i think we have established that one can't prove the null ...
so, nothing about the p value says anything about the truth of the stated null
in fact, p values don't really say anything about the falsity of the null either
the p value DOES say what the p IS of getting some result (or greater) IF THE NULL (conditioned) IS TRUE
so in a way ... maybe the only way ... p only tells you how frequent or rare ... you might expect to see THE result you see WHEN the null is true
thus ... p only really gives us an idea of the liklihood of seeing some result ... WHEN the null is true
a p of .6 means we are likely to see such a result ... more often than ... seeing the result that produces a p of .09 ... if the null were true
of course, when the p value gets low ... or really low ... we start to ask the question: how could we have gotten that rare event ... in our only shot at collecting data ... IF THE NULL WERE REALLY TRUE? if the null really is true .... would it not be much more likely for US to get a result not nearly as distant/discrepant FROM the null? sure it would be
SOOOOOOOOOO ... instead of saying that we got a rare event WHEN the null is true ... we say that the result we got is more likely to belong to a sampling distribution does NOT have the null as the center ... but rather, the center of the true sampling distribution is more in alignment with what we IN FACT did get
bottom line: the null is not looking so plausible ...
we still don't know if the null is true or not ... all we are doing is asking ourselves: given the data we have in our hands ... how "good" is the null looking as the possible true parameter value?
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