> "Mean ACT Composite scores for homeschooled students were consistently higher than those for public school students" from 2001 through 2014, according (PDF) to that testing organization, although private school students scored higher still.
Graduates of religious schools also outperform public school graduates on the SAT: https://www.capenet.org/pdf/Outlook399.pdf
1) The most religious are the least likely to be college bound.
2) "Regarding ethnicity, for example, 72 percent of the homeschool students were White, 5 percent were Asian, Asian American, or Pacific Islander, and 4 percent were Black or African American, while of all college-bound seniors, the corresponding percentages were 49, 12, and 13. The average highest level of parental education was notably higher for the homeschool students than for all students."
Same study also points out that 60% of homeschooling in North Carolina is for religious reasons.
The studies without selection bias show that homeschooling is inferior in almost all cases. The big problem being that the cases of poor schools where homeschooling would be most helpful are also the same places where the parents are least likely to have the bandwidth and resources to homeschool properly.
HN has an extremely high selection bias because they are 1) the most likely to homeschool for quality-of-life reasons and 2) the most likely to be earning enough money that a parent can drop completely out of the workforce to homeschool.
Socialization is a hard problem to fix. I know they try with after school sports/activities/clubs, but that's not quite the same as being around peers for 8+ hours a day. In non-homeschool, the children are around other children more than adults/parents.
The other homeschooled kids I interacted with were homeschooled for religious reasons or so they could help on the farm. They were poorly socialized and poorly educated as best as my then eleven year old self could tell.
I was homeschooled for a while and saw a lot of the other homeschooling families via the school district resource center thing, which even the real extremists interacted with at least some. From my perspective, it was broken into three major groups: religious conservatives concerned with the moral purity of their kids, upper-middle class professionals interested in accelerating their kids as much as possible, and a grab bag of students from various socioeconomic stripes who'd had trouble with the standard school system for various reasons.
I was one of the second. My mom has advanced degrees in education. My dad's an attorney. I did fine, as did basically everybody else in that cohort. Even then, the impression my friends and I had was that the religious kids spent an awful lot of time on literal bible study and weren't so hot on "actual" education. These suspicions were borne out when it was time for the state standardized tests they wanted homeschooled kids to take - every kid from the second of those cohorts (and many from the third) blasted though them, while those from the first visibly struggled. The religiously-motivated cohort also managed to out-weird a bunch of kids who spent much of their time on mid-2000s 4chan as young teens, which is actually pretty impressive.
Anyway, I agree that the reason a student is homeschooled (and by proxy the resources and pedagogical methods available to them) is a much better predictor of overall outcomes than a simple homeschooled/not binary. When there's such significant clustering in a category, trying to make judgments only utilizing knowledge/stereotypes regarding the category as a whole is a good way to be misled.
Maybe raising kids in the city makes them more streetwise, informed and cautious by sheer number of social experiences in the real world, and rural maybe more Turnip Truck? Like socialized and unsocialized pets? So goes the stereotype. Dunno.