Table 1.15 shows that 35 bank supervisors recommended promotion and 13 did not. Now, suppose the bankers’ decisions were independent of gender. Then, if we conducted the experiment again with a different random arrangement of files, differences in promotion rates would be based only on random fluctuation. We can actually perform this randomization, which simulates what would have happened if the bankers’ decisions had been independent of gender but we had distributed the files differently.
In this simulation, we thoroughly shuffle 48 personnel files, 24 labelled male_ sim and 24 labelled female_ sim, and deal these files into two stacks. We will deal 35 files into the first stack, which will represent the 35 supervisors who recommended promotion. The second stack will have 13 files, and it will represent the 13 supervisors who recommended against promotion. Then, as we did with the original data, we tabulate the results and determine the fraction of male_ sim and female_ sim who were promoted. The randomization of files in this simulation is independent of the promotion decisions, which means any difference in the two fractions is entirely due to chance. Table 1.16 show the results of such a simulation.
| decision | ||||
|---|---|---|---|---|
| promoted | not promoted | Total | ||
| male_ sim | 18 | 6 | 24 | |
| gender_ sim | female_ sim | 17 | 7 | 24 |
| Total | 35 | 13 | 48 | |
What is the difference in promotion rates between the two simulated groups in Table 1.16? How does this compare to the observed 29.2% in the actual groups?
Answer. or about 4.2% in favour of the men. This difference due to chance is much smaller than the difference observed in the actual groups.