Miss rate of a well-powered test

Question

An experiment is designed with 90\% power to detect the effect the team cares about. If that effect is real, what is the probability the test fails to detect it (its type II error rate)?

Accepted Answer

Complement of power. The type II error rate is whatever probability is left over from power when the effect is real: \beta = 1 - 	ext{power} = 1 - 0.90 = 0.10. So a 90%-powered test still misses a real effect about one time in ten. Ninety percent power is often treated as a gold standard, yet it still leaves a nontrivial miss rate. Takeaway. Even a well-powered (90%) test has a 10% chance of missing a real effect, since \beta = 1 - 	ext{power}.

Miss rate of a well-powered test

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