Hi On 3 Apr 2003, Dennis Roberts wrote: > the fact is in this case ... there is either a difference in salaries (for > which they have the data) or not > > let's say for argument ... that there is a difference in favor of males ... > of $1000 a year ... but, because there is wide variation within the male > and female categories (because of years of experience) ... a t test fails > to reject the null > > what is the data analyst going to say ... that there is no difference ... > ??? how can you use the t test RETENTION of the null to persuade the > females that the $1000 dollars is just a figment of their imagination? > > we know there is a difference ... this issue then is ... is the difference > important ENOUGH that the company/organization ... should do something > about it? a t test is NOT going to help resolve that problem > > therefore ... i claim in this kind of a situation ... the FACTS are known > and ... an inferential test like a t test is completely inappropriate
The null hypothesis being tested is exactly the same as for other uses of the t-test, namely whether the observed difference could have occurred by chance, rather than be some systematic factor. If a difference of $1,000 being means is observed, we still need to know whether that is a large or small difference given the variability among individuals within groups (if large, perhaps for the kinds of systematic reasons that Radford mentioned). That this is a logical (and responsible) thing to do can be appreciated by recasting this as a randomization test. If the observed salaries were randomly assigned to males and females, what is the probability that the observed difference or larger would be observed. My understanding is that randomization and parametric tests generally converge on a common answer to this question. I would be interested in references either way on this point. As another related argument for the validity of statistical tests, consider a difference of 1$. That is a real difference for the population, but does it represent discrimination? Most of us would agree that a difference this large could readily occur just by chance. But how large must a difference be to be treated as a "real" difference ... a statistical test will address this question. In doing the statistical test, it would probably be appropriate to compare groups of males and females that are roughly equal along relevant dimensions. Throwing the President's salary of $250,000, for example, is likely to inflate the denominator and make it difficult to achieve significance. Best wishes Jim ============================================================================ James M. Clark (204) 786-9757 Department of Psychology (204) 774-4134 Fax University of Winnipeg 4L05D Winnipeg, Manitoba R3B 2E9 [EMAIL PROTECTED] CANADA http://www.uwinnipeg.ca/~clark ============================================================================ . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
