I failed the 4/5ths Rule. Can I prove it is not significant?

#1
I am a (hypothetical) employer who used an aptitude test to screen candidates for their trainability before hire. I am being sued for discriminating against Middle Eastern applicants.

I have data that shows how many Blacks, whites, Latinos, and Middle Eastern people were hired and not hired in each of my 5 factories. I fail the 4/5ths rule for every factory. The majority race differs in each factory, but in general the middle eastern people are hired at 40 to 60% of the majority.

I want to argue that the factory is not at fault for discrimination here. Is there a statistical test I can do to show these results are not significant (such as a t test?) Would I do a t test comparing the middle eastern # of people hired to the # of people hired in the majority race for each factory?

I guess I am a little unsure of my hypothesis because I am not sure how to go about comparing the relationship.
 

noetsi

Fortran must die
#2
This is actually a legal question not a statistical one so any statistical answers might not be correct depending on case law. Courts have taken strange positions on statistics notably the Supreme Court (Scalia argued in a key civil rights case for the majority that the use of statistical analysis for discrimination was not valid to prove discrimination). So you really need to determine what the courts have ruled on this, it might well conflict with what statisticians believe is correct. The 4/5 rule is based on politics not statistics to start with.

I would think you could do a test of proportions and see if the result was statistically significant (although I am not entirely clear what the hypothesis would be so I am not sure how you would use this test).