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  "body": "\n## Summary\n\nThe Neyman construction is a general method to build a [[confidence interval|0S6T9KQNC0]] for a parameter.\nIt starts from a family of acceptance regions, one for each value of the parameter.\nThe confidence set collects all parameter values whose acceptance region contains the observed data.\nIt is the inversion of a family of [[hypothesis tests|087P03NEND]], and it gives the required coverage without any pivot.\n\n## Explanations\n\n### L1 human\n\nFor each possible value of the parameter, draw a band of data values that are likely, with probability $1 - \\alpha$, under that value.\nAfter the experiment, keep every parameter value whose band contains what you saw.\nPicture a plot with the parameter on one axis and the data on the other.\nThe bands form a belt, and the confidence interval is the slice of the belt at the observed data.\nFor a coin with unknown head probability $p$, the bands are ranges of head counts, and the slice gives an interval for $p$ with at least the required coverage.\n",
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