"Because very few children from the other kind of state school ever get to university and therefore, are not included in the data"
Well they break that out separately.
They show that children from the best (top 20%) state schools should, like private schools, get a slightly higher offer.
But here the effect is smaller - it's less than one grade different at highest.
They also consider higher education access, and there's a small difference between the areas with fewest higher education entrants (children from these areas do better given the same grades) and those with the most.
The biggest gap is found with deprivation - children from the most deprived areas perform much better than those from the least deprived. This gap exists even with 3 As, and it's of consistent size across the grade ba, suggesting that whereas universities make some attempt to redress advantages of privately educated over state, they pay much less difference to socio-economic advantages of children within the state sector.
Presumably there is high overlap between the least deprived areas and the group of independently educated children, but it's at the AAA level that the difference is largest. Given that 14% of the total cohort went to private schools, presumably nearly all will live in the top 1 or 2 least deprived quintiles, that suggests that the set of children who:
- are socio-economically advantaged, but
- went to state school
are flying well under the radar - if you come from a nice home and got AAA at a state school then that that's perhaps an ABB from an average home.
So:
- university tutors at elite (Oxbridge+) universities appear to be adjusting fairly for the advantages of private over state
- but at lower levels this might not be the case
- and university tutors at all levels need to pay much more attention to the advantages of parental wealth, where that wealth is not expressed in private school fees, but in other, less obvious, still very important advantages.