Studies of student university grades suggest that private school students with the same ENTER scores as public school students achieve lower grades at university.
http://www.buseco.monash.edu.au/eco/research/seminars/chris-ryan.pdf
Good journal however I can see some problems.
Firstly, given the large amounts of parameters involved, this study could and should have incorporated a bit more. The assumption they used was
where i = catholic, independent. However they could have made it more generalised by incorporating it into some form such as
again with
being an error term.
Although they did justify this by saying:
the parameters on the school sector (and all other variables) cannot be estimated
consistently. The estimated parameter on the school choice variables will reflect some
combination of the ‘true’ effect of differing school types on the outcomes observed and the
impact of selection effects, to the extent that unobserved factors affect both the school sector
choices made and outcomes achieved by individuals.
So this study isn't a true reflection of the population standard.
Also the hypothesis testing should have been tested at a wider range of significance levels.
So no, this doesn't "prove" that "public school students perform better in uni than private school students". The study illustrates some fact that it is true for significance levels of
(which is pretty small imo for a subject like this)
protip: never read journals without verifying details yourself, most of the time studies relating to subjects which require a great deal of assumptions are most likely false for the real world.