# Statistically demonstrating that group has more outliers?

#### confusedbiologist

##### New Member
I am analyzing some research data and got stuck analyzing it. So I would really appreciate any help I could get at this point.

I have 3 different species. Species A has 2 individuals and 23 measurements. Species B has 6 individuals and 101 measurements. Species B also has 6 individuals but 111 measurements. The daI am analyzing some research data and got stuck analyzing it.

I have 3 different species. Species A has 2 individuals and 23 measurements. Species B has 6 individuals and 101 measurements. Species B also has 6 individuals but 111 measurements. The data are not normally distributed.

There does not appear to be much of a difference between species. However, one species has a lot of outliers whereas the others have relatively tightly clustered data. I believe that the outliers are biologically significant and would like to statistically express that species B has more outliers than the others. I am at a loss on how to do this though and would really appreciate your help.

So at this point I am stuck on figuring out what type of test would be good for me to use and why.

I would really appreciate your help and thank you so much in advance!

#### j58

##### Active Member
An elementary approach might be to test for significant differences among the variances of the three species. Try googing "test for difference in variance."

#### confusedbiologist

##### New Member
Thank you so much for your reply! I should have probably specified my problem a little more. I ran a bootstrap resampling test to run an ANOVA and t-tests. Those are non-significant. However, one of the groups has a ton of outliers. They play much less of a role after resampling, which is the point, of course. The only problem is that I think those outliers actually make a difference biologically. So I was asked to show the greater variation statistically in a manuscript revision, but I am a little stuck on how to do that. Thank you again for your comment!

#### j58

##### Active Member
Two possibilities come immediately to mind. The first would be to analyze the data using mixed linear models. You run two models: one that assumes that the variance is the same across species, and another with a separate variance parameter for each species. You can then compare the fit of the two models using a likelihood ratio test, AIC, or BIC.

The second approach would be to run a Bayesian analysis using a model that included separate variance parameters for each species. The result would be a posterior distribution for each variance parameter, from which you can easily calculate the probability that the variance of the species of interest is greater than the other two and/or obtain credible intervals for each variance parameter or for difference between any pair of them.