[syzarian]

The average person with no training in teaching or education isn't going to do better than the average person with said training.

Your stats aren't all that meaningful for the following reasons. What percent of homeschooled kids meet the criteria for "structured homeschooling"? Without this information it's not a meaningful stat.

There is also selection bias going on. They tested reading, writing, arithmetic. Did they test algebra? Did they test biology? I'll bet a fair number would fail at questions regarding evolution or have a skewed view of historical facts.