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(The p value) Which one of the statements about the p value is correct? a) The p value is the predefined probability of making a mistake when the null hypothesis is false. b) The p value is the estimated probability of making a mistake when the null hypothesis is false. c) The p value is the estimated probability of making a mistake when the null hypothesis is true. d) The p value is the predefined probability of making a mistake when the null hypothesis is true. I am stuck between predefined and estimated.

Nisha Nidhi
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  • It might be fair to distinguish the terms operationally like this: "predefined" means you could calculate the value without the data while any "estimated" value is based on the data. – whuber Sep 05 '19 at 22:34
  • Since we calculate the p value from our data, it will be estimated. So, would it be the answer C in this case? – Nisha Nidhi Sep 05 '19 at 22:39
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    You need to figure out the right choice yourself @NishaNidhi & the appropriate thing to do is to add the self study tag. – Michael R. Chernick Sep 05 '19 at 23:29

1 Answers1

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I answered your previous question, but this seems much more like homework or a test. I'll give you the definition and leave it up to you to answer based on the A-D answers. p-value is the probability of getting a test-statistic equal to or larger than the 1 calculated for that data at hand, given the data, model assumed, and assuming the null-hypothesis is true. Change your data, model, assumptions or even test-statistic, you change the p-value.

edited: Typo.

Kunio
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  • One might take issue with the generality of this characterization, especially the term "large." See [the example I posted in our thread on p-values.](https://stats.stackexchange.com/a/130772/919) A historically notable counterexample is Fisher's re-analysis of Mendel's experimental data on peas, where the relevant p-value was computed by the chance the test statistic would be *smaller than or equal to* the observed statistic. See, for instance, section 4.1 of https://arxiv.org/pdf/1104.2975.pdf. – whuber Sep 05 '19 at 22:43
  • @whuber Thanks for the comment. "Large" was a typo, meant larger. Did mean to also say equal to or larger than. Thanks for pointing out the opposite though! I had never seen that before. – Kunio Sep 05 '19 at 23:03
  • @Kunio A more precise definition would be "at least as extreme", since in many cases, significance can mean both sufficiently greater than, or less than the null. – Frans Rodenburg Sep 06 '19 at 05:01