The SAS System 10:50 Monday, April 6, 1992 1 Class Levels Values HERB 3 1 2 3 PLOT 12 1 2 3 4 5 6 7 8 9 11 13 15 FERT 4 1 2 3 4 Number of observations in data set = 48 Dependent Variable: HEIGHT Sum of Mean Source DF Squares Square F Value Pr > F Model 20 1692.45417 84.62271 34.90 0.0001 Error 27 65.46250 2.42454 Corrected Total 47 1757.91667 R-Square C.V. Root MSE HEIGHT Mean 0.962761 9.912525 1.55709 15.7083 Source DF Type I SS Mean Square F Value Pr > F HERB 2 195.06250 97.53125 40.23 0.0001 PLOT(HERB) 9 341.85417 37.98380 15.67 0.0001 FERT 3 1037.41667 345.80556 142.63 0.0001 HERB*FERT 6 118.12083 19.68681 8.12 0.0001 Source DF Type III SS Mean Square F Value Pr > F HERB 2 195.062500 97.531250 40.23 0.0001 PLOT(HERB) 9 341.854167 37.983796 15.67 0.0001 FERT 3 961.064096 320.354699 132.13 0.0001 HERB*FERT 6 118.120833 19.686806 8.12 0.0001 Source Type III Expected Mean Square HERB Var(Error) + 4 Var(PLOT(HERB)) + Q(HERB,HERB*FERT) PLOT(HERB) Var(Error) + 4 Var(PLOT(HERB)) FERT Var(Error) + Q(FERT,HERB*FERT) HERB*FERT Var(Error) + Q(HERB*FERT) Standard Errors and Probabilities calculated using the Type III MS for PLOT(HERB) as an Error term HERB HEIGHT Std Err Pr > |T| LSMEAN LSMEAN LSMEAN H0:LSMEAN=0 Number 1 12.4166667 1.7791336 0.0001 1 2 17.5000000 1.3781110 0.0001 2 3 15.9375000 1.5407749 0.0001 3 Pr > |T| H0: LSMEAN(i)=LSMEAN(j) i/j 1 2 3 1 . 0.0503 0.1689 2 0.0503 . 0.4691 3 0.1689 0.4691 . FERT HEIGHT Std Err Pr > |T| LSMEAN LSMEAN LSMEAN H0:LSMEAN=0 Number 1 8.2166667 0.4593741 0.0001 1 2 14.5500000 0.4593741 0.0001 2 3 18.0222222 0.4593741 0.0001 3 4 20.3500000 0.4593741 0.0001 4 Pr > |T| H0: LSMEAN(i)=LSMEAN(j) i/j 1 2 3 4 1 . 0.0001 0.0001 0.0001 2 0.0001 . 0.0001 0.0001 3 0.0001 0.0001 . 0.0013 4 0.0001 0.0001 0.0013 . HERB FERT HEIGHT Std Err Pr > |T| LSMEAN LSMEAN LSMEAN H0:LSMEAN=0 Number 1 1 7.0000000 0.8989878 0.0001 1 1 2 11.0000000 0.8989878 0.0001 2 1 3 14.6666667 0.8989878 0.0001 3 1 4 17.0000000 0.8989878 0.0001 4 2 1 11.4000000 0.6963529 0.0001 5 2 2 14.4000000 0.6963529 0.0001 6 2 3 20.4000000 0.6963529 0.0001 7 2 4 23.8000000 0.6963529 0.0001 8 3 1 6.2500000 0.7785462 0.0001 9 3 2 18.2500000 0.7785462 0.0001 10 3 3 19.0000000 0.7785462 0.0001 11 3 4 20.2500000 0.7785462 0.0001 12 Pr > |T| H0: LSMEAN(i)=LSMEAN(j) i/j 1 2 3 4 5 6 7 8 9 1 . 0.0040 0.0001 0.0001 0.0006 0.0001 0.0001 0.0001 0.5336 2 0.0040 . 0.0076 0.0001 0.7277 0.0059 0.0001 0.0001 0.0004 3 0.0001 0.0076 . 0.0775 0.0078 0.8164 0.0001 0.0001 0.0001 4 0.0001 0.0001 0.0775 . 0.0001 0.0303 0.0059 0.0001 0.0001 5 0.0006 0.7277 0.0078 0.0001 . 0.0051 0.0001 0.0001 0.0001 6 0.0001 0.0059 0.8164 0.0303 0.0051 . 0.0001 0.0001 0.0001 7 0.0001 0.0001 0.0001 0.0059 0.0001 0.0001 . 0.0018 0.0001 8 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0018 . 0.0001 9 0.5336 0.0004 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 . 10 0.0001 0.0001 0.0056 0.3025 0.0001 0.0010 0.0493 0.0001 0.0001 11 0.0001 0.0001 0.0011 0.1042 0.0001 0.0002 0.1913 0.0001 0.0001 12 0.0001 0.0001 0.0001 0.0109 0.0001 0.0001 0.8869 0.0021 0.0001 i/j 10 11 12 1 0.0001 0.0001 0.0001 2 0.0001 0.0001 0.0001 3 0.0056 0.0011 0.0001 4 0.3025 0.1042 0.0109 5 0.0001 0.0001 0.0001 6 0.0010 0.0002 0.0001 7 0.0493 0.1913 0.8869 8 0.0001 0.0001 0.0021 9 0.0001 0.0001 0.0001 10 . 0.5016 0.0804 11 0.5016 . 0.2662 12 0.0804 0.2662 . Tests of Hypotheses using the Type III MS for PLOT(HERB) as an error term Source DF Type III SS Mean Square F Value Pr > F HERB 2 195.062500 97.531250 2.57 0.1311 T for H0: Pr > |T| Std Error of Parameter Estimate Parameter=0 Estimate fert 1 8.21666667 17.89 0.0001 0.45937405