I know that some homeschooled students do exceptionally well, but so do some students from private and public schools.”
Yes, the Home School Legal Defense Association’s web site has a lot of it. But, I’m sure that in the case of each study, someone from the government school bureaucracy will question the “sampling methodology and analytical procedures,” as they do with everything that shows a negative portrayal of public education.
sampling methodology and analytical procedures of those studies have been called into question?
It does appear that they have some data to show that homeschooling can be very effective. I'm not sure that one could generalize that to say that homeschooling is always more effective, and I'm sure it would not be true to say that all children would do better if they were homeschooled.
Most of the homeschooled children I've met have been the epitome of homeschool success stories - bright, polite, well-read, and a joy to be around. I have known a few who claimed to be homeschooled, but in fact were not educated at all; it was just a ploy to keep the parents from being prosecuted for the child's truancy.
It also seems to me that if children don't know their numbers, colors, basic shapes, and most of the alphabet by the time they reach school age, their parents would not be good homeschool parents. (There are parents like that, by the way, and their children are the ones who bring the public school averages down.)