Choosing which error you prefer is critical. In medicine, we prefer Type I errors: if you are testing for cancer, better to get a few initial diagnoses that are incorrect than to miss a case where cancer is present. In law, we have generally established that we prefer Type II errors: better to have some criminals go free than to jail innocent men (and DNA tests are improving this tendency).

The DPS/DCTA teacher evaluation system is designed for Type II errors: the grievance process and collective bargaining agreement reduce the possibility that some teachers are dismissed unfairly – with the consequence that teachers that should be dismissed are not. All other things being equal, average teaching quality is lower with Type II errors.

A teacher evaluation system set up for Type I errors would dismiss more teachers who are poor performers – but with the consequence that some teachers might be dismissed unfairly. All other things being equal, average teacher quality is higher with Type I errors.

An evaluation system designed for Type II errors favors teachers (less likely to lose your job); a system designed for Type I errors favors students (less likely to have a bad teacher).

We have the correct results for the system that we have decided to use.