This study was done about 10 years ago, but I guess it takes some time to compile almost 12,000 results. There are lots of charts and graphs.
One of the biggest findings was that there was not difference in results if the homeschooler was taught be a certified teaching parent, or a parent without certification. They made sure to emphasize that this does NOT mean that public school teachers should not be certified. But it DID mean that there would be no benefit to requiring that homeschooling parent become certified to teach. The reasoning for this is that homeschool teachers are self selected – these people already WANT to teach their kids. There are many links in the “Table of Contents” just to the left of the article – don’t miss them.http://www.hslda.org/docs/study/rudner1999/Rudner1.asp