For purely nominal variables, you can use PROC FREQ and the chi-square statistic to test the association between variables.
If the variables are ordinal (they can be ordered, such as 'small', 'medium', and 'large'), you can use PROC FREQ to compute tetrachoric or polychoric correlations between discrete categories. Use the PLCORR options on the TABLES stmt.
Lastly, for multivariate statistics, you can use PROC CORRESP to study correlations between categorical variables. Roughly speaking, correspondence analysis for discrete variables is similar to principal component analysis for continuous variables, except contributions to the chi-square statistic are used instead of the variance.
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