a small significant difference in comparing educational outcomes between charter and traditional public schools. It may be that in some cases, charter schools actually improve other public schools by raising educational standards in the area. American Federation of Teachers study A report by the American Federation of Teachers, a teachers' union, stated that students attending charter schools tied to school boards do not fare any better or worse statistically in reading and math scores than students attending public schools. This report was based on a study conducted as part of the National Assessment of Educational Progress in 2003. The study included a sample of 6000 4th grade pupils and was the first national comparison of test scores among children in charter schools and regular public schools. Rod Paige, the U.S. Secretary of Education from 2001 to 2005, issued a statement saying (among other things) that, "according to the authors of the data the Times cites, differences between charter and regular public schools in achievement test scores vanish when examined by race or ethnicity." Additionally, a number of prominent research experts called into question the usefulness of the findings and the interpretation of the data in an advertisement funded by a pro-charter group. Harvard economist Caroline Hoxby also criticized the report and the sample data, saying "An analysis of charter schools that is statistically meaningful requires larger numbers of students." Caroline Hoxby studies A 2000 paper by Caroline Hoxby found that charter school students do better than public school students, although this advantage was found only "among white non-Hispanics, males, and students who have a parent with at least a high school diploma". Hoxby released a follow up paper in 2004 with Jonah Rockoff, assistant professor of economics and finance at the Columbia Graduate School of Business, claiming to have again found that charter school students do better than public school students. This second study compared charter school students "to the schools that their students would most likely otherwise attend: the nearest regular public school with a similar racial composition." It reported that the students in charter schools performed better in both math and reading. It also reported that the longer the charter school had been in operation, the more favorably its students compared. Criticism The paper was the subject of controversy in 2005 when Princeton assistant professor Jesse Rothstein was unable to replicate her results. Hoxby's methodology in this study