Hi Eddie
You can apply a statistical test to any data set. However, it is the interpretation and generalizability that may be affected by issues such as selection bias.
In case you can't ensure data reliability for generalization i advise you to do parametric tests as well as non parametric tests and give a higher priority and reliability for the non parametric results in your conclusion.
Dear Eddie
If you have a probabilistic sample of your objetive population, it is usually a representative sample of it. Besides the distribution of the statistics after the test have several assumptions that are met when they are based on a probabilistic sample, then your test of hypotesis are well supported by the theory. If you use the same test on a non probability sample you may or may not be incurring in inference problems because of the lack of support for the tests.
Adrian, Adel, Guillermo, and Sibarata
Thank you for the relevant information shared. May I also share this information I was able to search
"Probability sampling is the only one general approach that allows the researcher to use the principles of statistical inference to generalize from the sample to the population (Frankfort- Nachmias & Leon-Guerrero 2002), its characteristic is fundamental to the study of inferential statistics (Davis, Utts & Simon, 2002). It is the sampling technique that uses the probability theory to calculate the likelihood of selecting a particular sample and allows the drawing of conclusions about the population from the sample.(Pelosi, Sandifer, & Sekaram, 2001) and it has the advantage of projecting the sample survey results to the population (McDaniel & Gates, 2002). Inferential statistical analyses are based on the assumption that the samples being analyzed are probability samples (Burns & Grove 1997)."
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