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Why P value of a 2 tailed test is multiplied by 2 [=2 X P(Z>tcal)? I am looking for a answer which may explain the underlying reason except the answer 'because it is a two tailed test'. Why we also consider the opposite signed value of test statistic in two tailed test to calculate P value?

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  • $\begingroup$ What I am looking for is different from the question's answer link you have provided. $\endgroup$
    – Zed
    Commented Mar 9, 2016 at 15:32
  • $\begingroup$ No problem -- you will need to refine (i.e. edit) your question to ask something clearly distinct from that one, taking into account what's already covered there. Please try to be as clear as you can. $\endgroup$
    – Glen_b
    Commented Mar 10, 2016 at 0:17
  • $\begingroup$ I think I have specified my question pretty clearly. The question with which my question has been marked as duplicate, does not contain any clear answer/indication (from formal statistical perspective) about my question. Yet I don't know why you've marked my question as duplicate! can you kindly specify which portion of my question has a answer in that question? It seems that marking a question as duplicate doesn't work good for the question asker as no one checks duplicate questions. $\endgroup$
    – Zed
    Commented Mar 11, 2016 at 5:26
  • $\begingroup$ You ask "Why P value of a 2 tailed test is multiplied by 2". Max Gordon's answer at the linked question does (as far as I can see) explain why it is doubled (without saying "because it is two tailed"). That therefore seems to answer your question. However, since you say it doesn't (and for some reason refuse to explain further) I will reopen and try to directly answer the question. However, I expect my answer will also fail to satisfy you. $\endgroup$
    – Glen_b
    Commented Mar 11, 2016 at 6:43

1 Answer 1

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why the P value of a two tailed test is multiplied by 2?

Not all two-tailed tests have the property that a p-value of a two-tailed test should be double the p-value of a one-tailed test.

However, tests where

i. being in either of the tails are mutually exclusive events*, and

ii. the distribution of the test statistic is symmetric

will have the property that to compute the p-value of a two-tailed test you double the smaller p-value of the two one-tailed tests. This follows because a p-value is the probability of a test statistic at least as extreme as the one you observe under the null hypothesis; the two tailed test considers alternatives in either direction so "at least as extreme" can be in either tail; given the two conditions above, you get that doubling of the one-tailed p-value (which only considers one of the tails).

* consider the two one-tailed Kolmogorov-Smirnov tests compared to the two-tailed version to see a case where being in either tail are not mutually exclusive events.

For the asymmetric case, some discussion here may be relevant.

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