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  "body": "\n## Summary\n\nThe power of a [[hypothesis test|087P03NEND]] at a parameter value is the probability that the test rejects the null hypothesis.\nHere the data are assumed to come from that parameter value.\nUnder the alternative it equals one minus the probability of a [[type II error|03N8C8ZR4B]].\nPower is the main criterion to compare tests of the same level, and it guides the choice of a sample size.\n\n## Explanations\n\n### L1 human\n\nPower measures how good a test is at detecting an effect that is really there.\nA test with power $0.8$ finds a true effect of the given size in $80\\%$ of repeated experiments.\nFor a sensible test, such as a one-sided z-test, the power grows with the sample size and with the size of the effect.\nFor example, a test for a biased coin with $10$ tosses rarely detects a probability of heads of $0.55$, while $10000$ tosses detect it almost always.\n",
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