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As a mathematical comment, if these are two distributions are gaussians, and one has 120k above some cutoff, the other 78k, then the distributions above this c

by iguy 8y ago

As a mathematical comment, if these are two distributions are gaussians, and one has 120k above some cutoff, the other 78k, then the distributions above this cutoff are not the same. They will typically have slightly different means (not far above the cutoff) and quite strongly different tails.

mikekchar 8y ago
This is a great point and I wish these kinds of discussions always had someone to point out that kind of important detail. I think the parent's idea would be better expressed by saying that we can't say anything about individuals in either population without more information. You don't know where in the tail that individual lies. Assuming a continuous distribution it could be anywhere. So while it might be more likely for a random individual from population A to outperform a random individual from population B, there is no way to know a priori if it will happen for specific individuals. Obvious, I know, but it's the kind of thing that people often miss when they get into a heated discussion.
- iguy 8y ago
  Being that someone appears to be my regular job :) It's absolutely true that, if all you know about an individual is membership of one of these populations, then you know very little. Any new information about the actual person will quickly swamp this signal. If you've actually met A & B (or seen their work) then group membership is irrelevant. This is the situation in hiring people. But it's also true that these distributions lead you to make predictions about the tails. While any one individual is vanishingly unlikely to win a Nobel prize, you can predict that (if they are fairly awarded) there should be a huge slant in how many go to each group. And I really mean huge, this ratio (if things are Gaussian, etc) grows exponentially in how far along the tail you go. Seeing such a skew is thus no evidence that hiring/prize-awarding is biased.
cm2187 8y ago
Right, but if you define the skill as "good enough", i.e. score of 700 and above, then my point stands. My point is really that individuals aren't defined by the distribution, just the number of individuals is defined by the distribution. But many people take these distributions personally.

by iguy 8y ago

mikekchar 8y ago

This is a great point and I wish these kinds of discussions always had someone to point out that kind of important detail. I think the parent's idea would be better expressed by saying that we can't say anything about individuals in either population without more information. You don't know where in the tail that individual lies. Assuming a continuous distribution it could be anywhere. So while it might be more likely for a random individual from population A to outperform a random individual from population B, there is no way to know a priori if it will happen for specific individuals. Obvious, I know, but it's the kind of thing that people often miss when they get into a heated discussion.

iguy 8y ago
Being that someone appears to be my regular job :) It's absolutely true that, if all you know about an individual is membership of one of these populations, then you know very little. Any new information about the actual person will quickly swamp this signal. If you've actually met A & B (or seen their work) then group membership is irrelevant. This is the situation in hiring people. But it's also true that these distributions lead you to make predictions about the tails. While any one individual is vanishingly unlikely to win a Nobel prize, you can predict that (if they are fairly awarded) there should be a huge slant in how many go to each group. And I really mean huge, this ratio (if things are Gaussian, etc) grows exponentially in how far along the tail you go. Seeing such a skew is thus no evidence that hiring/prize-awarding is biased.

cm2187 8y ago

Right, but if you define the skill as "good enough", i.e. score of 700 and above, then my point stands. My point is really that individuals aren't defined by the distribution, just the number of individuals is defined by the distribution. But many people take these distributions personally.