Two independent tests, both catching a real effect

Question

Two independent labs each run a test with 80\% power on the same real effect. What is the probability that both tests detect it?

Accepted Answer

Each test detects with probability equal to its power. Each has an 80\% chance of correctly flagging the effect. Because the tests are independent, multiply: P(	ext{both detect}) = 0.80 	imes 0.80 = 0.64. So both succeed about 64% of the time. (For contrast, the chance that at least one detects it is 1 - 0.2 	imes 0.2 = 0.96: replication is far more likely to catch a real effect somewhere than to have both attempts succeed together.) Takeaway. Independent tests each detect with probability equal to their power, so both detecting a real effect has probability 0.80^2 = 0.64, even though at l…

Two independent tests, both catching a real effect

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