Instead, we must assume that the company has a policy of paying these employees different amounts, based on merit.
no ... we most certainly cannot make this assumption in ANY company/institution/organization ... in fact, evidence suggests just the opposite
take the university of toronto for example ... does anyone really think that differences in salary ... which there will be one and perhaps quite large ... between female and male associate professors with say n years in that rank ... will be just because of merit?
If we further assume that there is no reason why merit should be related to sex,
we can't necessarily make this assumption either ... could be that females are in reality, more meritorious
But of course there is chance variation.
not sampling error chance variation however
Even if men and women are equally meritorious on averge, the company may happen to have hired more good men than good women. To take the extreme case, suppose the company has only two employees, one male and one female. The male is paid $70,000. The female is paid $65,000. An obvious case of discrimination? Not if pay is supposed to be merit based and we have no knowledge of the degree of merit of these two employees.
but this is precisely what we can't know ... and can't assume
but, this is the issue that is being argued in salary cases like these ... usually not for an individual but, for a class of individuals
many institutions ... i know at least once at penn state ... a colleague did a fancy regression analysis ... given the large difference in male and female salaries ... tried to find as many variables as possible that when entered into the model ... would REDUCE the difference to the bare bones minimum ... down to a $$ value that could not be explained by any other factor ... then used THAT gap as the basis for salary adjustments ...
personally ... i thought this was rather silly once you got beyond certain factors but, in ANY case ... it was NOT an inferential problem ... and, the gap adjustment had nothing to do with a "significant" gap ... it was just THE gap that remained after the Rsquared got as big as they could make it
people in the business of trying to make sense out of salaries and differences in salaries ... don't use significance tests to make judgements about if there are differentials and what to do about them and i reiterate ... you CANNOT make the case that if there is no significant difference ... that there is really NO difference and certainly not an important one
depends on how big the gap is and what it will buy!
i am really amused by trying to invoke something like a t test inferential statistical procedure here to solve/resolve what are known facts ...
an aside ... if we use the merit argument to best "explain" differences in salaries ... that would mean that if we had an overall merit scale from say ... 1 to 50 ... and rated all employees (say university faculty) on this scale and also had their salaries ... that this correlation would be high ... but, it is not ... in fact, what is the factor that is the best single predictor of salary (in a case like university faculty) ??? DISCIPLINE ...
finally, if the government MAKES you do a t test ... fine, go ahead but ... it sure does not mean that they are correct in insisting you do it
Radford Neal
---------------------------------------------------------------------------- Radford M. Neal [EMAIL PROTECTED] Dept. of Statistics and Dept. of Computer Science [EMAIL PROTECTED] University of Toronto http://www.cs.utoronto.ca/~radford ---------------------------------------------------------------------------- . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
_________________________________________________________
dennis roberts, educational psychology, penn state university
208 cedar, AC 8148632401, mailto:[EMAIL PROTECTED]
http://roberts.ed.psu.edu/users/droberts/drober~1.htm
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