Uhh...did you just read the first sentence and not continue on?
Homeschooling Achievement, a compilation of studies published by the Home School Legal Defense Association
I'm sure they're really unbiased in their compiling efforts.
Also, the Wiki link mentions the Rudner study, and from Stanford.edu:
Rudner’s study was funded and sponsored by the Home School Legal Defense Assocation. It analyzed the test results of more than 20,000 home schooled students using the Iowa Test of Basic Skills, and it was interpreted by many to find that the average home schooled student outperformed his or her public school peer. But Rudner’s study reaches no such conclusion, and Rudner himself issued multiple cautionary notes in the report, including the following: “Because this was not a controlled experiment, the study does not demonstrate that home schooling is superior to public or private schools and the results must be interpreted with caution.” Rudner used a select and unrepresentative sample, culling all of his participants from families who had purchased curricular and assessment materials from Bob Jones University. Because Bob Jones University is an evangelical Christian university (a university which gained a national reputation in the 1980s for its policy of forbidding interracial dating), the sample of participating families in Rudner’s study is highly skewed toward Christian home schoolers. Extrapolations from this data to the entire population of home schoolers are consequently highly unreliable. Moreover, all the participants in Rudner’s study had volunteered their participation. According to Rudner, more than 39,000 contracted to take the Iowa Basic Skills Test through Bob Jones, but only 20,760 agreed to participate in his study. This further biases Rudner’s sample, for parents who doubt the capacity of their child to do well on the test are precisely the parents we might expect not to volunteer their participation. A careful social scientific comparison of test score data would also try to take account of the problem that public school students take the Iowa Basic Skills Test in a controlled environment; many in Rudner’s study tested their own children.
2011 Martin-Chang found that unschooling children ages 5-10 scored significantly below traditionally educated children, while academically oriented home schooled children scored from one half grade level above to 4.5 grade levels above traditionally school children on standardized tests (n=37 home schooled children matched with children from the same socioeconomic and educational background)
Stanford University political scientist Professor Rob Reich  (not to be confused with former U.S. Secretary of Labor, Robert Reich) wrote in The Civic Perils of Homeschooling (2002) that homeschooling can potentially give students a one-sided point of view, as their parents may, even unwittingly, block or diminish all points of view but their own in teaching. He also argues that homeschooling, by reducing students' contact with peers, reduces their sense of civic engagement with their community.
And from the common sense angle - I think that parents who choose to homeschool their children greatly care about their kids while many public school students are dropped off at local schools that parents see as a "babysitter" or a "magical-make-my-kid-successful-because-I-don't-know-what-I'm-doing" building. So the environment affects the sample making the conclusion "homeschooling is better than public schooling" null.
This post was edited on 2/2 at 10:46 am