School funding impact study

In most PISA-participating countries and economies, the average socio-economic background of students who attend privately managed schools is more advantaged than that of those who attend public schools. Yet in some countries, there is little difference in the socio-economic profiles between public and private schools. Why? An analysis of PISA results finds that while the prevalence of privately managed schools in a country is not related to socio-economic stratification within a school system, the level of public funding to privately managed schools is: the higher the proportion of public funding allocated to privately managed schools, the smaller the socio-economic divide between publicly and privately managed schools. This report also shows that those countries with narrow socio-economic stratification in their education systems not only maximize equity and social cohesion, but also perform well in the PISA survey.
OECD. (2012). Public and private schools: How management and funding relate to their socio-economic profile. Paris: OECD.
http://www.oecdbookshop.org/oecd/display.asp?sf1=identifiers&st1=982012061P1&LANG=EN

Voucher study

Students using vouchers score no better
Nearly 2000 D.C. students who attended private school with the aid of vouchers generally performed no differently after two years time than their public school counterparts, echoing other similar research. Students also reported no higher satisfaction with private schools, although their parents did.
U. S. Dept. of Education. (2008). Evaluation of the DC Opportunity Scholarship Program: Second Year Report on Participation. Washington, DC: Author.
http://ies.ed.gov/ncee/pubs/20064003/famstudents_usage.asp

Parents and performance study

Study: Parents make the difference in performance
Poor students who attend private and parochial schools scored about the same as their peers at urban public schools, according to a study released today. This study suggests that parental participation and other family characteristics account for differences in performance among poor students.
Wenglinsky, H. (2007). Are Private High Schools Better Academically Than Public High Schools? Washington, DC: Center on Education Policy. www.cep-dc.org