I'm not sure why I see so much hostility to homeschooling statistics in your posts, else I wouldn't have asked.
It's interesting that you say I shouldn't compare my individual kids to a population in the public schools. Following that dictum, no comparison could ever be made, statistically or otherwise. Anecdotal evidence in support of statistical analysis is valid. Anecdotal evidence by itself, of course, is commonly specious.
"I'm not sure why I see so much hostility to homeschooling statistics "
The statistics are self-selecting and misleading. I'm pointing it out and not backing down, and so far I've been challenged only with anecdotes - do not mistake it for hostility, though. I wish no homeschooler anything but the best.
I never said you shouldn't compare your kids to the population in public schools, I said it was pointless.
If you are satisfied that your kids are doing better than a population that contains a lot of low-achieving dysfunctional urban school districts (as just one example), then fine.
What you probably want to compare your children to is a statistically valid population of high-achieving kids.
I totally disagree with you about the value of anecdotes used with statistical analysis. In this case, the statistics are flawed - so what are the anecdotes supporting? I can also provide alternative anecdotes that lead to opposite conclusions (since no proof is required - it's an anecdote!) - so this sort of "analysis" rapidly degrades into nothing more than an exercise in imaginations