As another related argument for the validity of statistical tests, consider a difference of 1$. That is a real difference for the population, but does it represent discrimination?
if you want to discuss salary discrimination ... then one needs to consider the guidelines for organizations like EEOC and others ... to look at what they do
i do not recall that the original post was specific about salary discrimination based on sex ... what i recall was an interest in whether there were differences in salaries between males and females ... the interest in that could have been for any one of a batch of different reasons
the inferential problem here is NOT one of does discrimination exist or not ... it is one of considering the employees you have ... AS A SAMPLE from all possible employees in the future who might have these same sorts of jobs ... and asking is there likely to be a difference in the salaries in THAT LARGER population ... based on your "assumed to be" sample data
but, i will bet you a dime to a donut that the REAL interest in the case being originally posed is ... what evidence do we have that there is a CURRENT DIFFERENCE in salaries ... sufficiently large that we need to do something about it with THESE employees ... or else they are going to take us to court and sue the dickens out of us
this sort of issue has to do with current payroll employees and whether you are compensating them ... males and females doing the same sorts of jobs ... fairly
this is not an inferential problem in the sense of the way we teach them in intro stat ... it just is not
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