How can I compare the variance or correlation between ranked *single answer* polls?

Question

I am an undergrad psych major examining the differences in personal preferences between the extremist website 4chan and other websites, which will represent the pop norm. I would like to test whether 4channer's personal preferences are deviant from the norm, and hopefully, whether this deviation is significant or how correlated they are. I would appreciate any kind of help, even providing distinction on what I am seeking is greatly appreciated.
Specifically, the data from each participant is not a ranking. For example, instead, for each participant providing their preference of fruit consisting of the options apples, bananas, and carrots, they simply select their top pick and nothing else.

For an example of my data, I would like to compare 4chan's polls: https://www.strawpoll.me/20895006/r

To the pop norm (which in this case is Reddit): https://www.reddit.com/r/startrek/comments/g1spl0/poll_favorite_star_trek_series/

This will be repeated for different categorical questions, aiming to capture the overall variance of 4channer's non-political preferences.

My professor suggested simply comparing the means and SD, and possibly a t-test, but I have no idea how to conduct it with this kind of categorical data. Is it even possible to get a mean from this kind of ranked data? I did some independent research and it seems like finding the rank correlation might be the best way. However, I'm not sure what rank correlation test to run, or how to compare the overall data for 4chan and the pop norm(s). How can I test the difference between 4chan's polls and the pop norm for each individual poll and possibly the overall difference?

Answer 1

Your question is somewhat unclear. You will be collecting polls for 4chan and otherchan (I will just use that designation here.) How many? You say

Specifically, the data from each participant is not a ranking. For example, instead, for each participant providing their preference of fruit consisting of the options apples, bananas, and carrots, they simply select their top pick and nothing else.

With n people answering, that will give you n top choices from among k fruits (apples, bananas, carrots(?)). That will give k counts summing to n. When you do that for both 4chan and otherchan, you end up with a contingency table, for example

          apples    bananas     carrots
4chan       23       47          2
otherchan   35       32          10

and you can test homogeneity of this table with a chisquare test, either Pearson's chisquare or see G-test vs Pearson's chi-squared test.

Then I presume you do this for many other questions (how many?), and each give you a test. The null distribution of this tests will be chisquare with $k-1$ degrees of freedom, but presumably $k$ will vary between the tables. For an overall test maybe Combining multiple p-values.

For now I leave it as is, waiting for some reaction ... others may have better ideas.