I have been doing statistics as part of my job for a few years now. But now I have to try and explain the logic of Null Hypothesis Significance testing to a statistically naive audience.
Say I have the result of an unpaired t-test: t=0.01, p=0.999
I can conclude that there is no difference between groups but why can't I use this as evidence that the groups are the same or nearly the same?
Put another way, why does rejecting the null hypothesis allow us to make a conclusion but failing to reject it does not?
Why are a finding of equivalence and failing to find a difference not the same? (this is more a semantic question)