I have carried out a study in which I have gathered 3 sentences per participant. These sentences were then classified in 2 ways. I want to test if there are significant interactions between the classifications and find out the effect size. I have done a chi square test for independence and calculated Cramer's $V$ (on the counts of sentences for the cross of the 2 classifications).
However, I am concerned that this is not correct, since the sentences are not fully independent (because each participant has entered 3 sentences).
Is there a good way to correct for this (or are they other statistical tests that I should carry out instead of $\chi^2$ and/or Cramer's $V$)?
A colleague of mine suggested removing the sentences that were entered by participants who had sentences in more than 1 category of a classification.