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

Obs l1 l2 spec t count
1 9.33 19.14 SS 1 1
2 8.74 19.55 SS 1 2
3 9.31 19.24 SS 1 3
4 8.27 16.37 SS 1 4
5 10.22 25.00 SS 2 1
6 10.13 25.32 SS 2 2
7 10.42 27.12 SS 2 3
8 10.62 26.28 SS 2 4
9 15.25 38.89 SS 3 1
10 16.22 36.67 SS 3 2
11 17.24 40.74 SS 3 3
12 12.77 67.50 SS 3 4
13 12.07 33.03 JL 1 1
14 11.03 32.37 JL 1 2
15 12.48 31.31 JL 1 3
16 12.12 33.33 JL 1 4
17 15.38 40.00 JL 2 1
18 14.21 40.48 JL 2 2
19 9.69 33.90 JL 2 3
20 14.35 40.15 JL 2 4
21 38.71 77.14 JL 3 1
22 44.74 78.57 JL 3 2
23 36.67 71.43 JL 3 3
24 37.21 45.00 JL 3 4
25 8.73 23.27 LP 1 1
26 7.94 20.87 LP 1 2
27 8.37 22.16 LP 1 3
28 7.86 21.78 LP 1 4
29 8.45 26.32 LP 2 1
30 6.79 22.73 LP 2 2
31 8.34 26.67 LP 2 3
32 7.54 24.87 LP 2 4
33 14.04 44.44 LP 3 1
34 13.51 37.93 LP 3 2
35 13.33 37.93 LP 3 3
36 12.77 60.87 LP 3 4

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

Level of
spec		 N l1 l2
Mean Std Dev Mean Std Dev
JL 12 21.5550000 13.3561906 46.3925000 18.2252732
LP 12 9.8058333 2.7229311 30.8200000 12.2127221
SS 12 11.5433333 3.0732048 30.1516667 14.2783191