Why does p-value have to be defined as 'at least as extreme' as the test statistic rather than just the probability that T= t?

Asked Apr 25 '20 at 20:42

Active Apr 25 '20 at 20:42

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Say I am using a t statistic, the (two-tailed-t test) p-value as i understand is given as pr(t$\geq$|t| |null is true), why cant it be that pr(t=t|null) or at least some small relative frequency in an infinitesimal distance around t, such as f(t)dt ?

asked Apr 25 '20 at 20:42

Steve

It's a good question and, as you might imagine, occurs in many contexts, so you can find various answers (in passing) in quite a few threads. The duplicate is one with many answers and several of them address this question head-on. – whuber Apr 25 '20 at 21:15

Why does p-value have to be defined as 'at least as extreme' as the test statistic rather than just the probability that T= t?

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