Please post cite. Not that this is unsurprising; clealry, parents who are willing to go to some lengths to provide their kids with an alternative education are likely going to have kids that outperform the rest. It's not really a fair comparison unless you match the two groups demographically.
My source is the good old fashioned (not dumbed down) "Iowa test". Our children have taken it annually for the past four years. The test results rank the student's performance based upon state and national averages as well as home schooler's as a group.