Statistically, to avoid missing a case of appendicitis, one must send to the ER some patients with symptoms of appendicitis whose appendices turn out to be normal. This lesson from medical school is imprinted indelibly on my mind.
In my residency program, if a resident sent a patient to the ER, the resident was required to go the ER to evaluate them, to further their learning. However, this created a conflict of interest—if you had to meet a patient in the ER, you missed out on sleep. Hence I thought hard about the disposition of each patient.