Contrary to common wisdom, public schools score higher in math than private ones, when differences in student backgrounds are taken into account. . . .
The researchers looked at achievement and survey data from NAEP's [National Assessment of Educational Progress] 2003 national sample of 190,000 fourth-graders in 7,485 schools and 153,000 eighth-graders in 6,092 schools. The schools in the sample were categorized by NAEP as public (non-charter), charter and private, with the private schools broken down further by Catholic, Lutheran, conservative Christian and "other private."
NAEP is considered the only nationally representative ongoing assessment of U.S. academic achievement, and is often referred to as the "gold standard" of school performance data. . . .
Using a statistical analysis known as hierarchical linear modeling, the Lubienskis found that regular public schools scored "statistically significantly higher" than private and charter schools at the fourth-grade level. With 10 points roughly considered a grade-level difference in achievement, the regular public schools were trailed by 11.9 points by conservative Christian schools, 7.2 points by Catholic schools, 4.2 points by Lutheran schools, 5.6 points by all other private schools, and 4.4 points by charter schools.
At the eighth-grade level, the regular public schools were trailed by 10.6 points by conservative Christian schools and by 3.8 points by Catholic schools.
Lutheran and charter schools led regular public schools by 1.0 and 2.5 points, respectively, and all other private schools were 2.3 points below regular public schools, but all of these three gaps were determined to be statistically insignificant by the researchers.
To determine differences in students' backgrounds, the researchers used NAEP survey data related to the students' socioeconomic status, which included their eligibility for free or reduced lunch and their access to learning resources in the home, such as books and a computer. The researchers also incorporated survey data on students' race and ethnicity; gender; disability and limited English proficiency.
The more religious content a private school has, the more it impairs math learning. Secular private or charter schools (which are also, by necessity secular), and relatively mainline religious schools, which tend to have less religous content than conservative Christian or Catholic schools, teach math about as well as public schools.
The average student at a private school does better on standardized tests because they exclude poor students. This is the only reason for the difference. The full paper can be found here.