The SAS System 1 ----------------------------------- TRT=1 ------------------------------------ Correlation Analysis 5 'VAR' Variables: CKG_LOSS PH MOIST FAT HEX Covariance Matrix DF = 4 CKG_LOSS PH MOIST FAT HEX CKG_LOSS 2.545000000 0.302250000 -2.006250000 0.244750000 0.019000000 PH 0.302250000 0.223080000 0.440270000 -0.015450000 0.108980000 MOIST -2.006250000 0.440270000 4.493980000 -0.936400000 0.205620000 FAT 0.244750000 -0.015450000 -0.936400000 0.785900000 0.186600000 HEX 0.019000000 0.108980000 0.205620000 0.186600000 0.125880000 Simple Statistics Variable N Mean Std Dev Sum Minimum Maximum CKG_LOSS 5 37.1000 1.5953 185.5000 34.8000 38.5000 PH 5 6.5260 0.4723 32.6300 6.2000 7.3400 MOIST 5 58.1840 2.1199 290.9200 56.2500 61.4000 FAT 5 10.3500 0.8865 51.7500 9.3500 11.7200 HEX 5 1.0560 0.3548 5.2800 0.5800 1.4800 Pearson Correlation Coefficients / N = 5 CKG_LOSS PH MOIST FAT HEX CKG_LOSS 1.00000 0.40114 -0.59323 0.17306 0.03357 PH 0.40114 1.00000 0.43972 -0.03690 0.65034 MOIST -0.59323 0.43972 1.00000 -0.49827 0.27338 FAT 0.17306 -0.03690 -0.49827 1.00000 0.59327 HEX 0.03357 0.65034 0.27338 0.59327 1.00000 The SAS System 2 ----------------------------------- TRT=2 ------------------------------------ Correlation Analysis 5 'VAR' Variables: CKG_LOSS PH MOIST FAT HEX Covariance Matrix DF = 4 CKG_LOSS PH MOIST FAT HEX CKG_LOSS 1.752000000 -0.148800000 -0.101800000 0.198100000 0.421700000 PH -0.148800000 0.019070000 0.059545000 -0.013590000 -0.036430000 MOIST -0.101800000 0.059545000 0.437370000 0.039510000 -0.029355000 FAT 0.198100000 -0.013590000 0.039510000 0.144880000 0.055435000 HEX 0.421700000 -0.036430000 -0.029355000 0.055435000 0.102220000 Simple Statistics Variable N Mean Std Dev Sum Minimum Maximum CKG_LOSS 5 34.3200 1.3236 171.6000 33.0000 36.2000 PH 5 6.5820 0.1381 32.9100 6.3400 6.6700 MOIST 5 60.6520 0.6613 303.2600 59.9500 61.3700 FAT 5 9.8060 0.3806 49.0300 9.3200 10.1800 HEX 5 0.7220 0.3197 3.6100 0.4000 1.1800 Pearson Correlation Coefficients / N = 5 CKG_LOSS PH MOIST FAT HEX CKG_LOSS 1.00000 -0.81407 -0.11629 0.39320 0.99648 PH -0.81407 1.00000 0.65200 -0.25855 -0.82512 MOIST -0.11629 0.65200 1.00000 0.15696 -0.13883 FAT 0.39320 -0.25855 0.15696 1.00000 0.45552 HEX 0.99648 -0.82512 -0.13883 0.45552 1.00000 The SAS System 3 ----------------------------------- TRT=3 ------------------------------------ Correlation Analysis 5 'VAR' Variables: CKG_LOSS PH MOIST FAT HEX Covariance Matrix DF = 4 CKG_LOSS PH MOIST FAT HEX CKG_LOSS 10.42700000 -0.13440000 -2.81565000 -0.31835000 0.07220000 PH -0.13440000 0.01063000 0.02470500 -0.00933000 -0.01189000 MOIST -2.81565000 0.02470500 1.12163000 0.21319500 0.00006000 FAT -0.31835000 -0.00933000 0.21319500 0.07768000 0.01674000 HEX 0.07220000 -0.01189000 0.00006000 0.01674000 0.01412000 Simple Statistics Variable N Mean Std Dev Sum Minimum Maximum CKG_LOSS 5 30.6800 3.2291 153.4000 26.8000 33.8000 PH 5 6.6840 0.1031 33.4200 6.5200 6.7800 MOIST 5 61.8440 1.0591 309.2200 60.4000 63.3700 FAT 5 9.6860 0.2787 48.4300 9.3800 10.0800 HEX 5 0.3080 0.1188 1.5400 0.2000 0.5000 Pearson Correlation Coefficients / N = 5 CKG_LOSS PH MOIST FAT HEX CKG_LOSS 1.00000 -0.40369 -0.82333 -0.35373 0.18817 PH -0.40369 1.00000 0.22625 -0.32468 -0.97051 MOIST -0.82333 0.22625 1.00000 0.72227 0.00048 FAT -0.35373 -0.32468 0.72227 1.00000 0.50546 HEX 0.18817 -0.97051 0.00048 0.50546 1.00000 The SAS System 4 ----------------------------------- TRT=4 ------------------------------------ Correlation Analysis 5 'VAR' Variables: CKG_LOSS PH MOIST FAT HEX Covariance Matrix DF = 4 CKG_LOSS PH MOIST FAT HEX CKG_LOSS 3.120000000 -0.084250000 0.932000000 0.031000000 0.167750000 PH -0.084250000 0.009720000 -0.056520000 -0.012330000 -0.038970000 MOIST 0.932000000 -0.056520000 0.516170000 -0.082220000 0.220970000 FAT 0.031000000 -0.012330000 -0.082220000 0.578320000 0.023730000 HEX 0.167750000 -0.038970000 0.220970000 0.023730000 0.174670000 Simple Statistics Variable N Mean Std Dev Sum Minimum Maximum CKG_LOSS 5 34.9000 1.7664 174.5000 33.0000 37.5000 PH 5 6.5480 0.0986 32.7400 6.4700 6.6700 MOIST 5 60.1920 0.7184 300.9600 59.3400 61.0800 FAT 5 10.3080 0.7605 51.5400 9.2000 11.3200 HEX 5 1.1820 0.4179 5.9100 0.7300 1.5800 Pearson Correlation Coefficients / N = 5 CKG_LOSS PH MOIST FAT HEX CKG_LOSS 1.00000 -0.48379 0.73442 0.02308 0.22724 PH -0.48379 1.00000 -0.79794 -0.16445 -0.94578 MOIST 0.73442 -0.79794 1.00000 -0.15049 0.73592 FAT 0.02308 -0.16445 -0.15049 1.00000 0.07466 HEX 0.22724 -0.94578 0.73592 0.07466 1.00000 The SAS System 5 ----------------------------------- TRT=5 ------------------------------------ Correlation Analysis 5 'VAR' Variables: CKG_LOSS PH MOIST FAT HEX Covariance Matrix DF = 4 CKG_LOSS PH MOIST FAT HEX CKG_LOSS 4.695000000 -0.000500000 1.041250000 -0.070500000 0.226750000 PH -0.000500000 0.017920000 -0.059240000 -0.016780000 -0.030390000 MOIST 1.041250000 -0.059240000 1.478030000 -0.385940000 0.087255000 FAT -0.070500000 -0.016780000 -0.385940000 0.234920000 0.030510000 HEX 0.226750000 -0.030390000 0.087255000 0.030510000 0.075030000 Simple Statistics Variable N Mean Std Dev Sum Minimum Maximum CKG_LOSS 5 34.0000 2.1668 170.0000 32.0000 36.5000 PH 5 6.7120 0.1339 33.5600 6.5000 6.8600 MOIST 5 60.2060 1.2157 301.0300 58.5000 61.6100 FAT 5 9.8720 0.4847 49.3600 9.1800 10.4800 HEX 5 0.5960 0.2739 2.9800 0.3200 0.8800 Pearson Correlation Coefficients / N = 5 CKG_LOSS PH MOIST FAT HEX CKG_LOSS 1.00000 -0.00172 0.39527 -0.06713 0.38204 PH -0.00172 1.00000 -0.36400 -0.25862 -0.82879 MOIST 0.39527 -0.36400 1.00000 -0.65497 0.26202 FAT -0.06713 -0.25862 -0.65497 1.00000 0.22981 HEX 0.38204 -0.82879 0.26202 0.22981 1.00000 One-way MANOVA on Cooked Turkey Data using PROC IML 6 SSCP_Trt is B 106.724 -2.8562 -57.9292 11.691 13.8654 -2.8562 0.137816 1.397104 -0.396824 -0.500828 -57.9292 1.397104 34.850896 -6.565396 -6.811792 11.691 -0.396824 -6.565396 1.849416 2.017932 13.8654 -0.500828 -6.811792 2.017932 2.487624 SSCP_E is W 90.156 -0.2628 -11.8018 0.34 3.6296 -0.2628 1.12168 1.63504 -0.26992 -0.0348 -11.8018 1.63504 32.18872 -4.60742 1.9382 0.34 -0.26992 -4.60742 7.2868 1.25206 3.6296 -0.0348 1.9382 1.25206 1.96768 Wilks Lambda is LAMBDAST 0.1715492 Bartletts approximation gives the following p-value PVAL 0.0297522 Note that PROC GLM will give a more accurate p-value in some cases One-way MANOVA on Cooked Turkey Data Using PROC GLM 7 General Linear Models Procedure Class Level Information Class Levels Values TRT 5 1 2 3 4 5 Number of observations in data set = 25 One-way MANOVA on Cooked Turkey Data Using PROC GLM 8 General Linear Models Procedure Level of -----------CKG_LOSS---------- --------------PH------------- TRT N Mean SD Mean SD 1 5 37.1000000 1.59530561 6.52600000 0.47231346 2 5 34.3200000 1.32363137 6.58200000 0.13809417 3 5 30.6800000 3.22908656 6.68400000 0.10310189 4 5 34.9000000 1.76635217 6.54800000 0.09859006 5 5 34.0000000 2.16679487 6.71200000 0.13386560 Level of ------------MOIST------------ -------------FAT------------- TRT N Mean SD Mean SD 1 5 58.1840000 2.11990094 10.3500000 0.88651001 2 5 60.6520000 0.66133955 9.8060000 0.38063105 3 5 61.8440000 1.05907035 9.6860000 0.27871132 4 5 60.1920000 0.71844972 10.3080000 0.76047354 5 5 60.2060000 1.21574257 9.8720000 0.48468547 Level of -------------HEX------------- TRT N Mean SD 1 5 1.05600000 0.35479572 2 5 0.72200000 0.31971863 3 5 0.30800000 0.11882761 4 5 1.18200000 0.41793540 5 5 0.59600000 0.27391605 E = Error SS&CP Matrix CKG_LOSS PH MOIST FAT HEX CKG_LOSS 90.156 -0.2628 -11.8018 0.34 3.6296 PH -0.2628 1.12168 1.63504 -0.26992 -0.0348 MOIST -11.8018 1.63504 32.18872 -4.60742 1.9382 FAT 0.34 -0.26992 -4.60742 7.2868 1.25206 HEX 3.6296 -0.0348 1.9382 1.25206 1.96768 One-way MANOVA on Cooked Turkey Data Using PROC GLM 9 General Linear Models Procedure Multivariate Analysis of Variance Partial Correlation Coefficients from the Error SS&CP Matrix / Prob > |r| DF = 20 CKG_LOSS PH MOIST FAT HEX CKG_LOSS 1.000000 -0.026133 -0.219078 0.013265 0.272511 0.0001 0.9105 0.3400 0.9545 0.2320 PH -0.026133 1.000000 0.272108 -0.094413 -0.023424 0.9105 0.0001 0.2328 0.6840 0.9197 MOIST -0.219078 0.272108 1.000000 -0.300841 0.243540 0.3400 0.2328 0.0001 0.1851 0.2874 FAT 0.013265 -0.094413 -0.300841 1.000000 0.330658 0.9545 0.6840 0.1851 0.0001 0.1432 HEX 0.272511 -0.023424 0.243540 0.330658 1.000000 0.2320 0.9197 0.2874 0.1432 0.0001 One-way MANOVA on Cooked Turkey Data Using PROC GLM 10 General Linear Models Procedure Multivariate Analysis of Variance H = Type III SS&CP Matrix for TRT CKG_LOSS PH MOIST FAT HEX CKG_LOSS 106.724 -2.8562 -57.9292 11.691 13.8654 PH -2.8562 0.137816 1.397104 -0.396824 -0.500828 MOIST -57.9292 1.397104 34.850896 -6.565396 -6.811792 FAT 11.691 -0.396824 -6.565396 1.849416 2.017932 HEX 13.8654 -0.500828 -6.811792 2.017932 2.487624 Characteristic Roots and Vectors of: E Inverse * H, where H = Type III SS&CP Matrix for TRT E = Error SS&CP Matrix Characteristic Percent Characteristic Vector V'EV=1 Root CKG_LOSS PH MOIST FAT HEX 2.99769493 87.59 0.02355465 0.05532527 -0.14064716 -0.08752866 0.57917735 0.33030700 9.65 -0.03839091 -0.31498022 0.08444099 0.03362979 0.49379937 0.06626512 1.94 0.08187051 -0.44592063 0.10070132 -0.13778026 -0.15793395 0.02797955 0.82 0.02125879 0.82154119 0.02762290 -0.05359486 0.17018257 0.00000000 0.00 0.07056260 -0.06004036 0.11338031 0.41016030 -0.42763741 Manova Test Criteria and F Approximations for the Hypothesis of no Overall TRT Effect H = Type III SS&CP Matrix for TRT E = Error SS&CP Matrix S=4 M=0 N=7 Statistic Value F Num DF Den DF Pr > F Wilks' Lambda 0.17154924 1.8947 20 54.01587 0.0325 Pillai's Trace 1.08751461 1.4189 20 76 0.1401 Hotelling-Lawley Trace 3.42224660 2.4811 20 58 0.0037 Roy's Greatest Root 2.99769493 11.3912 5 19 0.0001 NOTE: F Statistic for Roy's Greatest Root is an upper bound.