Holly at Seeking Faithfulness has written a great post about homeschooling a large family. She recently got test scores back for her 3 oldest children and has listed the results.
Homeschooling has been shown time and again to be effective if the parents are dedicated to it. If you are concerned about your own homeschooled children or the homeschooled children of family or friends, read Holly's post. You will see that it doesn't take special certifications or degrees or training. Just good old determination.