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Hypothesis tests are commonly framed as

$H_0: p_0 = p_1$ vs. $H_1: p_0 \not= p_1$.

But I am interested in the case:

$H_0: |p_0 - p_1| < c $ vs. $H_1: |p_0 - p_1| \ge c $

for some constant $c$.

Could I apply a likelihood ratio test? - the degrees of freedom would be the same in both cases, I suppose?

Would I have to go Bayesian and apply an (arbitrary) prior?

kjetil b halvorsen
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cmo
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  • What are $p_0$ and $p_1$? Probabilities, statistics, models? – Peter Oct 20 '15 at 19:30
  • parametric parameters. "Hypothesis tests are **commonly** framed as..." and I do believe it is typically presented as a test of parametric parameter(s). – cmo Oct 20 '15 at 20:01
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    Look into tests of equivalence: See for instance https://stats.stackexchange.com/questions/52897/equivalence-tests-for-non-normal-data and search this site for [tag:equivalence] and [tag:tost] – kjetil b halvorsen Nov 12 '18 at 14:40

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