See Research by Barbara Preston at
http://theconversation.com/state-school-kids-do-better-at-uni-29155
State school graduates do better at university than private school graduates with the same end-of-school tertiary entrance score. That’s the clear finding in a number of Australian studies since the 1980s (here, here, here and here), and in England since the 1990s (here, here, and here).
The Australian research compared academic results at the end of first year at particular universities for cohorts whose entry was based on tertiary entrance scores (now ATAR) for the previous year in the same state. The most recent English research tracked all students who completed the end-of-school A-levels and went directly on to complete a full-time four-year degree course.
The differences between graduates of state and private schools were substantial (though less pronounced among those who did very well at university). The Australian research found that, on average, graduates of state schools received the same marks at the end of first-year university as graduates of private schools who had tertiary entrance scores around three to six points higher.
The English research found that at each A-level standard, on average around 7 percentage points more graduates of state schools than graduates of private schools received first or second-class, first division (upper second) honours.
Research in both Australia and England also found that with the same tertiary entrance scores:
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graduates of co-educational schools tend to do better than graduates of single-sex schools
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graduates of lower-fee private schools (in Australia, Catholic schools) tend to do better than graduates of higher-fee private schools (in Australia, independent schools)
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graduates of schools with lower average tertiary entrance scores tend to do better than graduates of schools with higher average tertiary entrance scores
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graduates of (English) state comprehensive schools do better (to a small extent) than graduates of state selective schools.
The general finding is that graduates of non-elite and co-educational schools do better at university than graduates of socially and academically elite and single-sex schools who achieved the same tertiary entrance score.