While you may receive this reply very late, but I saw it now.
About your question, I did it on a part of minitab datasets i.e. Exh_mvar dataset and created a trial with 3 factors as A, B, C in 2 replications (R).
The dataset and the outputs are brought about here. Shortly in my opinion, generally a similar trend is expected in both anova and manova.
So you could decide as anova for manova. i.e. when A*B effect is significant, we may ignore the significance of main factors (A or B) and so on.
And when interactions (either in anova or in manova) are significant, we can ignore the main effets, and vice versa, i.e. when a main effects is significant and the interaction is nonsign., then we focus on main effect. I wish I have told you the correct things. Because I have not seen any reports regarding multi-level manova.
data and outputs:
Data Display
Row A B C R HeatFlux Insolation
1 1 1 1 1 271.8 783.35
2 1 1 1 2 264.0 748.45
3 1 1 2 1 238.8 684.45
4 1 1 2 2 230.7 827.80
5 1 2 1 1 251.6 860.45
6 1 2 1 2 257.9 875.15
7 1 2 2 1 263.9 909.45
8 1 2 2 2 266.5 905.55
9 2 1 1 1 229.1 756.00
10 2 1 1 2 239.3 769.35
11 2 1 2 1 258.0 793.50
12 2 1 2 2 257.6 801.65
13 2 2 1 1 267.3 819.65
14 2 2 1 2 267.0 808.55
15 2 2 2 1 259.6 774.95
16 2 2 2 2 240.4 711.85
Analysis of Variance for HeatFlux, using Adjusted SS for Tests
Source DF Seq SS Adj SS Adj MS F P
R 1 17.43 17.43 17.43 0.40 0.547
A 1 45.23 45.23 45.23 1.04 0.343
B 1 450.50 450.50 450.50 10.32 0.015
C 1 66.02 66.02 66.02 1.51 0.258
A*B 1 15.41 15.41 15.41 0.35 0.571
A*C 1 212.43 212.43 212.43 4.87 0.063
B*C 1 2.03 2.03 2.03 0.05 0.835
A*B*C 1 1778.73 1778.73 1778.73 40.76 0.000
Error 7 305.48 305.48 43.64
Total 15 2893.25
S = 6.60611 R-Sq = 89.44% R-Sq(adj) = 77.37%
Analysis of Variance for Insolation, using Adjusted SS for Tests
Source DF Seq SS Adj SS Adj MS F P
R 1 277 277 277 0.15 0.710
A 1 8062 8062 8062 4.38 0.075
B 1 15691 15691 15691 8.52 0.022
C 1 9 9 9 0.00 0.947
A*B 1 16387 16387 16387 8.89 0.020
A*C 1 1080 1080 1080 0.59 0.469
B*C 1 788 788 788 0.43 0.534
A*B*C 1 6012 6012 6012 3.26 0.114
Error 7 12897 12897 1842
Total 15 61202
S = 42.9238 R-Sq = 78.93% R-Sq(adj) = 54.84%
Unusual Observations for Insolation
Obs Insolation Fit SE Fit Residual St Resid
3 684.450 751.966 32.193 -67.516 -2.38 R
4 827.800 760.284 32.193 67.516 2.38 R
R denotes an observation with a large standardized residual.
MANOVA for A
s = 1 m = 0.0 n = 2.0
Test DF
Criterion Statistic F Num Denom P
Wilks' 0.59203 2.067 2 6 0.208
Lawley-Hotelling 0.68911 2.067 2 6 0.208
Pillai's 0.40797 2.067 2 6 0.208
Roy's 0.68911
SSCP Matrix (adjusted) for A
HeatFlux Insolation
HeatFlux 45.23 603.8
Insolation 603.82 8061.8
SSCP Matrix (adjusted) for Error
HeatFlux Insolation
HeatFlux 305.5 340.1
Insolation 340.1 12897.2
Partial Correlations for the Error SSCP Matrix
HeatFlux Insolation
HeatFlux 1.00000 0.17135
Insolation 0.17135 1.00000
EIGEN Analysis for A
Eigenvalue 0.6891 0.00000
Proportion 1.0000 0.00000
Cumulative 1.0000 1.00000
Eigenvector 1 2
HeatFlux 0.017702 0.055310
Insolation 0.007920 -0.004143
MANOVA for B
s = 1 m = 0.0 n = 2.0
Test DF
Criterion Statistic F Num Denom P
Wilks' 0.30305 6.899 2 6 0.028
Lawley-Hotelling 2.29980 6.899 2 6 0.028
Pillai's 0.69695 6.899 2 6 0.028
Roy's 2.29980
SSCP Matrix (adjusted) for B
HeatFlux Insolation
HeatFlux 450.5 2659
Insolation 2658.7 15691
EIGEN Analysis for B
Eigenvalue 2.300 0.00000
Proportion 1.000 0.00000
Cumulative 1.000 1.00000
Eigenvector 1 2
HeatFlux 0.039855 -0.04224
Insolation 0.005353 0.00716
MANOVA for C
s = 1 m = 0.0 n = 2.0
Test DF
Criterion Statistic F Num Denom P
Wilks' 0.82029 0.657 2 6 0.552
Lawley-Hotelling 0.21908 0.657 2 6 0.552
Pillai's 0.17971 0.657 2 6 0.552
Roy's 0.21908
SSCP Matrix (adjusted) for C
HeatFlux Insolation
HeatFlux 66.02 23.867
Insolation 23.87 8.629
EIGEN Analysis for C
Eigenvalue 0.2191 0.00000
Proportion 1.0000 0.00000
Cumulative 1.0000 1.00000
Eigenvector 1 2
HeatFlux 0.057985 -0.003209
Insolation -0.001043 0.008877
MANOVA for A*B
s = 1 m = 0.0 n = 2.0
Test DF
Criterion Statistic F Num Denom P
Wilks' 0.40810 4.351 2 6 0.068
Lawley-Hotelling 1.45037 4.351 2 6 0.068
Pillai's 0.59190 4.351 2 6 0.068
Roy's 1.45037
SSCP Matrix (adjusted) for A*B
HeatFlux Insolation
HeatFlux 15.4 -502.4
Insolation -502.4 16387.2
EIGEN Analysis for A*B
Eigenvalue 1.450 0.00000
Proportion 1.000 0.00000
Cumulative 1.000 1.00000
Eigenvector 1 2
HeatFlux -0.02045 0.05436
Insolation 0.00878 0.00167
MANOVA for A*C
s = 1 m = 0.0 n = 2.0
Test DF
Criterion Statistic F Num Denom P
Wilks' 0.52969 2.664 2 6 0.149
Lawley-Hotelling 0.88789 2.664 2 6 0.149
Pillai's 0.47031 2.664 2 6 0.149
Roy's 0.88789
SSCP Matrix (adjusted) for A*C
HeatFlux Insolation
HeatFlux 212.4 -479.0
Insolation -479.0 1079.9
EIGEN Analysis for A*C
Eigenvalue 0.8879 0.00000
Proportion 1.0000 0.00000
Cumulative 1.0000 1.00000
Eigenvector 1 2
HeatFlux 0.055267 0.017834
Insolation -0.004162 0.007910
MANOVA for B*C
s = 1 m = 0.0 n = 2.0
Test DF
Criterion Statistic F Num Denom P
Wilks' 0.92862 0.231 2 6 0.801
Lawley-Hotelling 0.07687 0.231 2 6 0.801
Pillai's 0.07138 0.231 2 6 0.801
Roy's 0.07687
SSCP Matrix (adjusted) for B*C
HeatFlux Insolation
HeatFlux 2.03 -39.99
Insolation -39.99 787.50
EIGEN Analysis for B*C
Eigenvalue 0.07687 0.00000
Proportion 1.00000 0.00000
Cumulative 1.00000 1.00000
Eigenvector 1 2
HeatFlux -0.02634 0.05176
Insolation 0.00854 0.00263
MANOVA for A*B*C
s = 1 m = 0.0 n = 2.0
Test DF
Criterion Statistic F Num Denom P
Wilks' 0.14498 17.692 2 6 0.003
Lawley-Hotelling 5.89736 17.692 2 6 0.003
Pillai's 0.85502 17.692 2 6 0.003
Roy's 5.89736
SSCP Matrix (adjusted) for A*B*C
HeatFlux Insolation
HeatFlux 1779 3270
Insolation 3270 6012
EIGEN Analysis for A*B*C
Eigenvalue 5.897 0.00000
Proportion 1.000 0.00000
Cumulative 1.000 1.00000
Eigenvector 1 2
HeatFlux 0.055731 -0.01633
Insolation 0.001006 0.00888
