Analysis of Variance Procedure Class Level Information Class Levels Values TYPE 3 A B C SHAPE 3 X Y Z Number of observations in data set = 36 Analysis of Variance Procedure Dependent Variable: Y Sum of Mean Source DF Squares Square F Value Pr > F Model 8 33.95955173 4.24494397 2.93 0.0172 Error 27 39.13301772 1.44937103 Corrected Total 35 73.09256945 R-Square C.V. Root MSE Y Mean 0.464610 40.64413 1.2038983 2.9620472 Source DF Anova SS Mean Square F Value Pr > F TYPE 2 17.70894993 8.85447496 6.11 0.0065 SHAPE 2 13.65216428 6.82608214 4.71 0.0176 TYPE*SHAPE 4 2.59843752 0.64960938 0.45 0.7727 Analysis of Variance Procedure T tests (LSD) for variable: Y NOTE: This test controls the type I comparisonwise error rate not the experimentwise error rate. Alpha= 0.05 df= 27 MSE= 1.449371 Critical Value of T= 2.05 Least Significant Difference= 1.0085 Means with the same letter are not significantly different. T Grouping Mean N TYPE A 3.9353 12 B B 2.6409 12 A B 2.3099 12 C Analysis of Variance Procedure T tests (LSD) for variable: Y NOTE: This test controls the type I comparisonwise error rate not the experimentwise error rate. Alpha= 0.05 df= 27 MSE= 1.449371 Critical Value of T= 2.05 Least Significant Difference= 1.0085 Means with the same letter are not significantly different. T Grouping Mean N SHAPE A 3.8318 12 X B 2.5653 12 Y B 2.4890 12 Z Analysis of Variance Procedure Level of Level of --------------Y-------------- TYPE SHAPE N Mean SD A X 4 3.26244213 0.88776027 A Y 4 2.51719310 1.25364289 A Z 4 2.14316888 1.12274922 B X 4 4.95832943 1.41679063 B Y 4 3.05513538 1.99328760 B Z 4 3.79255005 0.46941614 C X 4 3.27470963 0.73014550 C Y 4 2.12347333 1.44561499 C Z 4 1.53142255 0.77477537 General Linear Models Procedure Class Level Information Class Levels Values TYPE 3 A B C SHAPE 3 X Y Z Number of observations in data set = 36 General Linear Models Procedure Dependent Variable: Y Sum of Mean Source DF Squares Square F Value Pr > F Model 8 33.95955173 4.24494397 2.93 0.0172 Error 27 39.13301772 1.44937103 Corrected Total 35 73.09256945 R-Square C.V. Root MSE Y Mean 0.464610 40.64413 1.2038983 2.9620472 Source DF Type I SS Mean Square F Value Pr > F TYPE 2 17.70894993 8.85447496 6.11 0.0065 SHAPE 2 13.65216428 6.82608214 4.71 0.0176 TYPE*SHAPE 4 2.59843752 0.64960938 0.45 0.7727 Source DF Type III SS Mean Square F Value Pr > F TYPE 2 17.70894993 8.85447496 6.11 0.0065 SHAPE 2 13.65216428 6.82608214 4.71 0.0176 TYPE*SHAPE 4 2.59843752 0.64960938 0.45 0.7727 General Linear Models Procedure Least Squares Means TYPE Y Std Err Pr > |T| LSMEAN LSMEAN LSMEAN H0:LSMEAN=0 Number A 2.64093470 0.34753549 0.0001 1 B 3.93533828 0.34753549 0.0001 2 C 2.30986850 0.34753549 0.0001 3 Pr > |T| H0: LSMEAN(i)=LSMEAN(j) i/j 1 2 3 1 . 0.0138 0.5063 2 0.0138 . 0.0027 3 0.5063 0.0027 . NOTE: To ensure overall protection level, only probabilities associated with pre-planned comparisons should be used. SHAPE Y Std Err Pr > |T| LSMEAN LSMEAN LSMEAN H0:LSMEAN=0 Number X 3.83182706 0.34753549 0.0001 1 Y 2.56526727 0.34753549 0.0001 2 Z 2.48904716 0.34753549 0.0001 3 Pr > |T| H0: LSMEAN(i)=LSMEAN(j) i/j 1 2 3 1 . 0.0158 0.0110 2 0.0158 . 0.8779 3 0.0110 0.8779 . General Linear Models Procedure Least Squares Means NOTE: To ensure overall protection level, only probabilities associated with pre-planned comparisons should be used. TYPE SHAPE Y Std Err Pr > |T| LSMEAN LSMEAN LSMEAN H0:LSMEAN=0 Number A X 3.26244213 0.60194913 0.0001 1 A Y 2.51719310 0.60194913 0.0003 2 A Z 2.14316888 0.60194913 0.0014 3 B X 4.95832943 0.60194913 0.0001 4 B Y 3.05513538 0.60194913 0.0001 5 B Z 3.79255005 0.60194913 0.0001 6 C X 3.27470963 0.60194913 0.0001 7 C Y 2.12347333 0.60194913 0.0015 8 C Z 1.53142255 0.60194913 0.0170 9 Pr > |T| H0: LSMEAN(i)=LSMEAN(j) i/j 1 2 3 4 5 6 7 8 9 1 . 0.3891 0.1996 0.0566 0.8094 0.5387 0.9886 0.1921 0.0519 2 0.3891 . 0.6639 0.0079 0.5328 0.1457 0.3814 0.6474 0.2570 3 0.1996 0.6639 . 0.0027 0.2935 0.0632 0.1949 0.9817 0.4786 4 0.0566 0.0079 0.0027 . 0.0338 0.1821 0.0582 0.0025 0.0004 5 0.8094 0.5328 0.2935 0.0338 . 0.3940 0.7984 0.2834 0.0847 6 0.5387 0.1457 0.0632 0.1821 0.3940 . 0.5481 0.0603 0.0131 7 0.9886 0.3814 0.1949 0.0582 0.7984 0.5481 . 0.1875 0.0504 8 0.1921 0.6474 0.9817 0.0025 0.2834 0.0603 0.1875 . 0.4927 9 0.0519 0.2570 0.4786 0.0004 0.0847 0.0131 0.0504 0.4927 . General Linear Models Procedure Least Squares Means NOTE: To ensure overall protection level, only probabilities associated with pre-planned comparisons should be used. Plot of RY*PY. Symbol is value of TYPE. RY | | 3 + | B | | | 2 + | | C | A A | A B 1 + C | C | C | C B | C A A B 0 + A A | CA B A | C | | C B -1 + B A | | A | A B | C -2 + B | ---+---------+---------+---------+---------+---------+---------+---------+-- 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 PY NOTE: 5 obs hidden. Plot of RY*PY. Symbol is value of SHAPE. RY | | 3 + | Y | | | 2 + | | Y | Z Y | X X 1 + Z | X | Y | X X | Z Z Y Z 0 + Y X | YZ Y X | Z | | Z Z -1 + Y X | | Z | Y Y | Y -2 + X | ---+---------+---------+---------+---------+---------+---------+---------+-- 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 PY NOTE: 5 obs hidden. Plot of LSMEAN*SHAPE. Symbol is value of TYPE. 5 + B | | | | | | 4 + | B | LSMEAN | | | A | 3 + B | | | A | | | C A 2 + | | | C | | | 1 + ---+----------------------+----------------------+-- SHAPE NOTE: 3 obs had missing values. 1 obs hidden.