Can someone explain what is meant by a confidence interval derived from an inverted hypothesis test? The Clopper-Pearson interval for a proportion seems to be an example.
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The idea is that your hypothesis test is comparing the statistic from you data to some parameter $\theta_0$. The confidence interval consists of all possible values of $\theta_0$ that the test would not reject for the given data. Usually instead of finding every possible value we just invert the equation for the test statistic to give us the boundary values and all values in between will be the interval.
Greg Snow
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