Consider a test followed by a re-test (which we are trying to predict). To calculate expected score on the re-test you need to apply regression to the mean.
This is only true if you assume there is some component of luck or guesswork to the score. I admit that this may be a good model for the kinds of tests you get in American high schools. However, it is not clear to me that “black people” is the correct population to use for the regression, because by construction you have an untypical member. Why not “high-scoring people” or “all students”?
Perhaps it would be helpful to construct an example using something other than race as the difference between populations, to avoid emotional entanglements?
If there is no component of luck or guesswork or something that varies from test to test, then the retest will be exactly the same as the original test, but that’s not what we see in pretty much any test. or any measurement of anything.
This is only true if you assume there is some component of luck or guesswork to the score. I admit that this may be a good model for the kinds of tests you get in American high schools. However, it is not clear to me that “black people” is the correct population to use for the regression, because by construction you have an untypical member. Why not “high-scoring people” or “all students”?
Perhaps it would be helpful to construct an example using something other than race as the difference between populations, to avoid emotional entanglements?
Try neuroskeptic.
If there is no component of luck or guesswork or something that varies from test to test, then the retest will be exactly the same as the original test, but that’s not what we see in pretty much any test. or any measurement of anything.