# $\chi^2$ test - correcting for not fully independent sample

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.

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I'm not quite clear on what your data look like. How does a "query" (in your last paragraph) relate to a "sentence" in the rest of the question? But I've answered it on the basis of what I think you are asking. –  Peter Ellis Apr 14 '12 at 2:52
Sorry I meant to write 'sentences' - edited. Thanks! –  Lars Grammel Apr 14 '12 at 5:45