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Why it doesn’t make sense in general to form confidence intervals by inverting hypothesis tests

Peter Bergman points me to this discussion from Cyrus of a presentation by Guido Imbens on design of randomized experiments. Cyrus writes: The standard analysis that Imbens proposes includes (1) a Fisher-type permutation test of the sharp null hypothesis–what Imbens referred to as “testing”–along with a (2) Neyman-type point estimate of the sample average treatment […]