1、協方差分析 年齡是肺活量的影響因素,年齡稱為混雜因素或協變量，要比較兩組工人肺活量的差異, 需控制年齡的混雜作用。 協方差分析是將直線回歸和方差分析結合起來的一種統計方法。其基本思想是在作多組均數(Y1Y2YK)比較之前, 用直線回歸的方法找出各組Y與協變量的數量關系, 求得在假定協變量相等時的修正均數, 然后用方差分析比較修正均數間的差別。協方差分析是控制混雜因素的重要手段之一。 協方差分析的假定: 各組樣本是從具有相同方差的正態總體中隨機抽出的 協變量與Y的線性關系在各組均成立, 而且各組間的總體回歸系數應相等65605550454035ageage6. 005. 004. 003. 00

2、l ungl ungFi t l i ne f or 10年Fi t l i ne f or 10年10年暴露分組R Sq Li near = 0. 342R Sq Li near = 0. 563初步判斷假設是否成立兩組散點圖: 兩組工人年齡和肺活量有明顯的線性趨勢, 初步判斷斜率相近兩組年齡分布基本一致, 離散程度差別不大 Tests of Between-Subjects EffectsDependent Variable: LUNG9.838a33.2797.191.00137.216137.21681.602.0007.412E-0217.412E-02.163.6908.64118

3、.64118.947.0002.842E-0212.842E-02.062.80510.94524.456479.5682820.78327SourceCorrected ModelInterceptGROUPAGEGROUP * AGEErrorTotalCorrected TotalType III Sumof SquaresdfMean SquareFSig.R Squared = .473 (Adjusted R Squared = .408)a. F交=0.062, P=0.805,交互作用無統計學意義 協方差分析AnalyzeGLMUnivariate Dependent List

4、: lung Fixed factor: group Covariates:age Model :custom Build term: main effect Model : group、age Options : Display means for: group Compare main effect（LSD） homogeneity testsOKLevenes Test of Equality of Error VariancesLevenes Test of Equality of Error Variancesa aDependent Variable: lung.237126.63

5、0Fdf1df2Sig.Tests the null hypothesis that the error variance ofthe dependent variable is equal across groups.Design: Intercept+group+agea. 方差齊性檢驗結果顯示：F=0.237,P=0.630方差齊Tests of Between-Subjects EffectsDependent Variable: LUNG9.810a24.90511.174.00039.422139.42289.809.000.4441.4441.011.3249.60519.605

6、21.882.00010.97425.439479.5682820.78327SourceCorrected ModelInterceptGROUPAGEErrorTotalCorrected TotalType III Sumof SquaresdfMean SquareFSig.R Squared = .472 (Adjusted R Squared = .430)a. 方差分析顯示兩組肺活量差異無統計學意義。年齡對肺活量有影響。EstimatesEstimatesDependent Variable: lung3.931a.1713.5804.2834.203a.1993.7944.61

7、3暴露分組10年MeanStd. ErrorLower BoundUpper Bound95% Confidence IntervalCovariates appearing in the model are evaluated at thefollowing values: age = 46.64.a. 上表顯示當兩組年齡均數都為46.64時，兩組 的修正均數分別為：3.931和4.203。P Pa ai ir rw wi is se e C Co om mp pa ar ri is so on ns sDependent Variable: lung-.272.270.324-.828.285.272.270.324-.285.828(J) 暴露分組10年10年(I) 暴露分組10年MeanDifference(I-J)Std. ErrorSig.aLower BoundUpper Bound95% Confidence Interval forDifferenceaBased on estimated marginal meansAdjustment for multiple comparisons: Least Significant Differen