How would you find correlation between a categorical variable and a continuous variable?
Distance Metrics: Although the concept of "distance" is often not synonymous with "correlation," distance metrics can nevertheless be used to compute the similarity between vectors, which is conceptually similar to other measures of correlation. There are many other distance metrics, and my intent here is less to introduce you to all the different ways in which distance between two points can be calculated, and more to introduce the general notion of distance metrics as an approach to measure similarity or correlation. I have noted ten commonly used distance metrics below for this purpose.
Contingency Table Analysis: When comparing two categorical variables, by counting the frequencies of the categories we can easily convert the original vectors into contingency tables. For example, imagine you wanted to see if there is a correlation between being a man and getting a science grant (unfortunately, there is a correlation but that's a matter for another day). Your data might have two columns in this case — one for gender which would be Male or Female (assume a binary world for this case) and another for grant (Yes or No). We could take the data from these columns and represent it as a cross tabulation by calculating the pair-wise frequencies.