Several recent large-scale studies have compared private schools to charter and regular public schools using the one common test taken by selected samples of students around the country.
That test is the National Assessment of Educational Progress (NAEP), otherwise known as the Nation’s Report Card. Administered by the U.S. Department of Education, the NAEP is given to students in grades 4, 8 and 12 in both private and public schools.
One of these studies, conducted by Christopher and Sarah Theule Lubienski, a husband-and-wife team at the University of Illinois, compared more than 340,000 students using math scores from the 2003 NAEP. The study found that after adjusting for socioeconomic factors, there is little difference between private and public school scores. According to the researchers, “Demographic differences between students in public and private schools more than account for the relatively high raw scores of private schools. Indeed, after controlling for these differences, the presumably advantageous ‘private school effect’ disappears, and even reverses in most cases.”
https://www.greatschools.org/gk/arti...l-test-scores/
Also should be noted that Private Schools in general, don't release their test scores.