[gizmo686]

Your example is quite possible, particularly at an organazation that would be embarrased by such a result.

Assume that the ability curve of male applicants and female applicants are identical; that the majority of applicants are male; and that Amazon wants to hire more females then would be expected given the portion of applicants that are female.

A natural way of accomplishing this goal is to give extra points to female applicants [0].

Due to selection bias, the ability curve of women within the population of Amazon engineers would skew lower then men within the population of Amazon engineers.

This is a special case of a more general phenomona. If you have signal S that is positivly correlated with a desired trait in the general population, and over select for S, you will find that S is negativly correlated within your population.

[0]. All proposals I have seen amount to either a good approximation of this or changing the applicant pool. And, by assumption, the latter is excluded.