# Violated Assumptions MANOVA

• I
• AWB
In summary: However, it is allowed as long as the deletion is completely random. As for running the Brown-Forsythe test in SPSS, there may not be an option for the multivariate version. In this case, you can use the univariate version to check for equality of the diagonal elements, which is most important. However, if you find unequal variances, it may not be a major issue since the sample sizes are equal.

#### 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?

AWB said:
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
micromass said:
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!

AWB said:
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
micromass said:
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!

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.

## 1. What is a "Violated Assumptions MANOVA"?

A "Violated Assumptions MANOVA" is a multivariate analysis of variance (MANOVA) test that is used to analyze data when the assumptions of the traditional MANOVA test are not met. This can happen when the data does not meet the assumptions of normality, homogeneity of variances, and/or independence.

## 2. What are the assumptions of a traditional MANOVA test?

The assumptions of a traditional MANOVA test include: normality of the data, homogeneity of variances, and independence of observations. These assumptions are necessary for the test to accurately assess the relationship between multiple dependent variables and one or more independent variables.

## 3. How do you know if the assumptions of a traditional MANOVA test are violated?

The assumptions of a traditional MANOVA test can be checked using various statistical tests, such as the Shapiro-Wilk test for normality, Levene's test for homogeneity of variances, and the Durbin-Watson test for independence. These tests can be run on the data before conducting the MANOVA test.

## 4. What are the consequences of violating the assumptions of a traditional MANOVA test?

If the assumptions of a traditional MANOVA test are violated, the results of the test may be inaccurate or biased. This can lead to incorrect conclusions being drawn from the data. It is important to address any violated assumptions before conducting the analysis.

## 5. How can you handle violated assumptions in a MANOVA analysis?

If the assumptions of a traditional MANOVA test are violated, there are a few options for handling the data. These include transforming the data to meet the assumptions, using a non-parametric MANOVA test, or using robust methods that are less affected by violations of the assumptions. It is important to consult with a statistician or conduct further research to determine the best approach for the specific data set.