003200395040004150345032504100365039503500390034503850 .1 數(shù)據(jù)準(zhǔn)備激活數(shù)據(jù)管理窗口，定義變量名：組變量為group（運(yùn)動(dòng)員=1，大學(xué)生=2），身高為x，肺活量為y，按順序輸入相應(yīng)數(shù)值，建立數(shù)據(jù)庫(kù)，結(jié)果見(jiàn)圖6.1。  圖6.1 原始數(shù)據(jù)的輸入 .2 統(tǒng)計(jì)分析 激活 Statistics 菜單選ANOVA Models中的Simple Fa

5、ctorial.項(xiàng)，彈出Simple Factorial ANOVA對(duì)話框（圖6.2）。在變量列表中選變量y，點(diǎn)擊Ø鈕使之進(jìn)入Dependent框；選分組變量group，點(diǎn)擊Ø鈕使之進(jìn)入Factor(s)框中, 并點(diǎn)擊Define Range.鈕在彈出的Simple Factorial ANOVA:Define Range框中確定分組變量group的起止值（1,2）；選協(xié)變量x，點(diǎn)擊Ø鈕使之進(jìn)入Covariate(s)框中。  圖6.2 協(xié)方差分析對(duì)話框 點(diǎn)擊Options.框，彈出Simple Factorial ANOVA:Opt

6、ions對(duì)話框。系統(tǒng)在協(xié)方差分析的方法（Method）上有三種選項(xiàng)：1、Unique：同時(shí)評(píng)價(jià)所有的效應(yīng)；2、Hierarchical：除主效應(yīng)外，逐一評(píng)價(jià)各因素的效應(yīng)；3、Experimental：評(píng)價(jià)因素干預(yù)之前的主效應(yīng)。本例選Unique方法，之后點(diǎn)擊Continue鈕返回Simple Factorial ANOVA對(duì)話框，再點(diǎn)擊OK鈕即可。 .3 結(jié)果解釋 在結(jié)果輸出窗口中可見(jiàn)如下統(tǒng)計(jì)數(shù)據(jù)：先輸出肺活量總均數(shù)和兩組的肺活量均數(shù)，總均數(shù)為4033.25，運(yùn)用員組均數(shù)為4399.00，大學(xué)生組為3667.50。接著協(xié)方差分析表明，混雜因素X（身高）兩組間是有差異的（F=

7、10.679，P=0.002），控制其影響后，兩組間肺活量的差別依然存在（F=9.220，P=0.004），故可以認(rèn)為兩組間肺活量的均數(shù)在消除了身高因素的影響之后仍有差別，運(yùn)動(dòng)員的肺活量大于大學(xué)生，即體育鍛煉會(huì)提高肺活量。最后系統(tǒng)輸出公共回歸系數(shù)，= 36.002，該值可用于求修正均數(shù)： = - ( - )本例為= 4399.00 - 36.002×（178.175 - 174.3325）= 4260.6623 = 3667.50 - 36.002×（170.49 - 174.3325）= 3805.8377 Y by GROUPTotal Population

8、4033.25 ( 40) GROUP 1 2 4399.00 3667.50 ( 20) ( 20)Y by GROUP with X UNIQUE sums of squares All effects entered simultaneously Sum of Mean SigSource of Variation Squares DF Square F of FCovariates 1630763 1 1630762.635 10.679 .002 X 1630763 1 1630762.635 10.679 .002Main Effects 1407847 1 140784

9、7.095 9.220 .004 GROUP 1407847 1 1407847.095 9.220 .004Explained 6981685 2 3490842.568 22.860 .000Residual 5649992 37 152702.496 Total 12631678 39 323889.167 40 cases were processed.0 cases (.0 pct) were missing.Covariate Raw Regression CoefficientX 36.002  返回目錄 返回全書(shū)目錄 第二節(jié) G

10、eneral Factorial過(guò)程  主要功能調(diào)用此過(guò)程可對(duì)完全隨機(jī)設(shè)計(jì)資料、配伍設(shè)計(jì)資料、析因設(shè)計(jì)資料、正交設(shè)計(jì)資料等等進(jìn)行多因素方差分析或協(xié)方差分析。返回目錄 返回全書(shū)目錄  實(shí)例操作例6-2下表為三因素析因?qū)嶒?yàn)的資料，請(qǐng)用方差分析說(shuō)明不同基礎(chǔ)液與不同血清種類對(duì)鉤端螺旋體的培養(yǎng)計(jì)數(shù)的影響。 基礎(chǔ)液（A）血清種類（B）兔血清濃度（C）胎盤血清濃度（C）5858緩沖液64812461398909114418771671184583085344110305786696431002蒸餾水1763124113812421144718831896192692070984

11、857493310241092742自來(lái)水580 1026102683017891215143416511126117612801212685546595566 .1 數(shù)據(jù)準(zhǔn)備 激活數(shù)據(jù)管理窗口，定義變量名：基礎(chǔ)液為base，血清種類為sero，血清濃度為pct，鉤端螺旋體的培養(yǎng)計(jì)數(shù)為X，按順序輸入相應(yīng)數(shù)值，建立數(shù)據(jù)庫(kù)。 .2 統(tǒng)計(jì)分析 激活Statistics菜單選ANOVA Models中的General Factorial.項(xiàng)，彈出General Factorial ANOVA對(duì)話框（圖6.3）。在對(duì)話框左側(cè)的變量列表中選變量x，點(diǎn)擊Ø鈕使之進(jìn)入Depend

12、ent Variable框；選要控制的分組變量base、sero和pct，點(diǎn)Ø鈕使之進(jìn)入Factor(s)框中，并分別點(diǎn)擊Define Range鈕，在彈出的General Factorial ANOVA:Define Range對(duì)話框中確定各變量的起止值，本例變量base的起止值為1、3，變量sero的起止值為1、2，變量pct的起止值為1、2。之后點(diǎn)擊OK鈕即可。  圖6.3 析因方差分析對(duì)話框  .3 結(jié)果解釋  在結(jié)果輸出窗口中，系統(tǒng)顯示48個(gè)觀察值進(jìn)入統(tǒng)計(jì)，三個(gè)因素按其各自水平共產(chǎn)生12種組合。分析表明，模型總效應(yīng)

13、的F值為10.55，P值 < 0.001，說(shuō)明三因素間存在有交互作用。單因素效應(yīng)和交互效應(yīng)導(dǎo)致的組間差別比較結(jié)果是：?jiǎn)我蛩亟M間比較：A：基礎(chǔ)液（BASE）F = 4.98，P = 0.012，說(shuō)明三種培養(yǎng)基培養(yǎng)鉤體的計(jì)數(shù)有差別；B：血清種類（SERO）F = 61.265，P < 0.001，說(shuō)明兩種血清培養(yǎng)鉤體的計(jì)數(shù)有差別；C：血清濃度（PCT）F = 3.49，P = 0.070，說(shuō)明兩種血清濃度培養(yǎng)鉤體的計(jì)數(shù)無(wú)差別。 兩因素構(gòu)成的一級(jí)交互作用： A×B：基礎(chǔ)液（BASE）×血清種類（SERO） F = 5.16，P = 0.011，交互作用明顯； B

14、15;C：血清種類（SERO）×血清濃度（PCT） F = 15.96，P < 0.001，交互作用明顯； A×C：基礎(chǔ)液（BASE）×血清濃度（PCT） F = 0.78，P = 0.465，交互作用不明顯。 三因素構(gòu)成的二級(jí)交互作用： A×B×C：基礎(chǔ)液（BASE）×血清種類（SERO）×血清濃度（PCT） F = 6.75，P = 0.003，交互作用明顯。 48 cases accepted. 0 cases rejected because of out-of-range factor values

15、. 0 cases rejected because of missing data.12 non-empty cells. 1 design will be processed. - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Univariate Homogeneity of Variance Tests Variable . X Cochrans C(3,12) = .34004, P = .036 (approx.) Bartlett-Box F(11,897) = 1.69822, P

16、 = .069 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -* * * * * * A n a l y s i s o f V a r i a n c e - design 1 * * * * * * Tests of Significance for X using UNIQUE sums of squares Source of Variation SS DF MS F Sig of F WITHIN+RESIDUAL 2459233.75 36 68312.05 BASE 679967.

17、38 2 339983.69 4.98 .012 PCT 238713.02 1 238713.02 3.49 .070 SERO 4184873.52 1 4184873.5 61.26 .000 BASE BY PCT 107005.54 2 53502.77 .78 .465 BASE BY SERO 705473.04 2 352736.52 5.16 .011 PCT BY SERO 1089922.69 1 1089922.7 15.96 .000 BASE BY PCT BY SERO 922307.37 2 461153.69 6.75 .003 (Model) 7928262

18、.56 11 720751.14 10.55 .000 (Total) 10387496.31 47 221010.56  R-Squared = .763 Adjusted R-Squared = .691  返回目錄 返回全書(shū)目錄 第三節(jié) Multivarite過(guò)程  主要功能 調(diào)用此過(guò)程可進(jìn)行多元方差分析。此外，對(duì)于一元設(shè)計(jì)，如涉及混合模型的設(shè)計(jì)、分割設(shè)計(jì)（又稱列區(qū)設(shè)計(jì)）、重復(fù)測(cè)量設(shè)計(jì)、嵌套設(shè)計(jì)、因子與協(xié)變量交互效應(yīng)設(shè)計(jì)等，此過(guò)程均能適用。 返回目錄 返回全書(shū)目錄  實(shí)例操作例6-3甲地區(qū)為大城市，乙地區(qū)為縣城，丙地區(qū)

19、為農(nóng)村。某地分別調(diào)查了上述三類地區(qū)8歲男生三項(xiàng)身體生長(zhǎng)發(fā)育指標(biāo)：身高、體重和胸圍，數(shù)據(jù)見(jiàn)下表，問(wèn)：三類地區(qū)之間男生三項(xiàng)身體生長(zhǎng)發(fā)育指標(biāo)的差異有無(wú)顯著性？ 學(xué)生編號(hào)甲地區(qū)乙地區(qū)丙地區(qū)身高體重胸圍身高體重胸圍身高體重胸圍123456789101112131415161718192021222324252627282930119.80121.70121.40124.40120.00117.00118.10118.80124.20124.90124.70123.00125.30124.20127.40128.20126.10128.70129.50126.90126.50128.20131.

20、40130.80133.90130.40131.30130.20136.00141.0022.6021.5019.1021.8021.4020.1018.8022.0021.3024.0023.3022.5022.9019.5022.9022.3022.7023.5024.5025.5025.0026.1027.9026.8027.2024.4024.4023.0026.3031.9060.5055.5056.5060.5057.7057.0057.1061.7058.4060.8060.0060.0065.2053.8059.5060.0057.4060.4051.0061.5063.906

21、3.0063.1061.5065.8062.6059.5062.6060.0063.70125.10127.00125.70114.90124.90117.60124.20117.90120.40115.00126.20125.10114.90121.50114.00118.70120.60122.90119.60112.30121.30121.20120.20120.30120.00123.30122.10123.30109.90125.6023.0021.5023.4017.5023.5018.9020.8020.3020.0019.7021.2022.1019.7022.0019.001

22、9.1020.0018.5019.5020.0020.0021.2023.1021.0022.2020.1021.0021.5017.8023.3062.0059.0061.5052.5058.5057.0058.5061.0056.0056.5056.5058.5056.0057.0054.5054.5055.5056.0059.5058.0058.0059.0059.5059.5059.5056.5057.5061.0056.5060.50118.30121.30121.80124.20123.50123.00134.90123.70105.20112.20118.60112.00121.

23、50124.50119.50122.50115.50122.50124.50125.00117.50127.30122.30121.30120.50116.00120.50114.50131.00122.5020.4020.0026.6022.1023.2022.9032.3022.7020.2020.8021.0023.2024.0021.5020.5023.0019.0022.5025.0025.5023.0022.5022.0021.0022.0019.0020.0019.0025.5024.5054.4054.3061.1058.6060.2058.2064.8059.9054.505

24、7.5057.6058.2060.3055.6055.5056.7054.2057.6057.9060.3059.0058.9058.2055.6055.1053.5054.4053.4058.3058.70 .1 數(shù)據(jù)準(zhǔn)備 激活數(shù)據(jù)管理窗口，定義變量名：地區(qū)為G，身高為X1，體重為X2，胸圍為X3，按順序輸入相應(yīng)數(shù)值，變量G的數(shù)值是：甲地區(qū)為1，乙地區(qū)為2，丙地區(qū)為3。 .2 統(tǒng)計(jì)分析 激活Statistics菜單選ANOVA Models中的Multivarite.項(xiàng)，彈出Multivarite ANOVA 對(duì)話框（圖6.8）。首先指定供分析用的變量x1、x2、x3，故

25、在對(duì)話框左側(cè)的變量列表中選變量x1、x2、x3，點(diǎn)擊Ø鈕使之進(jìn)入Dependent Variable框；然后選變量g（分組變量）點(diǎn)擊Ø鈕使之進(jìn)入Factor(s)框中，并點(diǎn)擊Define Range鈕，確定g的起始值和終止值。  圖6.4 多元方差分析對(duì)話框 點(diǎn)擊Options.鈕，彈出Multivarite ANOVA:Options對(duì)話框，選擇需要計(jì)算的指標(biāo)。在Factor(s)欄內(nèi)選變量g，點(diǎn)擊Ø鈕使之進(jìn)入Display Means for框，要求計(jì)算平均值指標(biāo)；在Matriced Within Cell欄內(nèi)選Correlati

26、on、Covariance、SSCP項(xiàng)，要求計(jì)算單元內(nèi)的相關(guān)矩陣、方差協(xié)方差矩陣和離均差平方和交叉乘積矩陣；在Error Matrices欄內(nèi)也選上述三項(xiàng)，要求計(jì)算誤差的相關(guān)矩陣、方差協(xié)方差矩陣和離均差平方和交叉乘積矩陣；在Diagnostics欄內(nèi)選Homogeneity test項(xiàng)，要求作變量的方差齊性檢驗(yàn)。之后點(diǎn)擊Continue鈕返回Multivarite ANOVA對(duì)話框，最后點(diǎn)擊OK鈕即可。 .3 結(jié)果解釋       在結(jié)果輸出窗口中將看到如下分析結(jié)果：系統(tǒng)首先顯示共90個(gè)觀察值進(jìn)入統(tǒng)計(jì)分析，因分組變量g為三個(gè)

27、地區(qū)，故分析的單元數(shù)為3。然后輸出3個(gè)應(yīng)變量（x1、x2、x3）的方差齊性檢驗(yàn)結(jié)果，分別輸出了Cochran C檢驗(yàn)值及其顯著性水平P值、Bartlett-Box F檢驗(yàn)值及其顯著性水平P值。其中身高：C = 0.39825，P = 0.540；F = 1.01272，P = 0.363；體重：C = 0.43787，P = 0.227；F = 4.48624, P = 0.011；胸圍：C = 0.47239, P = 0.089；F = 2.06585, P = 0.127；可見(jiàn)3項(xiàng)指標(biāo)的方差基本整齊（P值均大于0.05）。 90 cases accepted. 0 cases

28、rejected because of out-of-range factor values. 0 cases rejected because of missing data. 3 non-empty cells.  1 design will be processed.  CELL NUMBER 1 2 3 Variable G 1 2 3  Univariate Homogeneity of Variance Tests Variable . X1 Cochrans C(29,3) = .39825, P = .540 (approx.) Bartlett-

29、Box F(2,17030) = 1.01272, P = .363 Variable . X2 Cochrans C(29,3) = .43787, P = .227 (approx.) Bartlett-Box F(2,17030) = 4.48624, P = .011 Variable . X3 Cochrans C(29,3) = .47239, P = .089 (approx.) Bartlett-Box F(2,17030) = 2.06585, P = .127  Cochran C檢驗(yàn)和Bartlett-Box F檢驗(yàn)對(duì)考查協(xié)方差矩陣的相等性比較方便，但

30、還不夠。于是系統(tǒng)接著分別輸出了三類地區(qū)（即各個(gè)單元）各生長(zhǎng)發(fā)育指標(biāo)的離均差平方和交叉乘積矩陣和方差協(xié)方差矩陣。之后作Box M檢驗(yàn)，Box M檢驗(yàn)提供矩陣一致性的多元測(cè)試，本例Boxs M = 36.93910，在基于方差分析的顯著性檢驗(yàn)中F = 2.92393；在基于2的顯著性檢驗(yàn)中2 = 35.09922, 兩者P < 0.001，故認(rèn)為矩陣一致性不佳。 Cell Number . 1 Sum of Squares and Cross-Products matrix X1 X2 X3 X1 861.187 X2 380.137 230.519 X3 215.937 156.

31、559 314.859  Variance-Covariance matrix X1 X2 X3 X1 29.696 X2 13.108 7.949 X3 7.446 5.399 10.857  Cell Number . 1 (Cont.) Correlation matrix with Standard Deviations on Diagonal X1 X2 X3 X1 5.449 X2 .853 2.819 X3 .415 .581 3.295  Determinant of Covariance matrix of dependent variables

32、 = 444.98354 LOG(Determinant) = 6.09804  Cell Number . 2 Sum of Squares and Cross-Products matrix X1 X2 X3 X1 565.368 X2 147.222 78.910 X3 139.430 79.337 147.967  Variance-Covariance matrix X1 X2 X3 X1 19.495 X2 5.077 2.721 X3 4.808 2.736 5.102  Correlation matrix with Standard Deviat

33、ions on Diagonal X1 X2 X3 X1 4.415 X2 .697 1.650 X3 .482 .734 2.259  Determinant of Covariance matrix of dependent variables = 63.90640 LOG(Determinant) = 4.15742  Cell Number . 3 Sum of Squares and Cross-Products matrix X1 X2 X3 X1 944.128 X2 307.722 217.030 X3 261.130 186.252 203.702

34、0; Variance-Covariance matrix X1 X2 X3 X1 32.556 X2 10.611 7.484 X3 9.004 6.422 7.024  Correlation matrix with Standard Deviations on Diagonal X1 X2 X3 X1 5.706 X2 .680 2.736 X3 .595 .886 2.650  Determinant of Covariance matrix of dependent variables = 198.13507 LOG(Determinant) = 5.28895&

35、#160; Pooled within-cells Variance-Covariance matrix X1 X2 X3 X1 27.249 X2 9.599 6.051 X3 7.086 4.852 7.661  Determinant of pooled Covariance matrix of dependent vars. = 272.06906 LOG(Determinant) = 5.60606  Multivariate test for Homogeneity of Dispersion matrices  Boxs M = 36.93910 F

36、 WITH (12,36680) DF = 2.92393, P = .000 (Approx.) Chi-Square with 12 DF = 35.09922, P = .000 (Approx.)  下面系統(tǒng)輸出將三類地區(qū)看成一個(gè)大樣本時(shí)的離均差平方和交叉乘積矩陣。如X1、X2和X3的離均差平方和分別為662.884、121.562和114.902。在此基礎(chǔ)上，進(jìn)行多元差異的檢驗(yàn)。通常有四種方法：1、Pillai軌跡：V = 2、Wilks 值：W = 3、Hotelling軌跡：T = 4、Roy最大根：R = 式中max為最大特征值, i為第i個(gè)特征值,s為非零

37、特征值個(gè)數(shù)。根據(jù)這些值變換的F檢驗(yàn)均有顯著性（P<0.001），說(shuō)明三類地區(qū)各生長(zhǎng)發(fā)育指標(biāo)之間的差別有高度顯著性。 這一計(jì)算結(jié)果對(duì)上述三項(xiàng)生長(zhǎng)發(fā)育指標(biāo)進(jìn)行了單因素的方差分析，可見(jiàn)： X1: SS = 662.88356, F = 12.16335 X2: SS = 121.56200, F = 10.04439 X3: SS = 114.90200, F = 7.49893差別均有顯著性，說(shuō)明三項(xiàng)生長(zhǎng)發(fā)育指標(biāo)各地區(qū)間的差別均有顯著性。 Combined Observed Means for G Variable . X1 G 1 WGT. 126.46667 UNWGT. 12

38、6.46667 2 WGT. 120.52000 UNWGT. 120.52000 3 WGT. 120.92000 UNWGT. 120.92000 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Variable . X2 G 1 WGT. 23.50667 UNWGT. 23.50667 2 WGT. 20.69667 UNWGT. 20.69667 3 WGT. 22.49667 UNWGT. 22.49667 - - - - - - - - - - - - - - - - - - -

39、- - - - - - - - - - - - - - - - - - Variable . X3 G 1 WGT. 60.00667 UNWGT. 60.00667 2 WGT. 57.86667 UNWGT. 57.86667 3 WGT. 57.41667 UNWGT. 57.41667 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - WITHIN+RESIDUAL Correlations with Std. Devs. on Diagonal X1 X2 X3 X1 5.220 X2

40、.747 2.460 X3 .490 .713 2.768 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Statistics for WITHIN+RESIDUAL correlations Log(Determinant) = .00000 Bartlett test of sphericity = . with 3 D. F. Significance = . F(max) criterion = 4.50308 with (3,87) D. F.  WITHIN+RESIDU

41、AL Variances and Covariances X1 X2 X3 X1 27.249 X2 9.599 6.051 X3 7.086 4.852 7.661 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - WITHIN+RESIDUAL Sum-of-Squares and Cross-Products X1 X2 X3 X1 2370.683 X2 835.081 526.458 X3 616.497 422.147 666.527 - - - - - - - - - - - - -

42、 - - - - - - - - - - - - - - - - - - - - - - - - EFFECT . G Adjusted Hypothesis Sum-of-Squares and Cross-Products X1 X2 X3 X1 662.884 X2 230.323 121.562 X3 269.117 78.193 114.902 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Multivariate Tests of Significance (S = 2, M =

43、0, N = 41 1/2) Test Name Value Approx.F Hypoth. DF Error DF Sig. of F Pillais .51227 9.87080 6.00 172.00 .000 Hotellings .70427 9.85978 6.00 168.00 .000 Wilks .55014 9.86643 6.00 170.00 .000 Roys .31265 Note. F statistic for WILKS' Lambda is exact. - - - - - - - - - - - - - - - - - - - - - - - -

44、 - - - - - - - - - - - - - EFFECT . G (Cont.) Univariate F-tests with (2,87) D. F. Variable Hypoth. SS Error SS Hypoth. MS Error MS F Sig. of F X1 662.88356 2370.68267 331.44178 27.24923 12.16335 .000 X2 121.56200 526.45800 60.78100 6.05124 10.04439 .000 X3 114.90200 666.52700 57.45100 7.66123 7.49893 .001  之后按單元輸出各項(xiàng)指標(biāo)的觀察值均數(shù)（Obs.Mean）、調(diào)整均數(shù)（Adj.Mean）、估計(jì)均數(shù)（Est.Mean）、粗誤差（Raw Resid）、標(biāo)準(zhǔn)化誤差（Std.Resid）以及不分地區(qū)的總均數(shù)（Comined Adjusted Means for G）。 Adjusted and Estimated Means Variable . X1 CELL Obs. Mean