I have 2 independent variables (IV) and 8 dependent variables (DV) of production performance. Let's say IV one has 2 levels I and II. Independent two has 2 levels A and B. The sample sizes are as below:
Group IA: 76 farmers
IB: 60 farmers
IIA: 25 farmers
IIB: 40 farmers
I run 2 way MANOVA to examine the interaction between two IVs on the production performance of farmers. My data met most of the assumptions, except for homogeneity of the covariance (Box's m test show p value < 0.001). I am confused if my MANOVA analysis is valid if the homogeneity assumption is not met. I know that if the sample sizes are equal, MANOVA is robust to overcome the violation of homogeneity. However, my sample sizes are not equal. Some people suggested to use Pillai's Trace for my study due to unequal sizes and not homogeneity. Some others told me to use p value of 0.01 (rather than use p value of 0.05) to examine the significance.
I am looking for your advice.
Thanks
Duc
The Box test of equality of covariance matrices will tell you whether your analysis violates the assumption of homogeneity. If your sign is greater than .001 you have NOT violated the assumption. Your Box test shows p value < 0.001 so your MANOVA is not valid. It does not matter that your groups are unequal. So, follow Armin's advise.
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