Bayesian statistics allows these sorts of statements, but you have to be careful about making strong prior assumptions.

Under a prior assumption that the alternative hypothesis has a 50% chance of being true, a p-value of 0.05 give a posterior probability for the alternative hypothesis of LESS than 50%. I think. Going from memory here, but I will look for that paper…

I think we could do something along these lines that would give casual readers a much better idea of the strength of results.

Were working on that one already. An independent record of the primary hypothesis prior to looking at the data is a good idea.

I’m working on an exploratory analysis today which has a very “flat” likelihood, meaning it’s hard to pin down a single best estimate. The result we are reporting is somewhat tentative as a result. BUT, my experience here tells me we are onto something, and the investigator thinks this will change medical practice. IOW, it’s important to report, and even if it isn’t exactly right, it’s close enough to be useful. p=0.004, so not too bad.