1. Example: gender discrimination
The example in this chapter is taken from a paper on the "Influence of sex role stereotypes on personnel decisions" by Rosen and Jerdee.
2. Bank files
Forty-eight male bank supervisors were given personnel files and asked to judge whether the person should be promoted to a branch manager position.
3. Resumes
The files were all identical except that half of them indicated that the candidate was male and the other half indicated that the candidate was female.
4. The data
The data were then collected showing that 14 out of the 24 female files were selected for promotion and 21 of the 24 male files were selected for promotion.
5. Fewer women were promoted
After summarizing the data, the difference in promotions can be identified using rates. That is, 58 (point) 3% of the women were promoted whereas 87 (point) 5% of the men were promoted. The important statistical question to ask after looking at the data is as follows: is it plausible to observe such a difference in proportions in a scenario where men and women are equally likely to be promoted?
That is to say, if we shuffle the data so that gender and promotion are not linked in any way, what sort of chance differences are observed?
6. Random chance?
In the first shuffle of the data, we see that 17 women were promoted and 18 men were promoted, a difference in proportions of negative (point) 04. Notice that the shuffled difference is closer to zero than the observed difference of positive (point) 29.
Keep in mind that a fixed number of male and female resumes were given out, 24 of each. Additionally, assume that there were a fixed number of people allowed to be promoted, here, 35. However, the shuffling process breaks the relationship between sex and promotion, which allows us to understand the variability of the differences in promotion rates assuming there is no connection between the two variables.
7. Random chance?
Even though here gender doesn't play a role in determining promotion,
8. Random chance?
we still typically don't have a difference of zero.
9. Random chance?
That's because of the natural variability associated with which manager gets which file.
10. Random chance?
But the point of the randomization process is to identify how different the proportions can be naturally and,
11. Random chance?
on the other hand, how big a difference would have to be to make us think something unusual was going on.
12. Random chance?
By shuffling the promotion variable repeatedly, not only do we see the variability in the null differences,but we also see that the observed statistic of 0 (point) 29 is on the extreme end of the plausible values generated by natural variability.
13. Let's practice!
OK, now it's your turn to practice what you've learned.