On July 14, 2006, the U.S. Department of Education's National Center for Education Statistics (NCES) released a study that compared the performance in reading and math of 4th and 8th graders attending private and public schools. According to the NCES study, students attending private schools performed better than students attending public schools. But after statistical adjustments were made for student characteristics, the private school advantage among 4th graders disappeared, giving way to a 4.5-point public school advantage in math and parity between the sectors in reading. After the same adjustments were made for 8th graders, private schools retained a 7-point advantage in reading but achieved only parity in math. But, in fact, the NCES study's measures of student characteristics are flawed. Using the same data but substituting better measures of student characteristics, the authors estimated three alternative models that identify a private school advantage in nearly all comparisons. Similar results are found for Catholic and Lutheran schools taken separately, while evangelical Protestant schools achieve parity with public schools in math and have an advantage in reading. The results from the alternative models should not be understood as evidence that private schools outperform public schools. Without information on prior student achievement, one cannot make judgments about schools' efficacy in raising student test scores. Thus, NAEP data cannot be used to compare the performance of private and public schools. (Contains 1 figure.)