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Morendil comments on How to Fix Science - Less Wrong
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Wait, that confused me. I thought the p-value was the chance of the data given the null hypothesis.
Since NHST is "null hypothesis significance testing", the hypothesis being tested is the null hypothesis!
In the vernacular, when "testing a hypothesis" we refer to the hypothesis of interest as the one being tested, i.e. the alternative to the null - not the null itself. (For instance, we say things like "test the effect of gender", not the more cumbersome "test the null hypothesis of the absence of an effect of gender".)
In any case it wouldn't hurt the OP, and could only make it clearer, to reword it to remove the ambiguity.