# Interpretation of P value

**URL:** <https://discourse.datamethods.org/t/interpretation-of-p-value/3980>\
**Category:** general\
**Tags:** p-value, interpretation\
**Created:** [December 13, 2020, 2:23pm UTC](https://discourse.datamethods.org/t/interpretation-of-p-value/3980 "2020-12-13T14:23:37Z")\
**Posts on this page:** 5\
**Page:** 1

<div class="post-metadata">

**Author:** ![EpiLearneR](https://discourse.datamethods.org/letter_avatar_proxy/v4/letter/e/f9ae1b/32.png) [@EpiLearneR](https://discourse.datamethods.org/u/EpiLearneR)\
**Post date:** [December 13, 2020, 2:23pm UTC](https://discourse.datamethods.org/t/interpretation-of-p-value/3980/1 "2020-12-13T14:23:37Z")

</div>

Recently I came across someone asserting the following as the easy to comprehend intepretaiton of P values in an epidemilogy course.  
“If p= 0.90 \>\> 90% probability that, what we observed difference is due to chance  
If p= 0.03 \>\> 3% probability that, what we observed difference is due to chance”.  
My concept was it was one of the misintepretations of P values. I would like to have your expert opinions and references.

---

<div class="post-metadata">

**Author:** ![R\_cubed](https://discourse.datamethods.org/user_avatar/discourse.datamethods.org/r_cubed/32/1518_2.png) [@R\_cubed](https://discourse.datamethods.org/u/R_cubed)\
**Post date:** [December 13, 2020, 2:31pm UTC](https://discourse.datamethods.org/t/interpretation-of-p-value/3980/2 "2020-12-13T14:31:12Z")

</div>

A similar question was asked a few months ago. You might benefit from reading my post in this thread, and studying the paper I linked to.

Suffice it to say – you are right. I will borrow a quote from Sander Greenland

> Blockquote  
> “Statistics made easy is code for statistics done wrong.”

I prefer to think of low p-values as “sufficiently surprising” _if_ there is no effect.

> [@Appropriate statistical methods to derive a cut-off predictive values for a binary outcome](https://discourse.datamethods.org/t/appropriate-statistical-methods-to-derive-a-cut-off-predictive-values-for-a-binary-outcome/3246/12):
>
> Blockquote I would appreciate if you can help me understand. Philosophically – not statistics or some algebraic expression – I am doing a little experiment with GLM, my data is fixed … I cannot change it and my formula for this is fixed. A subtle point is that your data are a considered a sample from a hypothetical distribution for statistical purposes. Your data was one subset of a multitude of possible ones. This is a critical point that will be important a bit later. Blockquote I get…

This is also a good thread, that discusses the correct and unambiguous description of frequentist results.

> [@Language for communicating frequentist results about treatment effects](https://discourse.datamethods.org/t/language-for-communicating-frequentist-results-about-treatment-effects/934):
>
> Editorial Notes As Sander Greenland has so well stated below, this initial draft was still too “dichotomous” in that it was written assuming we would have different language for “positive” vs. “negative” studies. This implies a threshold for “positive” which is what we’re trying to get away from. So I’m trying to develop more “positive/negative agnostic” language. One initial stab at this is below in the Generic Interpretation section. The examples demonstrating incorrect and confusing sta…

---

<div class="post-metadata">

**Author:** ![med\_stat](https://discourse.datamethods.org/letter_avatar_proxy/v4/letter/m/b782af/32.png) [@med\_stat](https://discourse.datamethods.org/u/med_stat)\
**Post date:** [December 17, 2020, 8:48am UTC](https://discourse.datamethods.org/t/interpretation-of-p-value/3980/3 "2020-12-17T08:48:12Z")

</div>

You are right that this is incorrect.

As said before, attempts to “easy” or “simplify” statistics are often flat out incorrect. They are not “sort of correct” or even “a good approximation” as I have heard people say.

Saying a p-value is a probability “that what is observed is due to chance” demonstrates a serious deficit in understanding; people who understand what p-values are would not offer this as a “simplification.”

A real simplification (that still may lose some accuracy) is that a p-value tells us how much data “fit” with a particular hypothesis (whatever the null is chosen to be); smaller p-values mean data are less compatible with the chosen null. Never should a “probability due to chance” be mentioned.

---

<div class="post-metadata">

**Author:** ![DavidColquhoun](https://discourse.datamethods.org/user_avatar/discourse.datamethods.org/davidcolquhoun/32/132_2.png) [@DavidColquhoun](https://discourse.datamethods.org/u/DavidColquhoun)\
**Post date:** [December 22, 2020, 4:57pm UTC](https://discourse.datamethods.org/t/interpretation-of-p-value/3980/4 "2020-12-22T16:57:17Z")

</div>

You might find the references linked here useful.

> **[Some papers about p values](http://www.onemol.org.uk/?page_id=456)**
>
> Jump to follow-up These papers have nothing much to do with single molecule kinetics. They were written by David Colquhoun after his retirement from the world of single ion channels, as a way to ke…

  
Also try Gigerenzer, G., Krauss, S., & Vitouch, O. (2004), “The Null Ritual. What You Always Wanted to Know About Significance Testing but Were Afraid to Ask,” in ed. D. Kaplan, The Sage Handbook of Quantitative Methodology for the Social Sciences, Thousand Oaks, CA: Sage Publishing, pp. 391–408.

---

<div class="post-metadata">

**Author:** ![med\_stat](https://discourse.datamethods.org/letter_avatar_proxy/v4/letter/m/b782af/32.png) [@med\_stat](https://discourse.datamethods.org/u/med_stat)\
**Post date:** [December 31, 2020, 9:03pm UTC](https://discourse.datamethods.org/t/interpretation-of-p-value/3980/5 "2020-12-31T21:03:01Z")

</div>

Sorry, forgot to include a reference: [this](https://link.springer.com/article/10.1007/s10654-016-0149-3) and [this](https://www.tandfonline.com/doi/full/10.1080/00031305.2016.1154108) are pretty good starts.