Printout of 3-factor Data 1 13:13 Wednesday, November 19, 2003 Obs rep a b c yield 1 1 0 0 0 25.7 2 2 0 0 0 25.4 3 3 0 0 0 23.8 4 4 0 0 0 22.0 5 1 0 0 1 31.8 6 2 0 0 1 29.5 7 3 0 0 1 28.7 8 4 0 0 1 26.4 9 1 0 0 2 34.6 10 2 0 0 2 37.2 11 3 0 0 2 29.1 12 4 0 0 2 23.7 13 1 0 1 0 27.7 14 2 0 1 0 30.3 15 3 0 1 0 30.2 16 4 0 1 0 33.2 17 1 0 1 1 38.0 18 2 0 1 1 40.6 19 3 0 1 1 34.6 20 4 0 1 1 31.0 21 1 0 1 2 42.1 22 2 0 1 2 43.6 23 3 0 1 2 44.6 24 4 0 1 2 42.7 25 1 1 0 0 28.9 26 2 1 0 0 24.7 27 3 1 0 0 27.8 28 4 1 0 0 23.4 29 1 1 0 1 37.5 30 2 1 0 1 31.5 31 3 1 0 1 31.0 32 4 1 0 1 27.8 33 1 1 0 2 38.4 34 2 1 0 2 32.5 35 3 1 0 2 31.2 36 4 1 0 2 29.8 37 1 1 1 0 38.0 38 2 1 1 0 31.0 39 3 1 1 0 29.5 40 4 1 1 0 30.7 41 1 1 1 1 36.9 42 2 1 1 1 31.9 43 3 1 1 1 31.5 44 4 1 1 1 35.9 45 1 1 1 2 44.2 46 2 1 1 2 41.6 47 3 1 1 2 38.9 48 4 1 1 2 37.6 49 1 2 0 0 23.4 50 2 2 0 0 24.2 Printout of 3-factor Data 2 13:13 Wednesday, November 19, 2003 Obs rep a b c yield 51 3 2 0 0 21.2 52 4 2 0 0 20.9 53 1 2 0 1 25.3 54 2 2 0 1 27.7 55 3 2 0 1 23.7 56 4 2 0 1 24.3 57 1 2 0 2 29.8 58 2 2 0 2 29.9 59 3 2 0 2 24.3 60 4 2 0 2 23.8 61 1 2 1 0 20.8 62 2 2 1 0 23.0 63 3 2 1 0 25.2 64 4 2 1 0 23.1 65 1 2 1 1 29.0 66 2 2 1 1 32.0 67 3 2 1 1 26.5 68 4 2 1 1 31.2 69 1 2 1 2 36.6 70 2 2 1 2 37.8 71 3 2 1 2 34.8 72 4 2 1 2 40.2 ANOVA for A whole plot, BxC factorial arrangement forsubplot 3 All factors fixed 13:13 Wednesday, November 19, 2003 The ANOVA Procedure Class Level Information Class Levels Values rep 4 1 2 3 4 a 3 0 1 2 b 2 0 1 c 3 0 1 2 Number of observations 72 ANOVA for A whole plot, BxC factorial arrangement forsubplot 4 All factors fixed 13:13 Wednesday, November 19, 2003 The ANOVA Procedure Dependent Variable: yield Sum of Source DF Squares Mean Square F Value Pr > F Model 26 2593.765278 99.760203 18.19 <.0001 Error 45 246.840833 5.485352 Corrected Total 71 2840.606111 R-Square Coeff Var Root MSE yield Mean 0.913103 7.570709 2.342083 30.93611 Source DF Anova SS Mean Square F Value Pr > F rep 3 143.4561111 47.8187037 8.72 0.0001 a 2 443.6886111 221.8443056 40.44 <.0001 a(rep) 6 111.7580556 18.6263426 3.40 0.0076 b 1 706.8800000 706.8800000 128.87 <.0001 c 2 962.3352778 481.1676389 87.72 <.0001 a*b 2 40.6875000 20.3437500 3.71 0.0323 a*c 4 13.1097222 3.2774306 0.60 0.6663 b*c 2 127.8308333 63.9154167 11.65 <.0001 a*b*c 4 44.0191667 11.0047917 2.01 0.1098 Tests of Hypotheses Using the Anova MS for a(rep) as an Error Term Source DF Anova SS Mean Square F Value Pr > F a 2 443.6886111 221.8443056 11.91 0.0081 ANOVA for A whole plot, BxC factorial arrangement forsubplot 5 All factors fixed 13:13 Wednesday, November 19, 2003 The ANOVA Procedure t Tests (LSD) for yield NOTE: This test controls the Type I comparisonwise error rate, not the experimentwise error rate. Alpha 0.05 Error Degrees of Freedom 6 Error Mean Square 18.62634 Critical Value of t 2.44691 Least Significant Difference 3.0485 Means with the same letter are not significantly different. t Grouping Mean N a A 33.008 24 1 A A 32.354 24 0 B 27.446 24 2 ANOVA for A whole plot, BxC factorial arrangement forsubplot 6 All factors fixed 13:13 Wednesday, November 19, 2003 The ANOVA Procedure t Tests (LSD) for yield NOTE: This test controls the Type I comparisonwise error rate, not the experimentwise error rate. Alpha 0.05 Error Degrees of Freedom 45 Error Mean Square 5.485352 Critical Value of t 2.01410 Least Significant Difference 1.1119 Means with the same letter are not significantly different. t Grouping Mean N b A 34.0694 36 1 B 27.8028 36 0 ANOVA for A whole plot, BxC factorial arrangement forsubplot 7 All factors fixed 13:13 Wednesday, November 19, 2003 The ANOVA Procedure t Tests (LSD) for yield NOTE: This test controls the Type I comparisonwise error rate, not the experimentwise error rate. Alpha 0.05 Error Degrees of Freedom 45 Error Mean Square 5.485352 Critical Value of t 2.01410 Least Significant Difference 1.3617 Means with the same letter are not significantly different. t Grouping Mean N c A 35.3750 24 2 B 31.0125 24 1 C 26.4208 24 0 ANOVA for A whole plot, BxC factorial arrangement forsubplot 8 All factors fixed 13:13 Wednesday, November 19, 2003 The ANOVA Procedure Level of Level of ------------yield------------ a b N Mean Std Dev 0 0 12 28.1583333 4.60265898 0 1 12 36.5500000 6.06907212 1 0 12 30.3750000 4.45831705 1 1 12 35.6416667 4.72179826 2 0 12 24.8750000 2.90458102 2 1 12 30.0166667 6.42761561 Level of Level of ------------yield------------ a c N Mean Std Dev 0 0 8 27.2875000 3.75858541 0 1 8 32.5750000 4.83462216 0 2 8 37.2000000 7.60263112 1 0 8 29.2500000 4.45517356 1 1 8 33.0000000 3.39369163 1 2 8 36.7750000 5.13051097 2 0 8 22.7250000 1.61842075 2 1 8 27.4625000 3.08773495 2 2 8 32.1500000 6.15838569 Level of Level of ------------yield------------ b c N Mean Std Dev 0 0 12 24.2833333 2.43229534 0 1 12 28.7666667 3.85871701 0 2 12 30.3583333 4.87320285 1 0 12 28.5583333 4.86872362 1 1 12 33.2583333 4.02367049 1 2 12 40.3916667 3.22813155 Level of Level of Level of ------------yield------------ a b c N Mean Std Dev 0 0 0 4 24.2250000 1.70171482 0 0 1 4 29.1000000 2.22860195 0 0 2 4 31.1500000 6.00583050 0 1 0 4 30.3500000 2.24870333 0 1 1 4 36.0500000 4.16773320 0 1 2 4 43.2500000 1.09087121 1 0 0 4 26.2000000 2.57811301 1 0 1 4 31.9500000 4.04680944 1 0 2 4 32.9750000 3.78098312 1 1 0 4 32.3000000 3.85486705 ANOVA for A whole plot, BxC factorial arrangement forsubplot 9 All factors fixed 13:13 Wednesday, November 19, 2003 The ANOVA Procedure Level of Level of Level of ------------yield------------ a b c N Mean Std Dev 1 1 1 4 34.0500000 2.74893919 1 1 2 4 40.5750000 2.93527398 2 0 0 4 22.4250000 1.62557682 2 0 1 4 25.2500000 1.76162803 2 0 2 4 26.9500000 3.35509563 2 1 0 4 23.0250000 1.79698822 2 1 1 4 29.6750000 2.46762369 2 1 2 4 37.3500000 2.26495033 ANOVA for AxB factorial arrangement for whole plot, Csuplot. 10 All factors fixed 13:13 Wednesday, November 19, 2003 The ANOVA Procedure Class Level Information Class Levels Values rep 4 1 2 3 4 a 3 0 1 2 b 2 0 1 c 3 0 1 2 Number of observations 72 ANOVA for AxB factorial arrangement for whole plot, Csuplot. 11 All factors fixed 13:13 Wednesday, November 19, 2003 The ANOVA Procedure Dependent Variable: yield Sum of Source DF Squares Mean Square F Value Pr > F Model 35 2672.107778 76.345937 16.31 <.0001 Error 36 168.498333 4.680509 Corrected Total 71 2840.606111 R-Square Coeff Var Root MSE yield Mean 0.940682 6.993279 2.163448 30.93611 Source DF Anova SS Mean Square F Value Pr > F rep 3 143.4561111 47.8187037 10.22 <.0001 a 2 443.6886111 221.8443056 47.40 <.0001 b 1 706.8800000 706.8800000 151.03 <.0001 a*b 2 40.6875000 20.3437500 4.35 0.0204 a*b(rep) 15 190.1005556 12.6733704 2.71 0.0072 c 2 962.3352778 481.1676389 102.80 <.0001 a*c 4 13.1097222 3.2774306 0.70 0.5969 b*c 2 127.8308333 63.9154167 13.66 <.0001 a*b*c 4 44.0191667 11.0047917 2.35 0.0725 Tests of Hypotheses Using the Anova MS for a*b(rep) as an Error Term Source DF Anova SS Mean Square F Value Pr > F a 2 443.6886111 221.8443056 17.50 0.0001 b 1 706.8800000 706.8800000 55.78 <.0001 a*b 2 40.6875000 20.3437500 1.61 0.2335 ANOVA for AxB factorial arrangement for whole plot, Csuplot. 12 All factors fixed 13:13 Wednesday, November 19, 2003 The ANOVA Procedure t Tests (LSD) for yield NOTE: This test controls the Type I comparisonwise error rate, not the experimentwise error rate. Alpha 0.05 Error Degrees of Freedom 15 Error Mean Square 12.67337 Critical Value of t 2.13145 Least Significant Difference 2.1904 Means with the same letter are not significantly different. t Grouping Mean N a A 33.008 24 1 A A 32.354 24 0 B 27.446 24 2 ANOVA for AxB factorial arrangement for whole plot, Csuplot. 13 All factors fixed 13:13 Wednesday, November 19, 2003 The ANOVA Procedure t Tests (LSD) for yield NOTE: This test controls the Type I comparisonwise error rate, not the experimentwise error rate. Alpha 0.05 Error Degrees of Freedom 15 Error Mean Square 12.67337 Critical Value of t 2.13145 Least Significant Difference 1.7885 Means with the same letter are not significantly different. t Grouping Mean N b A 34.0694 36 1 B 27.8028 36 0 ANOVA for AxB factorial arrangement for whole plot, Csuplot. 14 All factors fixed 13:13 Wednesday, November 19, 2003 The ANOVA Procedure t Tests (LSD) for yield NOTE: This test controls the Type I comparisonwise error rate, not the experimentwise error rate. Alpha 0.05 Error Degrees of Freedom 36 Error Mean Square 4.680509 Critical Value of t 2.02809 Least Significant Difference 1.2666 Means with the same letter are not significantly different. t Grouping Mean N c A 35.3750 24 2 B 31.0125 24 1 C 26.4208 24 0 ANOVA for AxB factorial arrangement for whole plot, Csuplot. 15 All factors fixed 13:13 Wednesday, November 19, 2003 The ANOVA Procedure Level of Level of ------------yield------------ a b N Mean Std Dev 0 0 12 28.1583333 4.60265898 0 1 12 36.5500000 6.06907212 1 0 12 30.3750000 4.45831705 1 1 12 35.6416667 4.72179826 2 0 12 24.8750000 2.90458102 2 1 12 30.0166667 6.42761561 Level of Level of ------------yield------------ a c N Mean Std Dev 0 0 8 27.2875000 3.75858541 0 1 8 32.5750000 4.83462216 0 2 8 37.2000000 7.60263112 1 0 8 29.2500000 4.45517356 1 1 8 33.0000000 3.39369163 1 2 8 36.7750000 5.13051097 2 0 8 22.7250000 1.61842075 2 1 8 27.4625000 3.08773495 2 2 8 32.1500000 6.15838569 Level of Level of ------------yield------------ b c N Mean Std Dev 0 0 12 24.2833333 2.43229534 0 1 12 28.7666667 3.85871701 0 2 12 30.3583333 4.87320285 1 0 12 28.5583333 4.86872362 1 1 12 33.2583333 4.02367049 1 2 12 40.3916667 3.22813155 Level of Level of Level of ------------yield------------ a b c N Mean Std Dev 0 0 0 4 24.2250000 1.70171482 0 0 1 4 29.1000000 2.22860195 0 0 2 4 31.1500000 6.00583050 0 1 0 4 30.3500000 2.24870333 0 1 1 4 36.0500000 4.16773320 0 1 2 4 43.2500000 1.09087121 1 0 0 4 26.2000000 2.57811301 1 0 1 4 31.9500000 4.04680944 1 0 2 4 32.9750000 3.78098312 1 1 0 4 32.3000000 3.85486705 ANOVA for AxB factorial arrangement for whole plot, Csuplot. 16 All factors fixed 13:13 Wednesday, November 19, 2003 The ANOVA Procedure Level of Level of Level of ------------yield------------ a b c N Mean Std Dev 1 1 1 4 34.0500000 2.74893919 1 1 2 4 40.5750000 2.93527398 2 0 0 4 22.4250000 1.62557682 2 0 1 4 25.2500000 1.76162803 2 0 2 4 26.9500000 3.35509563 2 1 0 4 23.0250000 1.79698822 2 1 1 4 29.6750000 2.46762369 2 1 2 4 37.3500000 2.26495033