Large difference in estimated competence even when plenty of other information available; plausible differences in competence are mostly not large. Largest differences I’ve heard of from actual scientific investigations are about one standard deviation, for “mental rotation” tasks; most are smaller and they go in both directions. So for most tasks, and still more for most jobs (since a job typically involves multiple diverse tasks), I would expect average sex differences to be well under one standard deviation. Now suppose a nontrivial amount of relevant information is available (e.g., examination results); away from the extreme tails of the ability distribution this will make knowing the person’s sex substantially less informative. End result: in most cases of this sort, discovering whether someone is male or female makes a very small difference to any rational estimate of their competence given the other available information.
This could break down (1) looking at extreme tails of the distribution, especially if as commonly suggested there are substantial sex differences in variance (though I seem to recall hearing it claimed that most of the “men are more variable” finding comes specifically from men having more catastrophic failures rather than from the distribution being generally wider), or (2) in cases where there’s a really big typical difference between male and female (physical strength might be an example).
Large difference in estimated competence even when plenty of other information available; plausible differences in competence are mostly not large. Largest differences I’ve heard of from actual scientific investigations are about one standard deviation, for “mental rotation” tasks; most are smaller and they go in both directions. So for most tasks, and still more for most jobs (since a job typically involves multiple diverse tasks), I would expect average sex differences to be well under one standard deviation. Now suppose a nontrivial amount of relevant information is available (e.g., examination results); away from the extreme tails of the ability distribution this will make knowing the person’s sex substantially less informative. End result: in most cases of this sort, discovering whether someone is male or female makes a very small difference to any rational estimate of their competence given the other available information.
This could break down (1) looking at extreme tails of the distribution, especially if as commonly suggested there are substantial sex differences in variance (though I seem to recall hearing it claimed that most of the “men are more variable” finding comes specifically from men having more catastrophic failures rather than from the distribution being generally wider), or (2) in cases where there’s a really big typical difference between male and female (physical strength might be an example).