Interpretation of P value

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.


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

“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.

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


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.


You might find the references linked here useful.

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.
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Sorry, forgot to include a reference: this and this are pretty good starts.