In officer-involved shootings in these cities, officers were more likely to fire their weapons without having first been attacked when the suspects were white. Black and white civilians involved in police shootings were equally likely to have been carrying a weapon. Both of these results undercut the idea that the police wield lethal force with racial bias.

But this line of analysis included only encounters in which a shooting took place. A more fundamental question still remained: In the tense moments when a shooting may occur, are police officers more likely to fire if the suspect is black?

To answer this question, Mr. Fryer focused on one city, Houston. The Police Department there allowed the researchers to look at reports not only for shootings but also for arrests when lethal force might have been justified. Mr. Fryer defined this group to include suspects the police charged with serious offenses like attempting to murder an officer, or evading or resisting arrest. He also considered suspects shocked with Tasers.

And in the arena of “shoot” or “don’t shoot,” Mr. Fryer found that, in tense situations, officers in Houston were about 20 percent less likely to shoot a suspect if the suspect was black.