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Given a categorical ordered variable with more than two categories (e.g. education) and a binary variable (e.g. gender). Is it reasonable to use correlation as a measure of how both are related? My concern is that it would only take a handful of extreme datapoints (in terms of the categorical variable) to significantly alter the correlation value

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I have two groups, one that listens to a certain information source and one that does not. Each of these groups exhibits a certain behavior a number of times on average, between 0 and 10. I’m trying to determine whether individuals who get their information from that one source present a different behavior than the ones who don’t

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  • $\begingroup$ Your categorical variables have an order type? Replace the categories with ranks. The given p-value for correlation in most software packages assumes that the input variables were normally-distributed. I would recommend you get your p-value from an exact test since your input variable may violate this assumption quite strongly. $\endgroup$
    – Galen
    Jun 21, 2021 at 14:43
  • $\begingroup$ Yes, they are totally ordered and the categories match the ranks. One thing I was considering is instead testing the difference of the means of the categorical variable across the groups (binary variable) which should be theoretically sound by the CLT, correct? $\endgroup$
    – tvbc
    Jun 21, 2021 at 14:54
  • $\begingroup$ What is your research question, if the categorical ordered (ordinal) variables differ between the two binary groups? $\endgroup$
    – Dave
    Jun 21, 2021 at 14:59
  • $\begingroup$ Yes, is there a significant difference in the categorical variable responses between the two binary groups $\endgroup$
    – tvbc
    Jun 21, 2021 at 15:01
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    $\begingroup$ But what facet(s) of the data/distributions (e.g., median)? $\endgroup$
    – Dave
    Jun 21, 2021 at 15:06

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