# hypothesis test: difference greater than threshold

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?

• 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
• Look into tests of equivalence: See for instance stats.stackexchange.com/questions/52897/… and search this site for equivalence and tost – kjetil b halvorsen Nov 12 '18 at 14:40