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Power in testing of hypothesis is defined as the probability of making the correct decision. Then why do text books describe

power=1-P(type 2 error) and not 1-P(type 1 error)

Harry
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    See http://stats.stackexchange.com/questions/163957/what-follows-if-we-fail-to-reject-the-null-hypothesis/164094#164094. So a correct decision means 'correctly deciding that $H_1$ is true' as @JohnK says in his answer. You can never find a 'decision' on $H_0$. –  Oct 16 '16 at 14:22
  • *Who* defines power as the probability of making the correct decision? Please give a reference that does this. – Glen_b Oct 17 '16 at 00:00

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The power is defined as the probability of correctly rejecting the null hypothesis and thus accepting the alternative when it is true. This is related to the Type II error which is the probability of rejecting the alternative when the alternative is true. In fact, power is the complement of the Type II error and that is why we compute it like that.

The probability of incorrectly rejecting the null hypothesis is called the "significance level" of the test, and this probability is also known as the probability of a Type I error.

JohnK
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