Can MANOVA still be used with violated assumptions?

[AWB]

For my bachelor thesis I need to perform a MANOVA to compare two groups (N of group 1 is 80 and N of group 2 is 68) on 16 dependent variables. I checked the different assumptions and two of them were violated. The first one being the Univariate Normality for almost all dependent variables. Also, two dependent variables were significant for the Levene's test (.002 and .000). Are the results of the MANOVA still good or do I need to run more or different tests?

 

[micromass]

For my bachelor thesis I need to perform a MANOVA to compare two groups (N of group 1 is 80 and N of group 2 is 68) on 16 dependent variables. I checked the different assumptions and two of them were violated. The first one being the Univariate Normality for almost all dependent variables. Also, two dependent variables were significant for the Levene's test (.002 and .000). Are the results of the MANOVA still good or do I need to run more or different tests?

It is very rare that all assumptions of MANOVA are satisfied. It is therefore good that MANOVA is robust under certain deviations of the assumptions.

As for multivariate normality, as long as your number of observations are much (and they are), the central limit theorem will apply and your MANOVA result will be robust under violation of normality. Note however that the stronger your deviation for normality, the more the size of your population matters. In either case, you could always try a multivariate Box-Cox transformation to make things more normal.

As for equality of the covariance matrices, this is a bigger issue. Usually it is not a problem when the sample sizes are equal. But this is not the case with you, so it is doubtful that your MANOVA will be good. If you can take care that the sample sizes are equal, then your MANOVA should be good and you should use the Pillai trace as that is most stable under robustness.

While the Levene test is good for departures against normality, I would also suggest the Brown-Forsythe test since it is even more robust against departure from normality. In either case, you will want a multivariate version of the test since you're dealing with MANOVA.

 

[AWB]

It is very rare that all assumptions of MANOVA are satisfied. It is therefore good that MANOVA is robust under certain deviations of the assumptions.

As for multivariate normality, as long as your number of observations are much (and they are), the central limit theorem will apply and your MANOVA result will be robust under violation of normality. Note however that the stronger your deviation for normality, the more the size of your population matters. In either case, you could always try a multivariate Box-Cox transformation to make things more normal.

As for equality of the covariance matrices, this is a bigger issue. Usually it is not a problem when the sample sizes are equal. But this is not the case with you, so it is doubtful that your MANOVA will be good. If you can take care that the sample sizes are equal, then your MANOVA should be good and you should use the Pillai trace as that is most stable under robustness.

While the Levene test is good for departures against normality, I would also suggest the Brown-Forsythe test since it is even more robust against departure from normality. In either case, you will want a multivariate version of the test since you're dealing with MANOVA.

First of all, thank you for your elaborate answer! I am glad to hear that the results would be robust enough despite the violation of normality.

Furthermore, the sample that is the smallest is the sample of people with a burnout and it is not possible for me to get more participants in the time that I have left. So the only option for making the sample sizes equal would be to eliminate some participants for the other group. But is it even allowed to do that?

Also, I tried to find out how to run the Brown-Forsythe test in SPSS. I did find the univariate version, but I could not find an option to do the multivariate version. How can I run this test either with SPSS or in another way?

Thank you again for the earlier answers and I'm waiting to hear from you!

 

[micromass]

Furthermore, the sample that is the smallest is the sample of people with a burnout and it is not possible for me to get more participants in the time that I have left. So the only option for making the sample sizes equal would be to eliminate some participants for the other group. But is it even allowed to do that?

Yes, on the condition that you don't go out selecting which observations to keep and which to delete. The deletion must happen completely at random.
Deleting data points means that you will reduce the power of your analysis. This means that you will more often fail to find effects that are really there. But at least your type I error rate won't be skewed. If you want to be safe, get a random number generator to tell you which observations to leave out.

Also, I tried to find out how to run the Brown-Forsythe test in SPSS. I did find the univariate version, but I could not find an option to do the multivariate version. How can I run this test either with SPSS or in another way?

Testing equality of the covariance matrices is much less important if the sample sizes are equal. I would use the Brown-Forsythe test to check for equality of the diagonal elements since that is most robust against departures of normality. But there is no problem if you find the test to give unequality of variances.

 

[AWB]

Yes, on the condition that you don't go out selecting which observations to keep and which to delete. The deletion must happen completely at random.
Deleting data points means that you will reduce the power of your analysis. This means that you will more often fail to find effects that are really there. But at least your type I error rate won't be skewed. If you want to be safe, get a random number generator to tell you which observations to leave out.
Testing equality of the covariance matrices is much less important if the sample sizes are equal. I would use the Brown-Forsythe test to check for equality of the diagonal elements since that is most robust against departures of normality. But there is no problem if you find the test to give unequality of variances.

Thank you very much! Now I can move on with my thesis, it helped a lot!

 

[chiro]

Hey AWB.

Just to add to micromass' posts I'm wondering whether you have checked how much information is estimated in your sample.

The amount of information needed for assumptions often is exponential as you increase the number of dimensions and regardless of what you choose - it can be a good idea to estimate the information content of your sample (there are many criterion you can use over a variety of test statistics) and that is good to know if a particular kind of test is able to be used.