To do it right, you ought to understand which test is appropriate for the information you are analyzing. But it has been my experience that you don't need to know anything about the rules of statistical assumptions to just plug any ol' data into any ol' tool, create some kind of output and carry on with your day. I have enrolled in an ESRI-hosted course that had us run basic stats on a dataset that showed extreme kurtosis, and then was instructed to use Parametric Statistics in the ensuing analyses. 😫
Just remember, "Garbage In, Garbage Out." If the Test you want to run is inappropriate to use with the data you have, use a different, more appropriate test. Otherwise, while you will be handed a 'result' from the processing tool, it means bupkis.
...That ESRI doesn't really provide any context for the provided tools is a pet peeve.
Here is a small chart from one of my better University Professors. He taught Experimental Design/Quantitative Analysis.
I do miss being able to run Semivariograms to look at data distribution and autocorrelation properly.