If you surveyed a whole population and made a chi-2 test and found a significant association between two categorical variables, you could interpret it as there must be a mechanism that creates an association between the two variables in the population. Since Y is not just randomly distributet independantly of X.
Also if you did a Mann-Whitney test of differences in salaries between males and females, you could similarly interpret that there is a mechanism that prevents the ranks from being equally distributed between the two groups. It's possible to discuss the probability of different orderings. For the t-test it's more difficult, I think since the t-distribution is a continuous one. But then I think you can use the line of reasoning that Robert Frick uses in an article in Behavior Research Methods, Instruments, & Computers a couple of years back. Frick uses the concept of PROCESS saying that there are inferences to PROCESSES and there are inferences to POPULATIONS. I think that the mechanisms I refer to above belongs to processes which have created the population at hand. And the chi-2 test and the Mann- Whitney test could just as well refer to the process instead of the mechanism. My suggestions is as I see them not in opposition to Radford Neal's but rather in line with them. Just put in a wiew of Robert Fricks discussion in his article. (Now I read a preprint, but I believe it is published.) Rolf Dalin > In article <[EMAIL PROTECTED]>, > Tim Witort <trw7atixdotnetcomdotcom> wrote: > > >I'm developing a report in an analysis program. > >This report examines employee salaries - comparing > >the salaries of men to those of women in a particular > >job title in a particular company. The goal is to > >determine if the difference in their mean salaries > >is statistically significant. > > > >I have been directed to the t-test to gather this > >information. When I look at the t-test, however, > >it appears to be geared toward *estimating* the > >difference in the means of a population based on > >a *sample* of the population. Since I am using > >the entire population, can I still use the t-test > >to determine if the difference in the means is > >statistically significant? > > Yes, because the "population" you are presumably interested in is not > the population of actual current employees, but rather the population of > possible employees and their salaries that would hypothetically result > from continued appliation of the company's current employment and > promotion policies into the indefinite future. Only by making > inferences about that hypothetical population can you conclude anything > about the nature of these policies. > > 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/ . > ================================================================= ************************************************** Rolf Dalin Department of Information Tchnology and Media Mid Sweden University S-870 51 SUNDSVALL Sweden Phone: 060 148690, international: +46 60 148690 Fax: 060 148970, international: +46 60 148970 Mobile: 070 6740094, intnational: +46 70 6740094 mailto:[EMAIL PROTECTED] http://www.ite.mh.se/~roldal/ ************************************************** . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
