LAMB WEIGHT FOR 3 LAMB CHOWS - YOUR NAME 1 THE DATA AS SAS SEES IT Obs chow feednum lambwt matwt 1 AZenith 1 45 98 2 AZenith 1 47 93 3 AZenith 1 46 89 4 AZenith 1 45 101 5 AZenith 1 56 127 6 AZenith 1 56 99 7 AZenith 1 43 82 8 AZenith 1 38 81 9 AZenith 1 44 91 10 AZenith 1 46 95 11 AZenith 1 47 103 12 AZenith 1 46 87 13 AZenith 1 48 84 14 AZenith 1 50 106 15 AZenith 1 48 89 16 BXQ11 2 52 92 17 BXQ11 2 48 99 18 BXQ11 2 54 111 19 BXQ11 2 45 102 20 BXQ11 2 50 91 21 BXQ11 2 46 105 22 BXQ11 2 47 82 23 BXQ11 2 56 103 24 BXQ11 2 44 81 25 BXQ11 2 46 96 26 BXQ11 2 53 109 27 BXQ11 2 49 103 28 BXQ11 2 54 120 29 BXQ11 2 53 120 30 BXQ11 2 53 95 31 Clover7 3 45 116 32 Clover7 3 55 99 33 Clover7 3 56 111 34 Clover7 3 58 85 35 Clover7 3 49 110 36 Clover7 3 55 94 37 Clover7 3 50 105 38 Clover7 3 54 110 39 Clover7 3 51 104 40 Clover7 3 51 99 41 Clover7 3 55 91 42 Clover7 3 43 105 43 Clover7 3 45 99 44 Clover7 3 50 104 45 Clover7 3 55 122 LAMB WEIGHT FOR 3 LAMB CHOWS - YOUR NAME 2 ONE-WAY ANOVA FOR WEIGHT ON FEED BRAND THIS IS (BORDERLINE) SIGNIFICANT, BUT IS IT THE ENTIRE STORY? NOTE THAT THE MODEL RSQUARE IS ONLY 0.166 The GLM Procedure Class Level Information Class Levels Values chow 3 AZenith BXQ11 Clover7 Number of Observations Read 45 Number of Observations Used 45 LAMB WEIGHT FOR 3 LAMB CHOWS - YOUR NAME 3 ONE-WAY ANOVA FOR WEIGHT ON FEED BRAND THIS IS (BORDERLINE) SIGNIFICANT, BUT IS IT THE ENTIRE STORY? NOTE THAT THE MODEL RSQUARE IS ONLY 0.166 The GLM Procedure Dependent Variable: lambwt Sum of Source DF Squares Mean Square F Value Pr > F Model 2 155.5111111 77.7555556 4.18 0.0221 Error 42 781.7333333 18.6126984 Corrected Total 44 937.2444444 R-Square Coeff Var Root MSE lambwt Mean 0.165924 8.717601 4.314244 49.48889 Source DF Type I SS Mean Square F Value Pr > F chow 2 155.5111111 77.7555556 4.18 0.0221 Source DF Type III SS Mean Square F Value Pr > F chow 2 155.5111111 77.7555556 4.18 0.0221 LAMB WEIGHT FOR 3 LAMB CHOWS - YOUR NAME 4 TRY AGAIN WITH MATERNAL WEIGHT INCLUDED (AN ANCOVA MODEL) NOW LAMB WEIGHT SEEMS TO DEPEND MOSTLY ON MATERNAL WEIGHT. The GLM Procedure Class Level Information Class Levels Values chow 3 AZenith BXQ11 Clover7 Number of Observations Read 45 Number of Observations Used 45 LAMB WEIGHT FOR 3 LAMB CHOWS - YOUR NAME 5 TRY AGAIN WITH MATERNAL WEIGHT INCLUDED (AN ANCOVA MODEL) NOW LAMB WEIGHT SEEMS TO DEPEND MOSTLY ON MATERNAL WEIGHT. The GLM Procedure Dependent Variable: lambwt Sum of Source DF Squares Mean Square F Value Pr > F Model 3 250.3190155 83.4396718 4.98 0.0049 Error 41 686.9254289 16.7542788 Corrected Total 44 937.2444444 R-Square Coeff Var Root MSE lambwt Mean 0.267080 8.270946 4.093199 49.48889 Source DF Type I SS Mean Square F Value Pr > F chow 2 155.5111111 77.7555556 4.64 0.0152 matwt 1 94.8079044 94.8079044 5.66 0.0221 Source DF Type III SS Mean Square F Value Pr > F chow 2 76.45735087 38.22867544 2.28 0.1149 matwt 1 94.80790440 94.80790440 5.66 0.0221 LAMB WEIGHT FOR 3 LAMB CHOWS - YOUR NAME 6 WILL MEANS AND STANDARD DEVIATIONS GIVE ANY CLUES? NOTE THAT THE CLASS MEANS OF LAMB AND MATERNAL WEIGHTS SEEM TO BE CORRELATED ACROSS FEED TYPE. The MEANS Procedure N chow Obs Variable N Mean Std Dev ---------------------------------------------------------------- AZenith 15 lambwt 15 47.0000000 4.5512949 matwt 15 95.0000000 11.6863779 BXQ11 15 lambwt 15 50.0000000 3.8359205 matwt 15 100.6000000 11.6973746 Clover7 15 lambwt 15 51.4666667 4.5176901 matwt 15 103.6000000 9.6124919 ---------------------------------------------------------------- LAMB WEIGHT FOR 3 LAMB CHOWS - YOUR NAME 7 FINALLY, ALLOW FOR A FEED*MATWT 'INTERACTION' THIS FITS A SIMPLE REGRESSION WITHIN EACH TREATMENT GROUP THE FEED BRANDS NOW SEEM TO BE TOO HETEROGENEOUS TO COMPARE CAN YOU SEE WHY? The GLM Procedure Class Level Information Class Levels Values chow 3 AZenith BXQ11 Clover7 Number of Observations Read 45 Number of Observations Used 45 LAMB WEIGHT FOR 3 LAMB CHOWS - YOUR NAME 8 FINALLY, ALLOW FOR A FEED*MATWT 'INTERACTION' THIS FITS A SIMPLE REGRESSION WITHIN EACH TREATMENT GROUP THE FEED BRANDS NOW SEEM TO BE TOO HETEROGENEOUS TO COMPARE CAN YOU SEE WHY? The GLM Procedure Dependent Variable: lambwt Sum of Source DF Squares Mean Square F Value Pr > F Model 5 389.6327788 77.9265558 5.55 0.0006 Error 39 547.6116656 14.0413248 Corrected Total 44 937.2444444 R-Square Coeff Var Root MSE lambwt Mean 0.415722 7.571751 3.747176 49.48889 Source DF Type I SS Mean Square F Value Pr > F chow 2 155.5111111 77.7555556 5.54 0.0076 matwt 1 94.8079044 94.8079044 6.75 0.0131 matwt*chow 2 139.3137633 69.6568817 4.96 0.0120 Source DF Type III SS Mean Square F Value Pr > F chow 2 158.0717386 79.0358693 5.63 0.0071 matwt 1 55.9843007 55.9843007 3.99 0.0529 matwt*chow 2 139.3137633 69.6568817 4.96 0.0120 LAMB WEIGHT FOR 3 LAMB CHOWS - YOUR NAME 9 FINALLY, LET'S SEE WHAT THE DATA LOOKS LIKE (WE SHOULD HAVE DONE THIS FIRST) Plot of matwt*lambwt. Symbol is value of chow. matwt | | | 130 + | A | | | C 120 + B B | | C | | B C 110 + C B C | | C B A | A B C C B | A 100 + C B C C A | A | A B | A C | A B B C 90 + A A | A | C | A | A A B B 80 + | ---+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+-- 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 lambwt NOTE: 3 obs hidden. LAMB WEIGHT FOR 3 LAMB CHOWS - YOUR NAME 10 LET'S LOOK AT SIMPLE REGRESSIONS WITHIN EACH FEED BRAND chow=AZenith The REG Procedure Model: MODEL1 Dependent Variable: lambwt Number of Observations Read 15 Number of Observations Used 15 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 144.70502 144.70502 12.95 0.0032 Error 13 145.29498 11.17654 Corrected Total 14 290.00000 Root MSE 3.34313 R-Square 0.4990 Dependent Mean 47.00000 Adj R-Sq 0.4604 Coeff Var 7.11305 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept 1 20.86506 7.31440 2.85 0.0136 matwt 1 0.27510 0.07646 3.60 0.0032 LAMB WEIGHT FOR 3 LAMB CHOWS - YOUR NAME 11 LET'S LOOK AT SIMPLE REGRESSIONS WITHIN EACH FEED BRAND chow=AZenith The REG Procedure Model: MODEL1 Dependent Variable: lambwt ---+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+---- lambwt | | | | 60 + + | | | | | | | | | A ? | 55 + + | | | | | | | | | | 50 + ? + | 1 | | A A 1 1 | | 1 | | ? 1 A | | A A 1 A | 45 + 1 2 A A + | 1 A | | 1? | | | | | | | 40 + + | | | A | | | | | | | 35 + + | | ---+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+---- 80 85 90 95 100 105 110 115 120 125 130 matwt LAMB WEIGHT FOR 3 LAMB CHOWS - YOUR NAME 12 LET'S LOOK AT SIMPLE REGRESSIONS WITHIN EACH FEED BRAND chow=BXQ11 The REG Procedure Model: MODEL1 Dependent Variable: lambwt Number of Observations Read 15 Number of Observations Used 15 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 64.31458 64.31458 5.90 0.0304 Error 13 141.68542 10.89888 Corrected Total 14 206.00000 Root MSE 3.30135 R-Square 0.3122 Dependent Mean 50.00000 Adj R-Sq 0.2593 Coeff Var 6.60269 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept 1 31.56682 7.63589 4.13 0.0012 matwt 1 0.18323 0.07543 2.43 0.0304 LAMB WEIGHT FOR 3 LAMB CHOWS - YOUR NAME 13 LET'S LOOK AT SIMPLE REGRESSIONS WITHIN EACH FEED BRAND chow=BXQ11 The REG Procedure Model: MODEL1 Dependent Variable: lambwt -----+------+------+------+------+------+------+------+------+------ lambwt | | | | 56 + B + | | | | | | | | 54 + B B + | 4 | | B B B | | | | | 52 + B 2 + | 2 | | | | 2 | | 24 | 50 + B + | 2 | | 2 B | | 2 | | 2 2 | 48 + B + | | | B | | | | 2 2 | 46 + B B + | | | B | | | | | 44 + B + | | -----+------+------+------+------+------+------+------+------+------ 80 85 90 95 100 105 110 115 120 matwt LAMB WEIGHT FOR 3 LAMB CHOWS - YOUR NAME 14 LET'S LOOK AT SIMPLE REGRESSIONS WITHIN EACH FEED BRAND chow=Clover7 The REG Procedure Model: MODEL1 Dependent Variable: lambwt Number of Observations Read 15 Number of Observations Used 15 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 25.10207 25.10207 1.25 0.2834 Error 13 260.63126 20.04856 Corrected Total 14 285.73333 Root MSE 4.47756 R-Square 0.0879 Dependent Mean 51.46667 Adj R-Sq 0.0177 Coeff Var 8.69993 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept 1 65.89827 12.94909 5.09 0.0002 matwt 1 -0.13930 0.12449 -1.12 0.2834 LAMB WEIGHT FOR 3 LAMB CHOWS - YOUR NAME 15 LET'S LOOK AT SIMPLE REGRESSIONS WITHIN EACH FEED BRAND chow=Clover7 The REG Procedure Model: MODEL1 Dependent Variable: lambwt -----+------+------+------+------+------+------+------+------+------ lambwt | | | | | | 60.0 + + | | | | | C | 57.5 + + | | | C | | | 55.0 + C C C C + | | | 3 C | | 3 | 52.5 + 3 + | 9 | | C ?6 | | 63 | 50.0 + CC 3 + | | | C 3 | | | 47.5 + + | | | | | | 45.0 + C C + | | | | | C | 42.5 + + | | | | -----+------+------+------+------+------+------+------+------+------ 85 90 95 100 105 110 115 120 125 matwt LAMB WEIGHT FOR 3 LAMB CHOWS - YOUR NAME 16 WE COULD SHOW FITTED AND OBSERVED VALUES FOR EACH LAMB CHOW, BUT A PLOT WITH THE THREE FITTED REGRESSION LINES TOGETHER GIVES A CLEARER PICTURE OF THE CHOW*MATWT INTERACTION: Plot of predicted*matwt. Symbol is value of chow. predicted | 57.5 + | | | A 55.0 + | | C B | C 52.5 + C | C B | CC B | B B CC 50.0 + B B A C | B A | B A C | BB AA 47.5 + | B A | B A | A A 45.0 + A | | A | AA 42.5 + | --+-----------+-----------+-----------+-----------+-----------+-- 80 90 100 110 120 130 matwt NOTE: 8 obs hidden. LAMB WEIGHT FOR 3 LAMB CHOWS - YOUR NAME 17 FINALLY, LET'S LOOK ARE CORRELATIONS WITHIN EACH CHOW: chow=AZenith The CORR Procedure 2 Variables: lambwt matwt Pearson Correlation Coefficients, N = 15 Prob > |r| under H0: Rho=0 lambwt matwt lambwt 1.00000 0.70639 0.0032 matwt 0.70639 1.00000 0.0032 LAMB WEIGHT FOR 3 LAMB CHOWS - YOUR NAME 18 FINALLY, LET'S LOOK ARE CORRELATIONS WITHIN EACH CHOW: chow=BXQ11 The CORR Procedure 2 Variables: lambwt matwt Pearson Correlation Coefficients, N = 15 Prob > |r| under H0: Rho=0 lambwt matwt lambwt 1.00000 0.55875 0.0304 matwt 0.55875 1.00000 0.0304 LAMB WEIGHT FOR 3 LAMB CHOWS - YOUR NAME 19 FINALLY, LET'S LOOK ARE CORRELATIONS WITHIN EACH CHOW: chow=Clover7 The CORR Procedure 2 Variables: lambwt matwt Pearson Correlation Coefficients, N = 15 Prob > |r| under H0: Rho=0 lambwt matwt lambwt 1.00000 -0.29640 0.2834 matwt -0.29640 1.00000 0.2834