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I have read now a couple of times that the rate of false positives is upper bounded by the significance level alpha regarding hypothesis testing, and does not depend on sample size. But how so? As far as I can see, the probability of drawing only extreme values is much smaller when the sample size is 1000 than say 3..

Thanks

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  • $\begingroup$ Its not a duplicate, I hadnt seen the other question (and I am not the other user neither) $\endgroup$
    – Pugl
    May 19 '14 at 20:17
  • $\begingroup$ "duplicate" does not mean that you posted the same question twice. It means this thread is asking the same question as was asked there. The words & superficial aspects of the questions differ, but the substantive issue is the same. $\endgroup$
    – gung - Reinstate Monica
    May 19 '14 at 20:20
  • $\begingroup$ I think this provides a much more straightforward answer to the question, so I would not delete it, at least to me its more accessible than the other answer. $\endgroup$
    – Pugl
    May 19 '14 at 21:01
  • $\begingroup$ This question is closed, but it won't be deleted. You can learn more about what it means for a question to be closed in our help center. $\endgroup$
    – gung - Reinstate Monica
    May 19 '14 at 21:05
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It does not, because you are the one picking $\alpha$. Once you pick $\alpha$, you can, for example, generate a confidence interval for the mean $\bar{X} \pm t_{\alpha/2}s/\sqrt{n}$ and the width of that C.I. will depend on $n$.

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  • $\begingroup$ So if I understand correctly what is actually defined as region of rejection is a function of sample size, and hence a constant proportion? $\endgroup$
    – Pugl
    May 19 '14 at 20:21
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    $\begingroup$ Yes the probability (under null hypothesis) to be rejected is constant. The curve gets narrower, but the bound also gets narrower. $\endgroup$
    – PA6OTA
    May 19 '14 at 20:23

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