# Statistical Test for Staffing Agency Selection of Employees

I am looking for the statistical test to measure the selection pattern from a pool of people. The staffing agency receives requests from a contract and then selects a person to fill the order. The question is are males more likey to be selected than females from the pool of available people? There is a time component because you have to eligible for selection (i.e. not already on another contract). Do this voliate the assumption of independce? Here are e few thoughts that I had...

1) Test the mean number of selections over the course of two years and see if they diff by gender

2) Repeated Measure logistic regression to account for the fact there are multipe selections for each employee over time

Any help would really appreciated.

At a basic level, you would certainly have to account for the number of men and women in the pool at each time when a selection is made. Do that for each selection. Then you can calculate (for the 2 year period) the number of men and women that would have been selected if the choice was random.

Suppose there were only two selections (to keep it simple). At time 1, there are 60 women and 40 men available and a man is chosen. At time 2, there are 50 men and 50 women and a woman is chosen. So, a total of 1 man is chosen. If the choice was random, then there would, on average be:

• 0 men 0.6*0.5 = 0.3 of the time
• 1 man 0.6*0.5 + 0.4*0.5 = 0.5 of the time
• 2 men 0.4*0.5 = 0.2 of the time

and the average number of men would be 0.5*1 + 0.2*2 = 0.9.

Clearly you would have to do this with a much larger N.

But that is surely not enough. If this is some sort of class exercise, that might be a good solution, but in the real world (that is, if you are trying to prove or disprove discrimination) you will have to look at all sorts of things related to the qualifications each person has for each job. You might also have to look at whether those qualifications are, themselves, fair.

Issues of sex-based discrimination are really complicated. It is a whole field of expertise for statisticians who serve as expert witnesses at trials.

• +1 for recognizing and emphasizing the need to control for relevant variables. – whuber Jan 11 at 14:07