# Is it okay to run a chi square if each participant is contributing multiple counts?

I have data where each participant is giving binary responses (let's say a/b) to 9 questions each in two different categories.

I ran a 2x2 chi-square that has in the columns, {a, b} and in the rows {category1, category2}.

Is this okay given that each participant is providing multiple answers (presumably each participant will contribute to the counts in all four of the cells)?

I am thinking, for instance, if I was running a regression, I would need to include a participant random effect term because the data points are not independent. Is there a similar problem with my chi-square?

• Yes, Pearson's chi-squared test also assumes independence. The regression with a random effect would be a better approach. – TPM Apr 17 '18 at 19:15

Yes, there is a problem with your $\chi^2$. A simple approach and pragmatic approach would be to sum up each individual's responses and perform a linear regression regressing the sum score on predictor variables of interest. The substantive findings from this should not be too different from those from the GLMM.