I have the following case:
Two groups of people produce a bunch of different words, those words are categories.
So I get a table:

The numbers in the in the cells are for the words each group produced in the categories.
I would like to test if the two groups differ significantly from each other.
The Problem is following: Every person in group 1 and 2 doesn’t only get a single word, but 3. So I feel like I’m dealing with a dependent sample, since the first word one person uses might have an influence on the other words.
I talked to my Professor and he recommends do a fisher-exact test with Monte Carlo simulation, but added, because of the dependent data the test would tend to be conservative.
Is he right with the assumption that it is conservative? And if he is, is there a way how I can justify the test being conservative or a source that I can quote?