Discussion on the SJS invited paper by Sander Greenland Divergence vs. DecisionP$$ P $$‐values: A Distinction worth making in theory and keeping in Practice.

Considering two-sided HT <math display="inline" altimg="urn:x-wiley:sjos:media:sjos12649:sjos12649-math-0018" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi></mrow><annotation encoding="application/x-tex">$$ p $$</annotation></semantics></math> ht -values would not solve the problem, any departure of the goodness-of-fit test statistics from its median would be then interpreted as negative evidence of some level. As Sander Greenland points out, these should not be confused with the HT <math display="inline" altimg="urn:x-wiley:sjos:media:sjos12649:sjos12649-math-0003" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi></mrow><annotation encoding="application/x-tex">$$ p $$</annotation></semantics></math> ht -values of realized goodness of-fit-test statistics. [Extracted from the article]