The SAS System 10:13 Wednesday, April 8, 1998 1 General Linear Models Procedure Class Level Information Class Levels Values TEMP 3 High Low Medium BATCH 2 1 2 Number of observations in data set = 18 The SAS System 10:13 Wednesday, April 8, 1998 2 General Linear Models Procedure Dependent Variable: CRUSTY Crustiness of bread Sum of Mean Source DF Squares Square F Value Pr > F Model 5 284.44444444 56.88888889 21.79 0.0001 Error 12 31.33333333 2.61111111 Corrected Total 17 315.77777778 R-Square C.V. Root MSE CRUSTY Mean 0.900774 13.59163 1.6158933 11.888889 Source DF Type I SS Mean Square F Value Pr > F TEMP 2 235.44444444 117.72222222 45.09 0.0001 BATCH(TEMP) 3 49.00000000 16.33333333 6.26 0.0084 Source DF Type III SS Mean Square F Value Pr > F TEMP 2 235.44444444 117.72222222 45.09 0.0001 BATCH(TEMP) 3 49.00000000 16.33333333 6.26 0.0084 The SAS System 10:13 Wednesday, April 8, 1998 3 General Linear Models Procedure Source Type III Expected Mean Square TEMP Var(Error) + 3 Var(BATCH(TEMP)) + Q(TEMP) BATCH(TEMP) Var(Error) + 3 Var(BATCH(TEMP)) The SAS System 10:13 Wednesday, April 8, 1998 4 General Linear Models Procedure Tests of Hypotheses for Mixed Model Analysis of Variance Dependent Variable: CRUSTY Source: TEMP Error: MS(BATCH(TEMP)) Denominator Denominator DF Type III MS DF MS F Value Pr > F 2 117.72222222 3 16.333333333 7.207 0.0715 Source: BATCH(TEMP) Error: MS(Error) Denominator Denominator DF Type III MS DF MS F Value Pr > F 3 16.333333333 12 2.6111111111 6.255 0.0084 The SAS System 10:13 Wednesday, April 8, 1998 5 Level of ------------CRUSTY----------- TEMP N Mean SD High 6 16.5000000 1.87082869 Low 6 7.6666667 3.01109061 Medium 6 11.5000000 1.87082869 Level of Level of ------------CRUSTY----------- BATCH TEMP N Mean SD 1 High 3 15.3333333 1.52752523 2 High 3 17.6666667 1.52752523 1 Low 3 5.3333333 1.52752523 2 Low 3 10.0000000 2.00000000 1 Medium 3 12.6666667 1.52752523 2 Medium 3 10.3333333 1.52752523 The SAS System 10:13 Wednesday, April 8, 1998 6 General Linear Models Procedure Class Level Information Class Levels Values TEMP 3 High Low Medium BATCH 2 1 2 Number of observations in data set = 18 The SAS System 10:13 Wednesday, April 8, 1998 7 General Linear Models Procedure Dependent Variable: CRUSTY Crustiness of bread Sum of Mean Source DF Squares Square F Value Pr > F Model 5 284.44444444 56.88888889 21.79 0.0001 Error 12 31.33333333 2.61111111 Corrected Total 17 315.77777778 R-Square C.V. Root MSE CRUSTY Mean 0.900774 13.59163 1.6158933 11.888889 Source DF Type I SS Mean Square F Value Pr > F TEMP 2 235.44444444 117.72222222 45.09 0.0001 BATCH(TEMP) 3 49.00000000 16.33333333 6.26 0.0084 Source DF Type III SS Mean Square F Value Pr > F TEMP 2 235.44444444 117.72222222 45.09 0.0001 BATCH(TEMP) 3 49.00000000 16.33333333 6.26 0.0084 The SAS System 10:13 Wednesday, April 8, 1998 8 General Linear Models Procedure Source Type III Expected Mean Square TEMP Var(Error) + 3 Var(BATCH(TEMP)) + 6 Var(TEMP) BATCH(TEMP) Var(Error) + 3 Var(BATCH(TEMP)) The SAS System 10:13 Wednesday, April 8, 1998 9 General Linear Models Procedure Tests of Hypotheses for Random Model Analysis of Variance Dependent Variable: CRUSTY Source: TEMP Error: MS(BATCH(TEMP)) Denominator Denominator DF Type III MS DF MS F Value Pr > F 2 117.72222222 3 16.333333333 7.207 0.0715 Source: BATCH(TEMP) Error: MS(Error) Denominator Denominator DF Type III MS DF MS F Value Pr > F 3 16.333333333 12 2.6111111111 6.255 0.0084