Question about parametric and nonparametric tests and non-probability sampling

I think I am pretty clear on the differences between parametric and nonparametric tests and which is more appropriate to use given the data you have collected.

My question is about non-probability sampling and the use of the aforementioned tests.

To my knowledge, both parametric and nonparametric have the same assumption that the data is from a random sample/random sampling procedures.

So how we handle the data from non-probability samples? Can we only complete descriptive statistics?

Also, I was informed there are such a thing as "non probability statistics", do these exist? I cannot find anything of the sort when I search.


Super Moderator
Whether you need a random sample depends on whether you're trying to make inferences about a population. In some cases you might be wanting to make inferences about causal effects in a sample. With random assignment you can do the latter even with a convenience sample. (E.g., I can collect 100 students from my uni, do an experiment testing a causal effect, and then calculate the probability of observing a difference as large as that I've seen in my sample under the null hypothesis that the manipulation had zero effect).

For inference to a population from a sample, multilevel regression and poststratification (Mr P) is something that can be applied in some contexts.

The participants will be recruited from a database (persons self select to be entered into this database). Definitely would like to use inferential statistics for this sample.

From what my search is telling me is non-probability statistics (designed without the assumption a random sample is being used) may not exist

Honestly, I am more confused by the use of the term "non-probability statistics" than anything else