We consider a study investigating gender discrimination in the 1970s, which is set in the context of personnel decisions within a bank.1717Rosen B and Jerdee T. 1974. Influence of sex role stereotypes on personnel decisions. Journal of Applied Psychology 59(1):9-14. The research question we hope to answer is, ‘‘Are females unfairly discriminated against in promotion decisions made by male managers?"
The participants in this study are 48 male bank supervisors attending a management institute at the University of North Carolina in 1972. They were asked to assume the role of the personnel director of a bank and were given a personnel file to judge whether the person should be promoted to a branch manager position. The files given to the participants were identical, except that half of them indicated the candidate was male and the other half indicated the candidate was female. These files were randomly assigned to the subjects.
Is this an observational study or an experiment? What implications does the study type have on what can be inferred from the results?
Answer. The study is an experiment, as subjects were randomly assigned a male file or a female file. Since this is an experiment, the results can be used to evaluate a causal relationship between gender of a candidate and the promotion decision. For each supervisor we record the gender associated with the assigned file and the promotion decision. Using the results of the study summarized in Table 1.15, we would like to evaluate if females are unfairly discriminated against in promotion decisions. In this study, a smaller proportion of females are promoted than males (0.583 versus 0.875), but it is unclear whether the difference provides convincing evidence that females are unfairly discriminated against.
Statisticians are sometimes called upon to evaluate the strength of evidence. When looking at the rates of promotion for males and females in this study, what comes to mind as we try to determine whether the data show convincing evidence of a real difference?
Answer. The observed promotion rates (58.3% for females versus 87.5% for males) suggest there might be discrimination against women in promotion decisions. However, we cannot be sure if the observed difference represents discrimination or is just from random chance. Generally there is a little bit of fluctuation in sample data, and we wouldn’t expect the sample proportions to be exactly equal, even if the truth was that the promotion decisions were independent of gender.
| decision | ||||
|---|---|---|---|---|
| promoted | not promoted | Total | ||
| male | 21 | 3 | 24 | |
| gender | female | 14 | 10 | 24 |
| Total | 35 | 13 | 48 | |
Example 1.8.4 is a reminder that the observed outcomes in the sample may not perfectly reflect the true relationships between variables in the underlying population. Table 1.15 shows there were 7 fewer promotions in the female group than in the male group, a difference in promotion rates of 29.2% . This difference is large, but the sample size for the study is small, making it unclear if this observed difference represents discrimination or whether it is simply due to chance. We label these two competing claims, and :
Independence model. The variables gender and decision are independent. They have no relationship, and the observed difference between the proportion of males and females who were promoted, 29.2%, was due to chance.
Alternative model. The variables gender and decision are not independent. The difference in promotion rates of 29.2% was not due to chance, and equally qualified females are less likely to be promoted than males.
What would it mean if the independence model, which says the variables gender and decision are unrelated, is true? It would mean each banker was going to decide whether to promote the candidate without regard to the gender indicated on the file. That is, the difference in the promotion percentages was due to the way the files were randomly divided to the bankers, and the randomization just happened to give rise to a relatively large difference of 29.2%.
Consider the alternative model: bankers were influenced by which gender was listed on the personnel file. If this was true, and especially if this influence was substantial, we would expect to see some difference in the promotion rates of male and female candidates. If this gender bias was against females, we would expect a smaller fraction of promotion decisions for female personnel files relative to the male files.
We choose between these two competing claims by assessing if the data conflict so much with that the independence model cannot be deemed reasonable. If this is the case, and the data support , then we will reject the notion of independence and conclude there was discrimination.