From a USA Today piece on kids and imaginary friends:

In her study, 27% of children described pretend pals their parents didn’t know about, she says. If they know, reactions vary widely. “We’ve seen everything from parents who are excited and proud, even kind of implying, ‘My child has a better friend than your child,’ to a fundamentalist Christian who brought a Bible to the lab and said she was praying every day for the devil to leave her child,” Taylor says.