Randomization may be random sampling or random allocation.
The phrase in block quotes above serves to justify the fact that we use p values in RCTs. But Dr.Senn’s blog piece linked above emphasizes how important it is to not confuse random sampling with random allocation. In the first instance (random sampling) we seem to have access to the entire population of potential interest, whereas in the second instance (randomization that occurs in the context of an RCT), we are using a convenience sample that has presented for medical care and is willing to participate in a trial, and then assigning treatments “at random” to this sample.
If it’s kosher to use p values in the second instance (i.e., convenience sample/RCT context), even though the formal p value definition invokes the idea of random “sampling,” then shouldn’t this be stated clearly and with justification in introductory stats texts?
I suspect hat much of the confusion among physicians learning critical appraisal stems from the fact that our teachers are often (?usually) practising MDs, who might not understand the historical foundations of statistics well enough to address questions like this. As a result, these types of questions get glossed over.