That depends very much to specific priors and correlations.
If you’re looking for the expected score on a re-test, you should apply regression towards the mean, and for a lower mean, that’s more regression. A school may be interested in the probability of student success on a course, which is not a measure of inherent ability either but very much depends to the same disadvantages that lower the test score.
edit: that is to say, if you made a programming contest where the contestants write programs to predict re-test scores from score and a profile photo, given huge enough database of US students (split in two, one available to our contestants, one for the final test), winner code will literally measure skin albedo, and in some cases maybe also try to detect eyeglasses. Of course, the morale of the story is not that racism is good but that socially sometimes we don’t want the most accurate guess.
edit2: Subtler measures may correlate too, besides the racial ones. E.g. angle between line connecting pupils of the eyes, and horizontal, the pupil dilation in the photo, use/non use of flash, strength of red eye effect, and who knows what else (how busy does the background look, maybe?). I don’t think many people here want to have their math scores be adjusted depending to how they held their head in a photograph. edit3: ohh, and the image metadata, or noise signatures, that’d be a big one—is the image taken by an expensive camera? Get free points on your math test. And a free tip: squint. It will think you’re asian or smart enough to squint.
I think fubar may be right in a certain way: if you observe someone reaching a very high score while having a known poor environment (let’s say you’ve tested them enough so one can ignore issues of <1 reliability causing a regression to the mean on subsequent retests), then you might then estimate that the non-environmental contributions must be unusually high—because something must be causing him to score very high, and it’s sure not the environment. So for example, we might infer that his genes or prenatal environment or personality are better than average.
Yes. As I say, depends to what we are trying to predict and priors. Even with 1 test and significant regression, it’s correct to infer higher non-environmental contribution, just not higher combination of environmental and non-environmental.
That depends very much to specific priors and correlations.
If you’re looking for the expected score on a re-test, you should apply regression towards the mean, and for a lower mean, that’s more regression. A school may be interested in the probability of student success on a course, which is not a measure of inherent ability either but very much depends to the same disadvantages that lower the test score.
edit: that is to say, if you made a programming contest where the contestants write programs to predict re-test scores from score and a profile photo, given huge enough database of US students (split in two, one available to our contestants, one for the final test), winner code will literally measure skin albedo, and in some cases maybe also try to detect eyeglasses. Of course, the morale of the story is not that racism is good but that socially sometimes we don’t want the most accurate guess.
edit2: Subtler measures may correlate too, besides the racial ones. E.g. angle between line connecting pupils of the eyes, and horizontal, the pupil dilation in the photo, use/non use of flash, strength of red eye effect, and who knows what else (how busy does the background look, maybe?). I don’t think many people here want to have their math scores be adjusted depending to how they held their head in a photograph. edit3: ohh, and the image metadata, or noise signatures, that’d be a big one—is the image taken by an expensive camera? Get free points on your math test. And a free tip: squint. It will think you’re asian or smart enough to squint.
I think fubar may be right in a certain way: if you observe someone reaching a very high score while having a known poor environment (let’s say you’ve tested them enough so one can ignore issues of <1 reliability causing a regression to the mean on subsequent retests), then you might then estimate that the non-environmental contributions must be unusually high—because something must be causing him to score very high, and it’s sure not the environment. So for example, we might infer that his genes or prenatal environment or personality are better than average.
Yes. As I say, depends to what we are trying to predict and priors. Even with 1 test and significant regression, it’s correct to infer higher non-environmental contribution, just not higher combination of environmental and non-environmental.