One general approach to test if two columns are similarly distributed is using a nonparametric statistic. DBNL offers two such statistics: scaled_ks_stat for testing ordinal distributions and scaled_chi2_stat for testing nominal distributions.
Example Test Spec
{"name":"discrepancy_of_text_coherence_score","description":"Test the nonparametric discrepancy of the coherence score distributions","statistic_name":"scaled_ks_stat","statistic_params":{},"assertion":{"name":"less_than_or_equal_to","params":{"other":0.25,},},"statistic_inputs":[{"select_query_template":{"select":"{EXPERIMENT}.coherence_score"}},{"select_query_template":{"select":"{BASELINE}.coherence_score"}},],}
Example test on discrepancy of distribution of coherence_score