function compare_group_metrics(model, data, groups):

   metrics = {}
   for group in groups:
      subset = data.filter(group)
      metrics[group] = {"false_positive_rate": fpr(model, subset),
                  "false_negative_rate": fnr(model, subset)}
   return metrics

 # equalizing one fairness metric across groups can worsen another -- tradeoffs, not
 a free win
