The NY Times reports that family income is a predictor of SAT scores. They note:
New data shows, for the first time at this level of detail, how much students’ standardized test scores rise with their parents’ incomes — and how disparities start years before students sit for tests. One-third of the children of the very richest families scored a 1300 or higher on the SAT, while less than 5 percent of middle-class students did, according to the data, from economists at Opportunity Insights, based at Harvard. Relatively few children in the poorest families scored that high; just one in five took the test at all. The researchers matched all students’ SAT and ACT scores for 2011, 2013 and 2015 with their parents’ federal income tax records for the prior six years. Their analysis, which also included admissions and attendance records, found that children from very rich families are overrepresented at elite colleges for many reasons, including that admissions offices give them preference. But the test score data highlights a more fundamental reason: When it comes to the types of achievement colleges assess, the children of the rich are simply better prepared.
In 1959 I took the PSAT at a Catholic HS in NYC. No one told us this was important. It was a Christian Brothers school and the education was directed at allowing students to become police officers, ConEd techs and the like. No one said this was important. Just show up and when you finish you get the day off. Thus I just rushed through for a day off. Needless to say my performance was poor. My father was a police officer in NYPD and we had at best an upscale lower income life style.
Fortunately for a variety of reasons instead of playing basketball at the CYO I spent time at the Jewish Community center. There I found that these tests were critical. Furthermore that like a Regents exam one could get a Barron's book to study for them.
Thus from my small wages I purchased a Barron's regents exam book and did every math question 3 times and memorized every vocabulary word. Just as I had my Latin as an altar boy. As a lifeguard, I carried my Barron's around like a Bible. I then took an SAT prep course paying for it with some earnings as a lifeguard. So each Saturday I awoke at 4:30, took a bus, a ferry, a train to start at 8 AM in the Commodore Hotel.
Then in December 1960 I took the SAT. Finished in half the time and got well above 1400. In fact I even documented errors in problems to the College Board.
The conclusion is not that it is income, it is drive and awareness. It is a desire to achieve and take risks in doing so. The more wealth a family the more aware, possibly. But the counter is that the children of the more privileged may fail to have the drive, fail to have the necessary instinct to achieve and take those risks.
Unfortunately in today's world, it is the collection of many other factors that determine one's ability to get a better education. It is impossible for many to now overcome those social delimitations.