Use 'in mistake for' when clarifying a wrong identification or choice happened. She called out to a stranger in mistake for her friend.
Pro Tip 2/3
Error Emphasis
Emphasize errors due to similar appearance or qualities between items or people. The novice birdwatcher recorded a common thrush in mistake for a rare species.
Pro Tip 3/3
Accidental Choice
Highlight accidental selections, not deliberate choices when things look alike. He took the diet soda in mistake for the regular one due to identical packaging.