# $\chi^2$ 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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2
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

## 1 Answer

I read this to mean that each sentence is classified in both ways, so you are interested in whether there is any relationship between the two classification methods. If so I don't think it matters where the sentences came from - even if they are random or not.

The randomness that makes this a statistical question comes from the idea that under the null hypothesis the two classifications of each sentence are random and unrelated, and you are looking for evidence that this is not the case. You are making inferences about the population of classifications, not of sentences.

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