1 EXAMPLE 20. TWO-WAY ANOVA: BATTERY DATA 1 15:35 Tuesday, August 21, 2001 The ANOVA Procedure Class Level Information Class Levels Values PLATE 3 M1 M2 M3 TEMP 3 T1 T2 T3 Number of observations 36 1 EXAMPLE 20. TWO-WAY ANOVA: BATTERY DATA 2 15:35 Tuesday, August 21, 2001 The ANOVA Procedure Dependent Variable: LIFE Sum of Source DF Squares Mean Square F Value Model 8 59416.22222 7427.02778 11.00 Error 27 18230.75000 675.21296 Corrected Total 35 77646.97222 Source Pr > F Model <.0001 Error Corrected Total R-Square Coeff Var Root MSE LIFE Mean 0.765210 24.62372 25.98486 105.5278 Source DF Anova SS Mean Square F Value PLATE 2 10683.72222 5341.86111 7.91 TEMP 2 39118.72222 19559.36111 28.97 PLATE*TEMP 4 9613.77778 2403.44444 3.56 Source Pr > F PLATE 0.0020 TEMP <.0001 PLATE*TEMP 0.0186 1 EXAMPLE 20. TWO-WAY ANOVA: BATTERY DATA 3 15:35 Tuesday, August 21, 2001 The ANOVA Procedure Duncan's Multiple Range Test for LIFE NOTE: This test controls the Type I comparisonwise error rate, not the experimentwise error rate. Alpha 0.05 Error Degrees of Freedom 27 Error Mean Square 675.213 Number of Means 2 3 Critical Range 21.77 22.87 Means with the same letter are not significantly different. Duncan Grouping Mean N PLATE A 125.08 12 M3 A A 108.33 12 M2 B 83.17 12 M1 1 EXAMPLE 20. TWO-WAY ANOVA: BATTERY DATA 4 15:35 Tuesday, August 21, 2001 The ANOVA Procedure Duncan's Multiple Range Test for LIFE NOTE: This test controls the Type I comparisonwise error rate, not the experimentwise error rate. Alpha 0.05 Error Degrees of Freedom 27 Error Mean Square 675.213 Number of Means 2 3 Critical Range 21.77 22.87 Means with the same letter are not significantly different. Duncan Grouping Mean N TEMP A 144.83 12 T1 B 107.58 12 T2 C 64.17 12 T3 1 EXAMPLE 20. TWO-WAY ANOVA: BATTERY DATA 5 15:35 Tuesday, August 21, 2001 The ANOVA Procedure Level of Level of -------------LIFE------------ PLATE TEMP N Mean Std Dev M1 T1 4 134.750000 45.3532432 M1 T2 4 57.250000 23.5990819 M1 T3 4 57.500000 26.8514432 M2 T1 4 155.750000 25.6173769 M2 T2 4 119.750000 12.6589889 M2 T3 4 49.500000 19.2613603 M3 T1 4 144.000000 25.9743463 M3 T2 4 145.750000 22.5444006 M3 T3 4 85.500000 19.2786583 1 EXAMPLE 20. TWO-WAY ANOVA: BATTERY DATA 6 15:35 Tuesday, August 21, 2001 ------------------------------- TEMP=T1 -------------------------------- The ANOVA Procedure Class Level Information Class Levels Values PLATE 3 M1 M2 M3 Number of observations 12 1 EXAMPLE 20. TWO-WAY ANOVA: BATTERY DATA 7 15:35 Tuesday, August 21, 2001 ------------------------------- TEMP=T1 -------------------------------- The ANOVA Procedure Dependent Variable: LIFE Sum of Source DF Squares Mean Square F Value Model 2 886.16667 443.08333 0.39 Error 9 10163.50000 1129.27778 Corrected Total 11 11049.66667 Source Pr > F Model 0.6865 Error Corrected Total R-Square Coeff Var Root MSE LIFE Mean 0.080198 23.20234 33.60473 144.8333 Source DF Anova SS Mean Square F Value PLATE 2 886.1666667 443.0833333 0.39 Source Pr > F PLATE 0.6865 1 EXAMPLE 20. TWO-WAY ANOVA: BATTERY DATA 8 15:35 Tuesday, August 21, 2001 ------------------------------- TEMP=T1 -------------------------------- The ANOVA Procedure Duncan's Multiple Range Test for LIFE NOTE: This test controls the Type I comparisonwise error rate, not the experimentwise error rate. Alpha 0.05 Error Degrees of Freedom 9 Error Mean Square 1129.278 Number of Means 2 3 Critical Range 53.75 56.11 Means with the same letter are not significantly different. Duncan Grouping Mean N PLATE A 155.75 4 M2 A A 144.00 4 M3 A A 134.75 4 M1 1 EXAMPLE 20. TWO-WAY ANOVA: BATTERY DATA 9 15:35 Tuesday, August 21, 2001 ------------------------------- TEMP=T2 -------------------------------- The ANOVA Procedure Class Level Information Class Levels Values PLATE 3 M1 M2 M3 Number of observations 12 1 EXAMPLE 20. TWO-WAY ANOVA: BATTERY DATA 10 15:35 Tuesday, August 21, 2001 ------------------------------- TEMP=T2 -------------------------------- The ANOVA Procedure Dependent Variable: LIFE Sum of Source DF Squares Mean Square F Value Model 2 16552.66667 8276.33333 20.26 Error 9 3676.25000 408.47222 Corrected Total 11 20228.91667 Source Pr > F Model 0.0005 Error Corrected Total R-Square Coeff Var Root MSE LIFE Mean 0.818268 18.78608 20.21070 107.5833 Source DF Anova SS Mean Square F Value PLATE 2 16552.66667 8276.33333 20.26 Source Pr > F PLATE 0.0005 1 EXAMPLE 20. TWO-WAY ANOVA: BATTERY DATA 11 15:35 Tuesday, August 21, 2001 ------------------------------- TEMP=T2 -------------------------------- The ANOVA Procedure Duncan's Multiple Range Test for LIFE NOTE: This test controls the Type I comparisonwise error rate, not the experimentwise error rate. Alpha 0.05 Error Degrees of Freedom 9 Error Mean Square 408.4722 Number of Means 2 3 Critical Range 32.33 33.74 Means with the same letter are not significantly different. Duncan Grouping Mean N PLATE A 145.75 4 M3 A A 119.75 4 M2 B 57.25 4 M1 1 EXAMPLE 20. TWO-WAY ANOVA: BATTERY DATA 12 15:35 Tuesday, August 21, 2001 ------------------------------- TEMP=T3 -------------------------------- The ANOVA Procedure Class Level Information Class Levels Values PLATE 3 M1 M2 M3 Number of observations 12 1 EXAMPLE 20. TWO-WAY ANOVA: BATTERY DATA 13 15:35 Tuesday, August 21, 2001 ------------------------------- TEMP=T3 -------------------------------- The ANOVA Procedure Dependent Variable: LIFE Sum of Source DF Squares Mean Square F Value Model 2 2858.666667 1429.333333 2.93 Error 9 4391.000000 487.888889 Corrected Total 11 7249.666667 Source Pr > F Model 0.1047 Error Corrected Total R-Square Coeff Var Root MSE LIFE Mean 0.394317 34.42318 22.08821 64.16667 Source DF Anova SS Mean Square F Value PLATE 2 2858.666667 1429.333333 2.93 Source Pr > F PLATE 0.1047 1 EXAMPLE 20. TWO-WAY ANOVA: BATTERY DATA 14 15:35 Tuesday, August 21, 2001 ------------------------------- TEMP=T3 -------------------------------- The ANOVA Procedure Duncan's Multiple Range Test for LIFE NOTE: This test controls the Type I comparisonwise error rate, not the experimentwise error rate. Alpha 0.05 Error Degrees of Freedom 9 Error Mean Square 487.8889 Number of Means 2 3 Critical Range 35.33 36.88 Means with the same letter are not significantly different. Duncan Grouping Mean N PLATE A 85.50 4 M3 A A 57.50 4 M1 A A 49.50 4 M2 1 EXAMPLE 20. TWO-WAY ANOVA: BATTERY DATA 15 15:35 Tuesday, August 21, 2001 The GLM Procedure Class Level Information Class Levels Values PLATE 3 M1 M2 M3 TEMP 3 T1 T2 T3 Number of observations 36 1 EXAMPLE 20. TWO-WAY ANOVA: BATTERY DATA 16 15:35 Tuesday, August 21, 2001 The GLM Procedure General Form of Estimable Functions Effect Coefficients Intercept L1 PLATE M1 L2 PLATE M2 L3 PLATE M3 L1-L2-L3 TEMP T1 L5 TEMP T2 L6 TEMP T3 L1-L5-L6 PLATE*TEMP M1 T1 L8 PLATE*TEMP M1 T2 L9 PLATE*TEMP M1 T3 L2-L8-L9 PLATE*TEMP M2 T1 L11 PLATE*TEMP M2 T2 L12 PLATE*TEMP M2 T3 L3-L11-L12 PLATE*TEMP M3 T1 L5-L8-L11 PLATE*TEMP M3 T2 L6-L9-L12 PLATE*TEMP M3 T3 L1-L2-L3-L5-L6+L8+L9+L11+L12 Type I Estimable Functions ----------------Coefficients---------------- Effect PLATE TEMP Intercept 0 0 PLATE M1 L2 0 PLATE M2 L3 0 PLATE M3 -L2-L3 0 TEMP T1 0 L5 TEMP T2 0 L6 TEMP T3 0 -L5-L6 PLATE*TEMP M1 T1 0.3333*L2 0.3333*L5 PLATE*TEMP M1 T2 0.3333*L2 0.3333*L6 PLATE*TEMP M1 T3 0.3333*L2 -0.3333*L5-0.3333*L6 PLATE*TEMP M2 T1 0.3333*L3 0.3333*L5 PLATE*TEMP M2 T2 0.3333*L3 0.3333*L6 PLATE*TEMP M2 T3 0.3333*L3 -0.3333*L5-0.3333*L6 PLATE*TEMP M3 T1 -0.3333*L2-0.3333*L3 0.3333*L5 PLATE*TEMP M3 T2 -0.3333*L2-0.3333*L3 0.3333*L6 PLATE*TEMP M3 T3 -0.3333*L2-0.3333*L3 -0.3333*L5-0.3333*L6 1 EXAMPLE 20. TWO-WAY ANOVA: BATTERY DATA 17 15:35 Tuesday, August 21, 2001 The GLM Procedure Type I Estimable Functions -Coefficients- Effect PLATE*TEMP Intercept 0 PLATE M1 0 PLATE M2 0 PLATE M3 0 TEMP T1 0 TEMP T2 0 TEMP T3 0 PLATE*TEMP M1 T1 L8 PLATE*TEMP M1 T2 L9 PLATE*TEMP M1 T3 -L8-L9 PLATE*TEMP M2 T1 L11 PLATE*TEMP M2 T2 L12 PLATE*TEMP M2 T3 -L11-L12 PLATE*TEMP M3 T1 -L8-L11 PLATE*TEMP M3 T2 -L9-L12 PLATE*TEMP M3 T3 L8+L9+L11+L12 Type II Estimable Functions ----------------Coefficients---------------- Effect PLATE TEMP Intercept 0 0 PLATE M1 L2 0 PLATE M2 L3 0 PLATE M3 -L2-L3 0 TEMP T1 0 L5 TEMP T2 0 L6 TEMP T3 0 -L5-L6 PLATE*TEMP M1 T1 0.3333*L2 0.3333*L5 PLATE*TEMP M1 T2 0.3333*L2 0.3333*L6 PLATE*TEMP M1 T3 0.3333*L2 -0.3333*L5-0.3333*L6 PLATE*TEMP M2 T1 0.3333*L3 0.3333*L5 PLATE*TEMP M2 T2 0.3333*L3 0.3333*L6 PLATE*TEMP M2 T3 0.3333*L3 -0.3333*L5-0.3333*L6 PLATE*TEMP M3 T1 -0.3333*L2-0.3333*L3 0.3333*L5 PLATE*TEMP M3 T2 -0.3333*L2-0.3333*L3 0.3333*L6 PLATE*TEMP M3 T3 -0.3333*L2-0.3333*L3 -0.3333*L5-0.3333*L6 1 EXAMPLE 20. TWO-WAY ANOVA: BATTERY DATA 18 15:35 Tuesday, August 21, 2001 The GLM Procedure Type II Estimable Functions -Coefficients- Effect PLATE*TEMP Intercept 0 PLATE M1 0 PLATE M2 0 PLATE M3 0 TEMP T1 0 TEMP T2 0 TEMP T3 0 PLATE*TEMP M1 T1 L8 PLATE*TEMP M1 T2 L9 PLATE*TEMP M1 T3 -L8-L9 PLATE*TEMP M2 T1 L11 PLATE*TEMP M2 T2 L12 PLATE*TEMP M2 T3 -L11-L12 PLATE*TEMP M3 T1 -L8-L11 PLATE*TEMP M3 T2 -L9-L12 PLATE*TEMP M3 T3 L8+L9+L11+L12 Type III Estimable Functions ----------------Coefficients---------------- Effect PLATE TEMP Intercept 0 0 PLATE M1 L2 0 PLATE M2 L3 0 PLATE M3 -L2-L3 0 TEMP T1 0 L5 TEMP T2 0 L6 TEMP T3 0 -L5-L6 PLATE*TEMP M1 T1 0.3333*L2 0.3333*L5 PLATE*TEMP M1 T2 0.3333*L2 0.3333*L6 PLATE*TEMP M1 T3 0.3333*L2 -0.3333*L5-0.3333*L6 PLATE*TEMP M2 T1 0.3333*L3 0.3333*L5 PLATE*TEMP M2 T2 0.3333*L3 0.3333*L6 PLATE*TEMP M2 T3 0.3333*L3 -0.3333*L5-0.3333*L6 PLATE*TEMP M3 T1 -0.3333*L2-0.3333*L3 0.3333*L5 PLATE*TEMP M3 T2 -0.3333*L2-0.3333*L3 0.3333*L6 PLATE*TEMP M3 T3 -0.3333*L2-0.3333*L3 -0.3333*L5-0.3333*L6 1 EXAMPLE 20. TWO-WAY ANOVA: BATTERY DATA 19 15:35 Tuesday, August 21, 2001 The GLM Procedure Type III Estimable Functions -Coefficients- Effect PLATE*TEMP Intercept 0 PLATE M1 0 PLATE M2 0 PLATE M3 0 TEMP T1 0 TEMP T2 0 TEMP T3 0 PLATE*TEMP M1 T1 L8 PLATE*TEMP M1 T2 L9 PLATE*TEMP M1 T3 -L8-L9 PLATE*TEMP M2 T1 L11 PLATE*TEMP M2 T2 L12 PLATE*TEMP M2 T3 -L11-L12 PLATE*TEMP M3 T1 -L8-L11 PLATE*TEMP M3 T2 -L9-L12 PLATE*TEMP M3 T3 L8+L9+L11+L12 Type IV Estimable Functions ----------------Coefficients---------------- Effect PLATE TEMP Intercept 0 0 PLATE M1 L2 0 PLATE M2 L3 0 PLATE M3 -L2-L3 0 TEMP T1 0 L5 TEMP T2 0 L6 TEMP T3 0 -L5-L6 PLATE*TEMP M1 T1 0.3333*L2 0.3333*L5 PLATE*TEMP M1 T2 0.3333*L2 0.3333*L6 PLATE*TEMP M1 T3 0.3333*L2 -0.3333*L5-0.3333*L6 PLATE*TEMP M2 T1 0.3333*L3 0.3333*L5 PLATE*TEMP M2 T2 0.3333*L3 0.3333*L6 PLATE*TEMP M2 T3 0.3333*L3 -0.3333*L5-0.3333*L6 PLATE*TEMP M3 T1 -0.3333*L2-0.3333*L3 0.3333*L5 PLATE*TEMP M3 T2 -0.3333*L2-0.3333*L3 0.3333*L6 PLATE*TEMP M3 T3 -0.3333*L2-0.3333*L3 -0.3333*L5-0.3333*L6 1 EXAMPLE 20. TWO-WAY ANOVA: BATTERY DATA 20 15:35 Tuesday, August 21, 2001 The GLM Procedure Type IV Estimable Functions -Coefficients- Effect PLATE*TEMP Intercept 0 PLATE M1 0 PLATE M2 0 PLATE M3 0 TEMP T1 0 TEMP T2 0 TEMP T3 0 PLATE*TEMP M1 T1 L8 PLATE*TEMP M1 T2 L9 PLATE*TEMP M1 T3 -L8-L9 PLATE*TEMP M2 T1 L11 PLATE*TEMP M2 T2 L12 PLATE*TEMP M2 T3 -L11-L12 PLATE*TEMP M3 T1 -L8-L11 PLATE*TEMP M3 T2 -L9-L12 PLATE*TEMP M3 T3 L8+L9+L11+L12 1 EXAMPLE 20. TWO-WAY ANOVA: BATTERY DATA 21 15:35 Tuesday, August 21, 2001 The GLM Procedure Dependent Variable: LIFE Sum of Source DF Squares Mean Square F Value Model 8 59416.22222 7427.02778 11.00 Error 27 18230.75000 675.21296 Corrected Total 35 77646.97222 Source Pr > F Model <.0001 Error Corrected Total R-Square Coeff Var Root MSE LIFE Mean 0.765210 24.62372 25.98486 105.5278 Source DF Type I SS Mean Square F Value PLATE 2 10683.72222 5341.86111 7.91 TEMP 2 39118.72222 19559.36111 28.97 PLATE*TEMP 4 9613.77778 2403.44444 3.56 Source Pr > F PLATE 0.0020 TEMP <.0001 PLATE*TEMP 0.0186 Source DF Type II SS Mean Square F Value PLATE 2 10683.72222 5341.86111 7.91 TEMP 2 39118.72222 19559.36111 28.97 PLATE*TEMP 4 9613.77778 2403.44444 3.56 Source Pr > F PLATE 0.0020 TEMP <.0001 PLATE*TEMP 0.0186 Source DF Type III SS Mean Square F Value PLATE 2 10683.72222 5341.86111 7.91 TEMP 2 39118.72222 19559.36111 28.97 1 EXAMPLE 20. TWO-WAY ANOVA: BATTERY DATA 22 15:35 Tuesday, August 21, 2001 The GLM Procedure Dependent Variable: LIFE Source DF Type III SS Mean Square F Value PLATE*TEMP 4 9613.77778 2403.44444 3.56 Source Pr > F PLATE 0.0020 TEMP <.0001 PLATE*TEMP 0.0186 Source DF Type IV SS Mean Square F Value PLATE 2 10683.72222 5341.86111 7.91 TEMP 2 39118.72222 19559.36111 28.97 PLATE*TEMP 4 9613.77778 2403.44444 3.56 Source Pr > F PLATE 0.0020 TEMP <.0001 PLATE*TEMP 0.0186 Contrast DF Contrast SS Mean Square F Value P1 VS P2,P3*TEMPS 2 7077.027778 3538.513889 5.24 Contrast Pr > F P1 VS P2,P3*TEMPS 0.0119 Standard Parameter Estimate Error t Value Pr > |t| P1 VS P2,P3 IN T1 -15.1250000 15.9124122 -0.95 0.3503 P1 VS P2,P3 IN T2 -75.5000000 15.9124122 -4.74 <.0001 P1 VS P2,P3 IN T3 -10.0000000 15.9124122 -0.63 0.5350 Standard Parameter Estimate Error t Value Pr > |t| Intercept 85.50000000 B 12.99243013 6.58 <.0001 PLATE M1 -28.00000000 B 18.37407090 -1.52 0.1392 PLATE M2 -36.00000000 B 18.37407090 -1.96 0.0605 PLATE M3 0.00000000 B . . . TEMP T1 58.50000000 B 18.37407090 3.18 0.0036 TEMP T2 60.25000000 B 18.37407090 3.28 0.0029 TEMP T3 0.00000000 B . . . PLATE*TEMP M1 T1 18.75000000 B 25.98486026 0.72 0.4768 PLATE*TEMP M1 T2 -60.50000000 B 25.98486026 -2.33 0.0276 1 EXAMPLE 20. TWO-WAY ANOVA: BATTERY DATA 23 15:35 Tuesday, August 21, 2001 The GLM Procedure Dependent Variable: LIFE Standard Parameter Estimate Error t Value Pr > |t| PLATE*TEMP M1 T3 0.00000000 B . . . PLATE*TEMP M2 T1 47.75000000 B 25.98486026 1.84 0.0771 PLATE*TEMP M2 T2 10.00000000 B 25.98486026 0.38 0.7034 PLATE*TEMP M2 T3 0.00000000 B . . . PLATE*TEMP M3 T1 0.00000000 B . . . PLATE*TEMP M3 T2 0.00000000 B . . . PLATE*TEMP M3 T3 0.00000000 B . . . NOTE: The X'X matrix has been found to be singular, and a generalized inverse was used to solve the normal equations. Terms whose estimates are followed by the letter 'B' are not uniquely estimable.