What probability indicates the p-value? (more than one answer possible)

a: The probability of a type I error.

b: The probability of a type II error.

c: The probability of rejecting the alternative hypothesis when it is false.

d: The probability of rejecting the null hypothesis when it is false.

I think None of the following answers is correct. Can anyone answer this question and explain to me?

  • $\begingroup$ self-study? please add the tag if so. $\endgroup$ – Xi'an Apr 5 '15 at 18:28
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    $\begingroup$ Check other questions tagged p-value: stats.stackexchange.com/questions/tagged/p-value I am sure you'll find there multiple relevant answers. Also check the tour on how the site works: stats.stackexchange.com/tour $\endgroup$ – Tim Apr 5 '15 at 19:26
  • $\begingroup$ I already put my effort on this question and understand that Type I Error is defined as rejecting the null hypothesis when it is in fact true. Type II error is defined as not rejecting the null hypothesis when it is false. p-value is the region when I want to make a decision about rejecting null hypothesis. However, I am not quite sure about this question, so I need help. Does anybody can help? $\endgroup$ – Nong Nick Apr 5 '15 at 19:40
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    $\begingroup$ Well this is rather upsetting. How about "Between zero and four answers possible"? See this paper distinguishing $\alpha$ from $p$ $\endgroup$ – conjugateprior Apr 5 '15 at 20:38
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    $\begingroup$ Genau. None are correct. P is not a type 1 (or a type 2) error rate, although it seems that your textbook or instructor thinks it is. $\endgroup$ – conjugateprior Apr 5 '15 at 23:14

Strictly speaking, none of them, but the closest is [a], not [c].

You cannot do [c] based on p-value comparisons. It is not an "error". Rejecting the alternative when it is false means accepting the null when it is true. Can't do that.

See the table at this wiki article on FDR: https://en.wikipedia.org/wiki/False_discovery_rate#Classification_of_m_hypothesis_tests

p-value is essentially V/m0.

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    $\begingroup$ Welcome to this site! Please, review our guidelines on how homework questions are handled on this site. $\endgroup$ – chl Apr 5 '15 at 20:37
  • $\begingroup$ @chl, not sure what you mean. Fairly certain that this was a homework question can be rejected at p<<0.01. $\endgroup$ – Guest Apr 5 '15 at 21:07
  • $\begingroup$ None of them are correct? @Guest $\endgroup$ – Nong Nick Apr 5 '15 at 22:58
  • $\begingroup$ @NongNick There are subtle differences between a p-value and the alpha-threshold that defines Type I error. The former is where your observed statistic falls among all the possible values of the statistic generated when the null is true. The latter is a threshold criterion you apply to test hypotheses. $\endgroup$ – Guest Apr 6 '15 at 1:20

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