Runner is to Marathon as XXXXXXXX is to Regatta

If you grew up on the coast in a wealthy family, you have a much higher chance of knowing what a Regatta is and that it involves boat races.

But if you read the papers cited in the GGGP comment, those hard problems aren't the problems that show the racial gap. The hardest problems show the least gap. Which doesn't fit the pat little sailboat jargon theory at all. However it does fit a common pattern, also seen in longevity statistics, where the most exceptional are more similar to one another than the average are.

Wait, can you elaborate?

As people get older, the mortality rate gaps between different groups get smaller on a relative basis. Like, the ratio between rich and poor 50 year olds' risk of death over the next year might be 3x or more, but as they age, they become more similar, and by 90 the ratio may be more like 1.3x, and after 100 it becomes indistinguishable from 1 (in part because of thin data).

The theory is that the genetics and environmental conditions needed to survive to an old age are fairly specific, so once you're down to those people, they have less variation from one another. The health risk factors that distinguish income and racial groups may mostly impact younger age mortality, and the people that get past those younger ages may have avoided or resisted those risk factors, regardless of race or income.

Similarly here, students who "survive" to do well on hard SAT questions may be fundamentally very similar to one another (sharing a high g-factor), and this may greatly reduce socioeconomic and racial gaps that are seen on the easier questions.

Does this mean the easier questions are biased? Not necessarily, I would argue. The concepts tested in the easy-medium questions are most likely to be intellectually foundational -- you are far, FAR more likely to get obscure rich people jargon in the hard questions than the easy-medium ones. We want people to have the basic intellectual exposure that enables them to do well on those easier questions, and we should reward it.

The problem is not the test, the problem is racially biased failure to educate in the lead-up to the test. This explains the pattern perfectly: the strongest students power through regardless of background, while the weaker are more sensitive to resources they were given. So you see the biggest gaps on easy-medium questions where basic educational background matters most to getting them right, rather than raw talent.

Have you explored broader implications of your idea? For example people who survived tribulations of a political career may end up close to each other despite their initial difference in political opinions, and maybe even across different countries. This doesn’t sound quite as convincing, but I’m kind of grasping in the dark trying to find some other examples.

I don't know of any examples outside of health but health is a big enough topic and closely related enough to education that I think it's likely to have some application.

Certain psychometric studies also support higher sensitivity to environment in the lower economic strata. Not exactly the same but you see the connection.

The studies cited by jedberg are very interesting, I just don't think they show what he thinks they do.

A better alternative to trashing the SAT is to provide an estimated adversity score, as ETS recently began to do, so schools have a sense of what a student may have had to overcome to reach their level of achievement.

Still there is something in the longevity example that’s evading the trivial explanation.

It's also a little unclear whether we should consider the % difference convergence remarkable, given that mortality at older ages is so much higher and the absolute difference may not show much convergence.