Who are the people who are running home schools? In general, they tend to have higher-than average incomes and educational levels.
Most are two-parent families, and their children watch less television than average-both factors that are likely to support superior educational performance.
The same students, with the same types of family and the same support from their parents, would probably do just as well in the public schools.
As research has repeatedly shown, small classes are better than big classes, and strong parental and community involvement is key.