Let us assume I want to compare men and women in their preference of four kinds of foods. I invite everyone who is interested into the lab and ask them: "Which food do you prefer? Apple, orange, pizza, or beer? Choose only one food."
My survey will result in a contingency table like the following, which I can then test with a chi-squared test of homogeneity to find, whether there are differences in food choice between men and women:
choice group apple orange pizza beer men 374 63 216 101 women 510 65 125 76
I can use the chi-squared test, because the samples are independent.
Now, let us assume that I invite all the participants into the lab again every day for one month and ask them the same question. My survey will reslult in a similar contingency table to the first one, and the samples (men versus women) will still be independent. The difference is that now I have repeated measures.
I have always understood that the requirements for independence are broken if there are repeated measures between samples, for example in a pre-post comparison. But in my example, the samples (men and women) are still independent. The dependence is within a sample.
So my question is:
Does my second example still meet the requirements of a chi-squared test of homogeneity?