All this reminded me of an exchange where similar games were closed the fastest.
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It’s not just p=0.048 vs. p=0.052
91–92 of 92 posts
Re: It’s not just p=0.048 vs. p=0.052
#92Earlier quoted context omitted.
They're right. If the null hypothesis is true, then the probability of getting any p value is equal. Put it another way, the p value is the probability of getting the observed data (or more extreme) under the null. So, under the null, 10% of the time you will get data with a p value of 10% or less; 20% of the time, you will get data with a p value of 20% or less; and so on. And that's the uniform distribution! Here's…
So I don't have (or know) R, but I do have access to Mathematica, and this is most definitely not giving me a uniform distribution (how could it?!): Why is your x variable though? If H0 is true shouldn't your x be fixed? I think if you remove the subtraction though then you do get a uniform distribution -- in which case I see what the claim is, yeah. Wasn't really clear to me earlier but indeed, getting p = 5% means…
You'd get the same result whether you test the hypothesis y > x (with both random variables) or y > 0. Under the null, the p-value is uniform on [0, 1], whatever that null is. It follows from the definition of a p value.
(Disclaimer: I am not a real statistician....)