4 ms·

Thanks for presenting this so clearly. However, note that, as you show in this scenario, males are, on a relative basis, 50% more likely than females to be good

Thanks for presenting this so clearly. However, note that, as you show in this scenario, males are, on a relative basis, 50% more likely than females to be good engineers, knowing nothing else about them other than gender (P(B|~A) = 1.5 * P(B|A)). While the absolute probabilities (and difference in probabilities) are small, the relative improvement in classification error rate attributable to knowing the person's gender could very well mean that gender is still a useful feature to include (among many others! it's not so useful on its own, as you note) in a classifier for good engineers.

logfromblammo 11y ago
If you were writing an automated Bayesian classifier to find good engineers, males would get one measly additional point towards the refer-to-a-human threshold. In contrast, there are many other hypothetical rules that would be better predictors. Liking Star Wars, 4 points. Star Trek, 9 points. Knowing how much mana a Lightning Bolt costs, 6 points. Owning a 3-wolf shirt, 2 points. Being left-handed, 15 points. Reading HN, 40 points. Anything you can glean statistically from a population of known-good engineers can be transformed into Bayesian classifier rules, in exactly the same way you can predict an e-mail is spam if it has certain strings in it. But even including the one point for knowing the sex could be considered sex discrimination, even though it would be totally supported by the math. But since you likely want your threshold value to be high enough to weed out false positives, while still low enough to avoid false negatives, that one point rule is practically a waste of time. The cases where that one point makes a difference will be just those people who barely meet the threshold. If you have two people who are only just barely good enough to be considered good engineers, and otherwise exactly the same, the statistical argument says to prefer the male. I have never met anyone that is content to hire engineers who are likely to be only barely adequate in preference to those who are likely much better. That hypothetical person is the only one who might care about male or female. Everyone else will be looking for the highest point totals, gained from criteria that are better predictors.
Retric 11y ago
This assumes it's independent of other data. If your classifier also knows that an applicant has a CS degree and hypothetically a higher percentage of females with CS degrees than males with CS degrees are talented. Then the relationship might reverse. The point is stats about populations often fail to carry over to sub populations. PS: This flip is actually fairly common in the face of discrimination. Basically, you would expect the first hundred female fighter pilots to be way above average.
- logfromblammo 11y ago
  There are three hypotheses: 1. The selection criteria are the same for different populations, and the there are significant statistical differences in the populations that may lead to the observed result. 2. The selection criteria are the same for different populations, and random noise produced the observed result. 3. The selection criteria are different for different populations. You cannot assert one without ruling out the others. In the fighter pilot case, I imagine that it would be easy to disprove #1 and #2. Not all cases of discrimination are so obvious that there are no non-imaginary solutions to the equations that conform to the assumptions of the hypothesis. It makes some people uncomfortable to face the idea that in order to prove discrimination is occurring, they must first employ accurate statistics for partitioned populations, which may be unflattering to one or more of the partitioned groups. You can't really say "because race" or "because sex" or "because disability" with certainty over "because selection-relevant attribute" using a statistical argument without showing the statistics. But those who attempt to gather accurate statistics are often accused of something-ism and vilified just because some people don't like the results. Some people just want to work without constantly watching their backs and covering their asses. And that's why we assume independence without having ironclad proof that is also easily understood by the general public. If you're going to suggest that there is something intrinsic to femaleness that causally links to less engineering skill, you had better have a flawless data set with mathematically perfect analysis, and then also invent a psychological "out" which absolves anyone of guilt for relying on the results. This is why all HR departments suck. Most of their job is covering someone else's ass, and if they choose to use statistics, they must be both factually correct and politically correct.

logfromblammo 11y ago

If you were writing an automated Bayesian classifier to find good engineers, males would get one measly additional point towards the refer-to-a-human threshold. In contrast, there are many other hypothetical rules that would be better predictors. Liking Star Wars, 4 points. Star Trek, 9 points. Knowing how much mana a Lightning Bolt costs, 6 points. Owning a 3-wolf shirt, 2 points. Being left-handed, 15 points. Reading HN, 40 points. Anything you can glean statistically from a population of known-good engineers can be transformed into Bayesian classifier rules, in exactly the same way you can predict an e-mail is spam if it has certain strings in it. But even including the one point for knowing the sex could be considered sex discrimination, even though it would be totally supported by the math. But since you likely want your threshold value to be high enough to weed out false positives, while still low enough to avoid false negatives, that one point rule is practically a waste of time. The cases where that one point makes a difference will be just those people who barely meet the threshold. If you have two people who are only just barely good enough to be considered good engineers, and otherwise exactly the same, the statistical argument says to prefer the male. I have never met anyone that is content to hire engineers who are likely to be only barely adequate in preference to those who are likely much better. That hypothetical person is the only one who might care about male or female. Everyone else will be looking for the highest point totals, gained from criteria that are better predictors.

Retric 11y ago

This assumes it's independent of other data. If your classifier also knows that an applicant has a CS degree and hypothetically a higher percentage of females with CS degrees than males with CS degrees are talented. Then the relationship might reverse. The point is stats about populations often fail to carry over to sub populations. PS: This flip is actually fairly common in the face of discrimination. Basically, you would expect the first hundred female fighter pilots to be way above average.

logfromblammo 11y ago
There are three hypotheses: 1. The selection criteria are the same for different populations, and the there are significant statistical differences in the populations that may lead to the observed result. 2. The selection criteria are the same for different populations, and random noise produced the observed result. 3. The selection criteria are different for different populations. You cannot assert one without ruling out the others. In the fighter pilot case, I imagine that it would be easy to disprove #1 and #2. Not all cases of discrimination are so obvious that there are no non-imaginary solutions to the equations that conform to the assumptions of the hypothesis. It makes some people uncomfortable to face the idea that in order to prove discrimination is occurring, they must first employ accurate statistics for partitioned populations, which may be unflattering to one or more of the partitioned groups. You can't really say "because race" or "because sex" or "because disability" with certainty over "because selection-relevant attribute" using a statistical argument without showing the statistics. But those who attempt to gather accurate statistics are often accused of something-ism and vilified just because some people don't like the results. Some people just want to work without constantly watching their backs and covering their asses. And that's why we assume independence without having ironclad proof that is also easily understood by the general public. If you're going to suggest that there is something intrinsic to femaleness that causally links to less engineering skill, you had better have a flawless data set with mathematically perfect analysis, and then also invent a psychological "out" which absolves anyone of guilt for relying on the results. This is why all HR departments suck. Most of their job is covering someone else's ass, and if they choose to use statistics, they must be both factually correct and politically correct.