I read one of those papers. Only between 10% and 25% of homeschool families completed the test. And that's of families that could be located because they had previously interacted with major homeschool testing companies; there isn't a national list of homeschooled kids and many parents homeschool precisely to avoid standardized testing. Plus in many cases the parents were the proctors. This is hardly a robust finding.
Thanks for investigating deeper than I did. I don't know where else to look. However, unlike the post I originally replied to, every homeschooled adult I know is doing better than average, but anecdote vs anecdote isn't helping.
I follow some homeschooling communities as a way to learn how to supplement my kids' schooling. There are many interwoven communities:
* religious families who don't want their kids exposed to the secular world
* families who don't trust adults to watch their kids and wouldn't ever consider public school, summer camp, sleepovers etc.
* families whose kids aren't being served by the public school system.
In all three scenarios (but especially in the first two) there is a sizeable population of parents who know their kid is several years behind grade level, but they tolerate it because they think kids learn at different paces. Or that it's fine for a kid to love one particular thing (cooking, machine repair, art) at the expense of a well-rounded education. And that's not even getting into the 'unschoolers' who treat never opening a textbook as a point of pride.
If you're well-educated and run in circles of people like you then you'll find the homeschoolers who also value education. But if you expose yourself to a wider variety of people your conclusions may change.