# Significance test for the difference in Simpson's Diversity Index values?

I've taken several samples of categorical data and calculated the spread of each using Simpson's Diversity Index. I would now like to perform a significance test to see if these spreads are similar or not. The data looks something like this:

sample    mode    diversity
-----     ----    ----
samp1     cat1    0.45
samp2     cat1    0.47
samp3     cat1    0.40
samp4     cat1    0.70
samp5     cat2    0.43


I've considered an F-test but that seems to require that the distributions are normal, which isn't actually possible since this is categorical data. The Fligner-Killeen test seems appropriate, but I'm not really sure. What would make the most sense here?

EDIT:

Here's the sort of data that would be in each sample. The data is all categorical data. These aren't the actual count, but it's an example of what the data might look like.

samp1
-----
category  count
--------  -----
cat1      26
cat2      5
cat3      12

samp2
-----
category  count
--------  -----
cat1      15
cat2      2
cat3      5
cat4      10

samp3
-----
category  count
--------  -----
cat1      31
cat2      4
cat3      0
cat4      2

etc...

• Are you testing for a difference in Simpson's diversity, between different samples? Because Simpson's Diversity isn't categorical - from your data it looks more like a proportion. So I don't really understand what the issue is? Maybe present your data so each row represents a sample that you want to test.
– rw2
May 21 at 7:49
• Simpson's Diversity isn't categorical but the data that it's calculated from is. Jun 2 at 14:26
• I'm not sure I understand how you calculated Simpson's Diversity Index. Could you please give an example of the sample data - it sounds like you want to test for differences in the raw sample data, so I think it would be more useful to show that than the table of diversity indices you've provided.
– rw2
Jun 11 at 12:44
• Some sort of permutation test might be useful here.
– mkt
Jun 12 at 16:09