soybean example 1 08:31 Wednesday, April 10, 2013 ---------------------------- treat=control ----------------------------- The MEANS Procedure Variable N Mean Std Dev Minimum Maximum -------------------------------------------------------------------- yield 15 12.2600000 0.5329165 11.3000000 13.2000000 height 15 49.3333333 9.1469485 33.0000000 65.0000000 -------------------------------------------------------------------- ----------------------------- treat=light ------------------------------ Variable N Mean Std Dev Minimum Maximum -------------------------------------------------------------------- yield 15 15.8600000 0.5053994 15.0000000 16.7000000 height 15 49.1333333 9.1172260 33.0000000 63.0000000 -------------------------------------------------------------------- ----------------------------- treat=shade ------------------------------ Variable N Mean Std Dev Minimum Maximum -------------------------------------------------------------------- yield 15 9.4666667 0.5690426 8.5000000 10.4000000 height 15 55.1333333 8.5009803 40.0000000 67.0000000 -------------------------------------------------------------------- soybean example 2 08:31 Wednesday, April 10, 2013 Plot of yield*height. Symbol is value of treat. yield | | 17 + | l | l | | l 16 + l l | l ll | l | l | 15 + l l | | | | 14 + | | | | c c 13 + | c | c | c cc c | c c 12 + c | c | | c c | 11 + | | | s | s 10 + | s | s s s ss | ss | s 9 + | s | ss | | 8 + | ---+------------+------------+------------+------------+-- 30 40 50 60 70 height NOTE: 5 obs hidden. adjusted means parameterization 3 08:31 Wednesday, April 10, 2013 The GLM Procedure Class Level Information Class Levels Values treat 3 control light shade Number of Observations Read 45 Number of Observations Used 45 adjusted means parameterization 4 08:31 Wednesday, April 10, 2013 The GLM Procedure Dependent Variable: yield Sum of Source DF Squares Mean Square F Value Model 4 7383.376699 1845.844175 110756 Error 41 0.683301 0.016666 Uncorrected Total 45 7384.060000 Source Pr > F Model <.0001 Error Uncorrected Total R-Square Coeff Var Root MSE yield Mean 0.997866 1.030390 0.129096 12.52889 Source DF Type I SS Mean Square F Value treat 3 7371.974667 2457.324889 147446 adjhgt1 1 11.402032 11.402032 684.15 Source Pr > F treat <.0001 adjhgt1 <.0001 Source DF Type II SS Mean Square F Value treat 3 7381.598520 2460.532840 147639 adjhgt1 1 11.402032 11.402032 684.15 Source Pr > F treat <.0001 adjhgt1 <.0001 Contrast DF Contrast SS Mean Square F Value light vs shade 1 315.6041651 315.6041651 18937.1 Contrast Pr > F light vs shade <.0001 adjusted means parameterization 5 08:31 Wednesday, April 10, 2013 The GLM Procedure Dependent Variable: yield Contrast DF Contrast SS Mean Square F Value control vs others 1 0.5623581 0.5623581 33.74 among (adjusted) 2 317.8109649 158.9054824 9534.77 Contrast Pr > F control vs others <.0001 among (adjusted) <.0001 Standard Parameter Estimate Error t Value Pr > |t| control mean: unadj 12.2600000 0.03333256 367.81 <.0001 light mean: unadj 15.8600000 0.03333256 475.81 <.0001 shade mean: unadj 9.4666667 0.03333256 284.01 <.0001 control mean: adj 12.3689540 0.03359182 368.21 <.0001 light mean: adj 15.9806276 0.03365008 474.91 <.0001 shade mean: adj 9.2370851 0.03446883 267.98 <.0001 light vs shade 6.7435425 0.04900394 137.61 <.0001 control vs others -0.2399024 0.04129927 -5.81 <.0001 light vs control 3.6116736 0.04714147 76.61 <.0001 control vs shade 3.1318688 0.04888388 64.07 <.0001 Parameter 95% Confidence Limits control mean: unadj 12.1926835 12.3273165 light mean: unadj 15.7926835 15.9273165 shade mean: unadj 9.3993502 9.5339831 control mean: adj 12.3011139 12.4367940 light mean: adj 15.9126699 16.0485853 shade mean: adj 9.1674739 9.3066963 light vs shade 6.6445770 6.8425080 control vs others -0.3233080 -0.1564968 light vs control 3.5164695 3.7068778 control vs shade 3.0331458 3.2305919 Standard Parameter Estimate Error t Value Pr > |t| treat control 12.36895396 0.03359182 368.21 <.0001 treat light 15.98062760 0.03365008 474.91 <.0001 treat shade 9.23708511 0.03446883 267.98 <.0001 Parameter 95% Confidence Limits treat control 12.30111389 12.43679402 treat light 15.91266988 16.04858532 treat shade 9.16747390 9.30669632 adjusted means parameterization 6 08:31 Wednesday, April 10, 2013 The GLM Procedure Dependent Variable: yield Standard Parameter Estimate Error t Value Pr > |t| adjhgt1 0.05836819 0.00223151 26.16 <.0001 Parameter 95% Confidence Limits adjhgt1 0.05386156 0.06287482 adjusted means parameterization 7 08:31 Wednesday, April 10, 2013 The GLM Procedure Level of ------------yield------------ treat N Mean Std Dev control 15 12.2600000 0.53291650 light 15 15.8600000 0.50539942 shade 15 9.4666667 0.56904264 adjusted means parameterization 8 08:31 Wednesday, April 10, 2013 The GLM Procedure Least Squares Means Standard treat yield LSMEAN Error Pr > |t| control 12.3689540 0.0335918 <.0001 light 15.9806276 0.0336501 <.0001 shade 9.2370851 0.0344688 <.0001 unadjusted means parameterization 9 08:31 Wednesday, April 10, 2013 The GLM Procedure Class Level Information Class Levels Values treat 3 control light shade Number of Observations Read 45 Number of Observations Used 45 unadjusted means parameterization 10 08:31 Wednesday, April 10, 2013 The GLM Procedure Dependent Variable: yield Sum of Source DF Squares Mean Square F Value Model 4 7383.376699 1845.844175 110756 Error 41 0.683301 0.016666 Uncorrected Total 45 7384.060000 Source Pr > F Model <.0001 Error Uncorrected Total R-Square Coeff Var Root MSE yield Mean 0.997866 1.030390 0.129096 12.52889 Source DF Type I SS Mean Square F Value treat 3 7371.974667 2457.324889 147446 adjhgt2 1 11.402032 11.402032 684.15 Source Pr > F treat <.0001 adjhgt2 <.0001 Source DF Type II SS Mean Square F Value treat 3 7371.974667 2457.324889 147446 adjhgt2 1 11.402032 11.402032 684.15 Source Pr > F treat <.0001 adjhgt2 <.0001 Contrast DF Contrast SS Mean Square F Value light vs shade 1 306.5603333 306.5603333 18394.5 Contrast Pr > F light vs shade <.0001 unadjusted means parameterization 11 08:31 Wednesday, April 10, 2013 The GLM Procedure Dependent Variable: yield Contrast DF Contrast SS Mean Square F Value control vs others 1 1.6267778 1.6267778 97.61 among (unadjusted) 2 308.1871111 154.0935556 9246.04 Contrast Pr > F control vs others <.0001 among (unadjusted) <.0001 Standard Parameter Estimate Error t Value Pr > |t| control mean: unadj 12.2600000 0.03333256 367.81 <.0001 light mean: unadj 15.8600000 0.03333256 475.81 <.0001 shade mean: unadj 9.4666667 0.03333256 284.01 <.0001 control mean: adj 12.3689540 0.03359182 368.21 <.0001 light mean: adj 15.9806276 0.03365008 474.91 <.0001 shade mean: adj 9.2370851 0.03446883 267.98 <.0001 light vs shade 6.3933333 0.04713935 135.63 <.0001 control vs others -0.4033333 0.04082388 -9.88 <.0001 Parameter 95% Confidence Limits control mean: unadj 12.1926835 12.3273165 light mean: unadj 15.7926835 15.9273165 shade mean: unadj 9.3993502 9.5339831 control mean: adj 12.3011139 12.4367940 light mean: adj 15.9126699 16.0485853 shade mean: adj 9.1674739 9.3066963 light vs shade 6.2981335 6.4885332 control vs others -0.4857788 -0.3208878 Standard Parameter Estimate Error t Value Pr > |t| treat control 12.26000000 0.03333256 367.81 <.0001 treat light 15.86000000 0.03333256 475.81 <.0001 treat shade 9.46666667 0.03333256 284.01 <.0001 adjhgt2 0.05836819 0.00223151 26.16 <.0001 Parameter 95% Confidence Limits treat control 12.19268354 12.32731646 treat light 15.79268354 15.92731646 treat shade 9.39935020 9.53398313 adjhgt2 0.05386156 0.06287482 unadjusted means parameterization 12 08:31 Wednesday, April 10, 2013 The GLM Procedure Level of ------------yield------------ treat N Mean Std Dev control 15 12.2600000 0.53291650 light 15 15.8600000 0.50539942 shade 15 9.4666667 0.56904264 unadjusted means parameterization 13 08:31 Wednesday, April 10, 2013 The GLM Procedure Least Squares Means Standard treat yield LSMEAN Error Pr > |t| control 12.2600000 0.0333326 <.0001 light 15.8600000 0.0333326 <.0001 shade 9.4666667 0.0333326 <.0001 alternate approach without adjusting height variable 14 08:31 Wednesday, April 10, 2013 The GLM Procedure Class Level Information Class Levels Values treat 3 control light shade Number of Observations Read 45 Number of Observations Used 45 alternate approach without adjusting height variable 15 08:31 Wednesday, April 10, 2013 The GLM Procedure Dependent Variable: yield Sum of Source DF Squares Mean Square F Value Model 3 319.5891430 106.5297143 6392.08 Error 41 0.6833015 0.0166659 Corrected Total 44 320.2724444 Source Pr > F Model <.0001 Error Corrected Total R-Square Coeff Var Root MSE yield Mean 0.997866 1.030390 0.129096 12.52889 Source DF Type I SS Mean Square F Value treat 2 308.1871111 154.0935556 9246.04 height 1 11.4020318 11.4020318 684.15 Source Pr > F treat <.0001 height <.0001 Source DF Type II SS Mean Square F Value treat 2 317.8109649 158.9054824 9534.77 height 1 11.4020318 11.4020318 684.15 Source Pr > F treat <.0001 height <.0001 Contrast DF Contrast SS Mean Square F Value light vs shade 1 315.6041651 315.6041651 18937.1 Contrast Pr > F light vs shade <.0001 alternate approach without adjusting height variable 16 08:31 Wednesday, April 10, 2013 The GLM Procedure Dependent Variable: yield Contrast DF Contrast SS Mean Square F Value shade vs others 1 0.5623581 0.5623581 33.74 Contrast Pr > F shade vs others <.0001 Standard Parameter Estimate Error t Value Pr > |t| light vs shade 6.74354249 0.04900394 137.61 <.0001 control vs others -0.23990239 0.04129927 -5.81 <.0001 Parameter 95% Confidence Limits light vs shade 6.64457703 6.84250795 control vs others -0.32330796 -0.15649683 alternate approach without adjusting height variable 17 08:31 Wednesday, April 10, 2013 The GLM Procedure Level of ------------yield------------ treat N Mean Std Dev control 15 12.2600000 0.53291650 light 15 15.8600000 0.50539942 shade 15 9.4666667 0.56904264 alternate approach without adjusting height variable 18 08:31 Wednesday, April 10, 2013 The GLM Procedure Least Squares Means Standard treat yield LSMEAN Error Pr > |t| control 12.3689540 0.0335918 <.0001 light 15.9806276 0.0336501 <.0001 shade 9.2370851 0.0344688 <.0001 Scheffe intervals for pairwise differences for adjusted means 19 08:31 Wednesday, April 10, 2013 Obs differ estimate stderr lowerCL upperCL 1 L-S 6.74354 0.049004 6.61907 6.86801 2 L-C 3.61167 0.047141 3.49194 3.73141 3 C-S 3.13187 0.048884 3.00771 3.25603