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.