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Let's say I am testing 5 products (e.g. 5 brands of apple juice) and I have 200 respondents. That is, my data consists of 200 rows and 5 columns (variables/products).

For each of the 5 products, each respondent indicates if he likes it or not (binary response). Each respondent can like all of the products, can like some of them, or can dislike all of them.

To compare the products, for each product I calculate what proportion of the total sample indicated liking.

Now, I am confused about what statistical test(s) I could use to compare these 5 proportions to see if all of the products are liked the same, or if some product(s) is (dis)liked significantly more/less.

I was thinking about using multiple proportions test, but, as I understand, it is only suitable for independent samples? Is there an equivalent for dependent samples?

Thanks in advance!

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There is a dependent samples test to compare multiple proportions of treatments on the same case. The test is known as Cochran's Q. You can find more on its Wikipedia page here. Its $H_0$ is that all proportions are equal.

Of course it's always a good idea to plot your data first.

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