Lest you believe that odds ratios are merely the domain of logistic regression, I’m here to tell you it’s not true.
One of the simplest ways to calculate an odds ratio is from a cross tabulation table.
We usually analyze these tables with a categorical statistical test. There are a few options, depending on the sample size and the design, but common ones are Chi-Square test of independence or homogeneity, or a Fisher’s exact test.