The SAS System 1 --------------------------------- IRISTYPE=1 --------------------------------- Correlation Analysis 2 'VAR' Variables: SWIDTH PWIDTH Covariance Matrix DF = 49 SWIDTH PWIDTH SWIDTH 0.1436897959 0.0092979592 PWIDTH 0.0092979592 0.0111061224 Simple Statistics Variable N Mean Std Dev Sum Minimum Maximum SWIDTH 50 3.4280 0.3791 171.4000 2.3000 4.4000 PWIDTH 50 0.2460 0.1054 12.3000 0.1000 0.6000 Pearson Correlation Coefficients / N = 50 SWIDTH PWIDTH SWIDTH 1.00000 0.23275 PWIDTH 0.23275 1.00000 The SAS System 2 --------------------------------- IRISTYPE=2 --------------------------------- Correlation Analysis 2 'VAR' Variables: SWIDTH PWIDTH Covariance Matrix DF = 49 SWIDTH PWIDTH SWIDTH 0.0984693878 0.0412040816 PWIDTH 0.0412040816 0.0391061224 Simple Statistics Variable N Mean Std Dev Sum Minimum Maximum SWIDTH 50 2.7700 0.3138 138.5000 2.0000 3.4000 PWIDTH 50 1.3260 0.1978 66.3000 1.0000 1.8000 Pearson Correlation Coefficients / N = 50 SWIDTH PWIDTH SWIDTH 1.00000 0.66400 PWIDTH 0.66400 1.00000 The SAS System 3 --------------------------------- IRISTYPE=3 --------------------------------- Correlation Analysis 2 'VAR' Variables: SWIDTH PWIDTH Covariance Matrix DF = 49 SWIDTH PWIDTH SWIDTH 0.1040040816 0.0476285714 PWIDTH 0.0476285714 0.0754326531 Simple Statistics Variable N Mean Std Dev Sum Minimum Maximum SWIDTH 50 2.9740 0.3225 148.7000 2.2000 3.8000 PWIDTH 50 2.0260 0.2747 101.3000 1.4000 2.5000 Pearson Correlation Coefficients / N = 50 SWIDTH PWIDTH SWIDTH 1.00000 0.53773 PWIDTH 0.53773 1.00000 One-way MANOVA on Iris Width Data using PROC IML 4 SSCP_Trt is B 11.344933 -22.93267 -22.93267 80.413333 SSCP_E is W 16.962 4.8084 4.8084 6.1566 SSCP_Tot is T 28.306933 -18.12427 -18.12427 86.569933 Wilks Lambda is LAMBDAST 0.0383157 TESTSTAT PVAL 299.93596 0 One-way MANOVA on Iris Width Data Using PROC GLM 5 General Linear Models Procedure Class Level Information Class Levels Values IRISTYPE 3 1 2 3 Number of observations in data set = 150 One-way MANOVA on Iris Width Data Using PROC GLM 6 General Linear Models Procedure Least Squares Means IRISTYPE SWIDTH PWIDTH LSMEAN LSMEAN 1 3.42800000 0.24600000 2 2.77000000 1.32600000 3 2.97400000 2.02600000 E = Error SS&CP Matrix SWIDTH PWIDTH SWIDTH 16.962 4.8084 PWIDTH 4.8084 6.1566 One-way MANOVA on Iris Width Data Using PROC GLM 7 General Linear Models Procedure Multivariate Analysis of Variance Partial Correlation Coefficients from the Error SS&CP Matrix / Prob > |r| DF = 147 SWIDTH PWIDTH SWIDTH 1.000000 0.470535 0.0001 0.0001 PWIDTH 0.470535 1.000000 0.0001 0.0001 One-way MANOVA on Iris Width Data Using PROC GLM 8 General Linear Models Procedure Multivariate Analysis of Variance H = Type III SS&CP Matrix for IRISTYPE SWIDTH PWIDTH SWIDTH 11.344933333 -22.93266667 PWIDTH -22.93266667 80.413333333 Characteristic Roots and Vectors of: E Inverse * H, where H = Type III SS&CP Matrix for IRISTYPE E = Error SS&CP Matrix Characteristic Percent Characteristic Vector V'EV=1 Root SWIDTH PWIDTH 20.1106009 98.84 -0.16388207 0.45174660 0.2362953 1.16 0.22104883 0.06738212 Manova Test Criteria and F Approximations for the Hypothesis of no Overall IRISTYPE Effect H = Type III SS&CP Matrix for IRISTYPE E = Error SS&CP Matrix S=2 M=-0.5 N=72 Statistic Value F Num DF Den DF Pr > F Wilks' Lambda 0.03831574 299.936 4 292 0.0001 Pillai's Trace 1.14376219 98.181 4 294 0.0001 Hotelling-Lawley Trace 20.34689616 737.575 4 290 0.0001 Roy's Greatest Root 20.11060086 1478.129 2 147 0.0001 NOTE: F Statistic for Roy's Greatest Root is an upper bound. NOTE: F Statistic for Wilks' Lambda is exact. One-way MANOVA on Iris Width Data Using PROC GLM 9 OBS _NAME_ _SOURCE_ _TYPE_ SWIDTH PWIDTH DF SS F PROB 1 SWIDTH ERROR ERROR 16.9620 4.8084 147 16.9620 . . 2 PWIDTH ERROR ERROR 4.8084 6.1566 147 6.1566 . . 3 SWIDTH IRISTYPE SS3 11.3449 -22.9327 2 11.3449 49.160 4.492E-17 4 PWIDTH IRISTYPE SS3 -22.9327 80.4133 2 80.4133 960.007 4.1694E-85 One-way MANOVA on Iris Width Data Using PROC GLM 10 OBS _NAME_ IRISTYPE LSMEAN STDERR 1 SWIDTH 1 3.428 0.048039 2 SWIDTH 2 2.770 0.048039 3 SWIDTH 3 2.974 0.048039 4 PWIDTH 1 0.246 0.028942 5 PWIDTH 2 1.326 0.028942 6 PWIDTH 3 2.026 0.028942 One-way MANOVA on Iris Width Data Using PROC GLM 11 Bonferroni Simultaneous Confidence intervals between treatments j,k I For variable 1 J K For difference between treatments 1 2 LOWLIM UPLIM 0.4763056 0.8396944 J K For difference between treatments 1 3 LOWLIM UPLIM 0.2723056 0.6356944 J K For difference between treatments 2 3 LOWLIM UPLIM -0.385694 -0.022306 I For variable 2 J K For difference between treatments 1 2 LOWLIM UPLIM -1.189465 -0.970535 J K For difference between treatments 1 3 LOWLIM UPLIM -1.889465 -1.670535 J K For difference between treatments 2 3 LOWLIM UPLIM -0.809465 -0.590535