Spectral Reflection Data (Page 355, Johnson and Wichern)
Multivariate Analysis of Variance
Univariate Two-Factor Anova

The GLM Procedure

Class Level Information
Class Levels Values
spec 3 JL LP SS
t 3 1 2 3

Number of Observations Read 36
Number of Observations Used 36

Spectral Reflection Data (Page 355, Johnson and Wichern)
Multivariate Analysis of Variance
Univariate Two-Factor Anova

The GLM Procedure
 
Dependent Variable: l1

Source DF Sum of Squares Mean Square F Value Pr > F
Model 8 3036.236856 379.529607 133.67 <.0001
Error 27 76.658775 2.839214    
Corrected Total 35 3112.895631      

R-Square Coeff Var Root MSE l1 Mean
0.975374 11.78205 1.684997 14.30139

Source DF Type III SS Mean Square F Value Pr > F
spec 2 965.181172 482.590586 169.97 <.0001
t 2 1275.247739 637.623869 224.58 <.0001
spec*t 4 795.807944 198.951986 70.07 <.0001

Spectral Reflection Data (Page 355, Johnson and Wichern)
Multivariate Analysis of Variance
Univariate Two-Factor Anova

The GLM Procedure
 
Dependent Variable: l2

Source DF Sum of Squares Mean Square F Value Pr > F
Model 8 7794.211339 974.276417 14.86 <.0001
Error 27 1769.642225 65.542305    
Corrected Total 35 9563.853564      

R-Square Coeff Var Root MSE l2 Mean
0.814966 22.62157 8.095820 35.78806

Source DF Type III SS Mean Square F Value Pr > F
spec 2 2026.856372 1013.428186 15.46 <.0001
t 2 5573.805706 2786.902853 42.52 <.0001
spec*t 4 193.549261 48.387315 0.74 0.5741

Spectral Reflection Data (Page 355, Johnson and Wichern)
Multivariate Analysis of Variance
Univariate Two-Factor Anova

The GLM Procedure
Multivariate Analysis of Variance

E = Error SSCP Matrix
  l1 l2
l1 76.658775 37.9299
l2 37.9299 1769.642225

Partial Correlation Coefficients from the Error SSCP Matrix / Prob > |r|
DF = 27 l1 l2
l1 1.000000
 0.102981
0.6020
l2 0.102981
0.6020		 1.000000

Spectral Reflection Data (Page 355, Johnson and Wichern)
Multivariate Analysis of Variance
Univariate Two-Factor Anova

The GLM Procedure
Multivariate Analysis of Variance

Characteristic Roots and Vectors of: E Inverse * H, where
H = Type III SSCP Matrix for spec
E = Error SSCP Matrix
Characteristic Root Percent Characteristic Vector V'EV=1
l1 l2
13.0712473 99.75 0.10981860 0.00458854
0.0333424 0.25 -0.03353388 0.02345396

MANOVA Test Criteria and F Approximations for
the Hypothesis of No Overall spec Effect
H = Type III SSCP Matrix for spec
E = Error SSCP Matrix

S=2 M=-0.5 N=12
Statistic Value F Value Num DF Den DF Pr > F
Wilks' Lambda 0.06877382 36.57 4 52 <.0001
Pillai's Trace 0.96119962 12.49 4 54 <.0001
Hotelling-Lawley Trace 13.10458966 84.21 4 30.19 <.0001
Roy's Greatest Root 13.07124729 176.46 2 27 <.0001
NOTE: F Statistic for Roy's Greatest Root is an upper bound.
NOTE: F Statistic for Wilks' Lambda is exact.

Characteristic Roots and Vectors of: E Inverse * H, where
H = Type III SSCP Matrix for t
E = Error SSCP Matrix
Characteristic Root Percent Characteristic Vector V'EV=1
l1 l2
18.4568938 99.75 0.10469772 0.00751699
0.0453490 0.25 -0.04714907 0.02268563

MANOVA Test Criteria and F Approximations
for the Hypothesis of No Overall t Effect
H = Type III SSCP Matrix for t
E = Error SSCP Matrix

S=2 M=-0.5 N=12
Statistic Value F Value Num DF Den DF Pr > F
Wilks' Lambda 0.04916603 45.63 4 52 <.0001
Pillai's Trace 0.99198604 13.29 4 54 <.0001
Hotelling-Lawley Trace 18.50224287 118.89 4 30.19 <.0001
Roy's Greatest Root 18.45689384 249.17 2 27 <.0001
NOTE: F Statistic for Roy's Greatest Root is an upper bound.
NOTE: F Statistic for Wilks' Lambda is exact.

Characteristic Roots and Vectors of: E Inverse * H, where
H = Type III SSCP Matrix for spec*t
E = Error SSCP Matrix
Characteristic Root Percent Characteristic Vector V'EV=1
l1 l2
10.3813996 99.91 0.11426805 -0.00011191
0.0090999 0.09 -0.01128981 0.02389834

MANOVA Test Criteria and F Approximations for
the Hypothesis of No Overall spec*t Effect
H = Type III SSCP Matrix for spec*t
E = Error SSCP Matrix

S=2 M=0.5 N=12
Statistic Value F Value Num DF Den DF Pr > F
Wilks' Lambda 0.08707032 15.53 8 52 <.0001
Pillai's Trace 0.92115522 5.76 8 54 <.0001
Hotelling-Lawley Trace 10.39049958 33.07 8 34.899 <.0001
Roy's Greatest Root 10.38139964 70.07 4 27 <.0001
NOTE: F Statistic for Roy's Greatest Root is an upper bound.
NOTE: F Statistic for Wilks' Lambda is exact.

Spectral Reflection Data (Page 355, Johnson and Wichern)
Multivariate Analysis of Variance
Univariate Two-Factor Anova

The GLM Procedure

Class Level Information
Class Levels Values
spec 3 JL LP SS
t 3 1 2 3

Number of Observations Read 36
Number of Observations Used 36

Spectral Reflection Data (Page 355, Johnson and Wichern)
Multivariate Analysis of Variance
Univariate Two-Factor Anova

The GLM Procedure
 
Dependent Variable: l1

Source DF Sum of Squares Mean Square F Value Pr > F
Model 4 2240.428911 560.107228 19.90 <.0001
Error 31 872.466719 28.144088    
Corrected Total 35 3112.895631      

R-Square Coeff Var Root MSE l1 Mean
0.719725 37.09500 5.305100 14.30139

Source DF Type III SS Mean Square F Value Pr > F
spec 2 965.181172 482.590586 17.15 <.0001
t 2 1275.247739 637.623869 22.66 <.0001

Spectral Reflection Data (Page 355, Johnson and Wichern)
Multivariate Analysis of Variance
Univariate Two-Factor Anova

The GLM Procedure
 
Dependent Variable: l2

Source DF Sum of Squares Mean Square F Value Pr > F
Model 4 7600.662078 1900.165519 30.00 <.0001
Error 31 1963.191486 63.328758    
Corrected Total 35 9563.853564      

R-Square Coeff Var Root MSE l2 Mean
0.794728 22.23629 7.957937 35.78806

Source DF Type III SS Mean Square F Value Pr > F
spec 2 2026.856372 1013.428186 16.00 <.0001
t 2 5573.805706 2786.902853 44.01 <.0001

Spectral Reflection Data (Page 355, Johnson and Wichern)
Multivariate Analysis of Variance
Univariate Two-Factor Anova

The GLM Procedure
Multivariate Analysis of Variance

E = Error SSCP Matrix
  l1 l2
l1 872.46671944 413.89301944
l2 413.89301944 1963.1914861

Partial Correlation Coefficients from the Error SSCP Matrix / Prob > |r|
DF = 31 l1 l2
l1 1.000000
 0.316251
0.0778
l2 0.316251
0.0778		 1.000000

Spectral Reflection Data (Page 355, Johnson and Wichern)
Multivariate Analysis of Variance
Univariate Two-Factor Anova

The GLM Procedure
Multivariate Analysis of Variance

Characteristic Roots and Vectors of: E Inverse * H, where
H = Type III SSCP Matrix for spec
E = Error SSCP Matrix
Characteristic Root Percent Characteristic Vector V'EV=1
l1 l2
1.61307657 98.56 0.02156884 0.01343340
0.02352494 1.44 -0.02843123 0.01963479

MANOVA Test Criteria and F Approximations for
the Hypothesis of No Overall spec Effect
H = Type III SSCP Matrix for spec
E = Error SSCP Matrix

S=2 M=-0.5 N=14
Statistic Value F Value Num DF Den DF Pr > F
Wilks' Lambda 0.37389481 9.53 4 60 <.0001
Pillai's Trace 0.64029358 7.30 4 62 <.0001
Hotelling-Lawley Trace 1.63660152 12.15 4 34.986 <.0001
Roy's Greatest Root 1.61307657 25.00 2 31 <.0001
NOTE: F Statistic for Roy's Greatest Root is an upper bound.
NOTE: F Statistic for Wilks' Lambda is exact.

Characteristic Roots and Vectors of: E Inverse * H, where
H = Type III SSCP Matrix for t
E = Error SSCP Matrix
Characteristic Root Percent Characteristic Vector V'EV=1
l1 l2
3.33660231 99.35 0.01382468 0.01789242
0.02184199 0.65 -0.03290027 0.01567936

MANOVA Test Criteria and F Approximations
for the Hypothesis of No Overall t Effect
H = Type III SSCP Matrix for t
E = Error SSCP Matrix

S=2 M=-0.5 N=14
Statistic Value F Value Num DF Den DF Pr > F
Wilks' Lambda 0.22566627 16.58 4 60 <.0001
Pillai's Trace 0.79077984 10.14 4 62 <.0001
Hotelling-Lawley Trace 3.35844430 24.93 4 34.986 <.0001
Roy's Greatest Root 3.33660231 51.72 2 31 <.0001
NOTE: F Statistic for Roy's Greatest Root is an upper bound.
NOTE: F Statistic for Wilks' Lambda is exact.