# Random sampling versus random allocation/randomization- implications for p-value interpretation

**URL:** <https://discourse.datamethods.org/t/random-sampling-versus-random-allocation-randomization-implications-for-p-value-interpretation/6177>\
**Category:** general\
**Created:** [November 6, 2022, 9:30pm UTC](https://discourse.datamethods.org/t/random-sampling-versus-random-allocation-randomization-implications-for-p-value-interpretation/6177 "2022-11-06T21:30:48Z")\
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**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:** [November 6, 2022, 9:55pm UTC](https://discourse.datamethods.org/t/random-sampling-versus-random-allocation-randomization-implications-for-p-value-interpretation/6177/2 "2022-11-06T21:55:01Z")

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> [@ESMD](#):
>
> **1. What exactly does a p value mean in the context of an RCT, given that “random sampling” from an underlying population of interest has not occurred?**

I remember posting a link that discusses this in a very old thread:

> **[Parametric Analyses In Randomized Clinical Trials](https://digitalcommons.wayne.edu/jmasm/vol1/iss1/11/)**
>
> One salient feature of randomized clinical trials is that patients are randomly allocated to treatment groups, but not randomly sampled from any target population. Without random sampling parametric analyses are inexact, yet they are still often used...

The textbooks discuss the distinction between model based inference (ie. 2 sample t-test), vs design based inference (again either 2 sample t test or permutation test). The design gives justification to the calculation of a p value in an RCT.

> [@Updates to NEJM Statistical Guidelines for Authors](https://discourse.datamethods.org/t/updates-to-nejm-statistical-guidelines-for-authors/1888/7):
>
> P values in clinical trials can always be justified (and calculated) by permutation tests based upon the design. Wasn’t that Fisher’s key justification for the randomization procedure? The same cannot be said for observational studies. I’m not sure how big of an error this is, however. At least in simulations, the t test results generally matches the permutation test results. Addendum: I re-read the first paper I posted by Berger, Lunneborg, Ernst, and Levene who argue that RCTs should …

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