To understand how well they actually are doing, we need to understand the measurements that researchers are using to draw their conclusions. In the case of academic performance, the measurement is almost always a standardized achievement test. A standardized achievement test is nothing more than a test that has been constructed to evaluate an individual's level of achievement in academic subjects. It does this by comparing that individual's scores on the test with a normative group--individuals who take the test before it is released for general use. On these tests an average score is expressed as being at the 50th percentile, with half of those taking the test scoring below the 50th percentile and half scoring above the 50th percentile. Also, the higher (and lower) you go in terms of percentiles, the fewer people will have those types of scores. When you begin to see that homeschool students score anywhere from the 80th to 87th percentile in all subjects in Brian Ray's study or from the 75th to 85th percentile in most subjects in Rudner's study, you begin to appreciate that homeschool students score significantly higher than public school students on tests of achievement. And these two research papers are not the only ones showing these drastic differences.
Paula Rothermel (Rothermel, P. (2000) "Home-Education: Rationales, Practices and Outcomes. A Working Paper." University of Durham. Click Here), drawing from the work at the PIPS project at the University of Durham (an assessment program), found that more than 63 percent of homeschool students score anywhere from the 75th to 84th percentile level in receptivity to math and language. By comparison, only 5.1 percent of the public school students scored as well. She also found that after three years of homeschooling, homeschool students begin to really outpace their public school peers. Patrick Basham(Basham, P. (2001) "Home Schooling: From Extreme to Mainstream. A Frasier Institute Occasional Paper." Public Policy Sources.Num. 51. Click Here) looked at the SAT scores of homeschool students in Pennsylvania and found that they scored at the 86th percentile in reading and at the 73rd percentile in math. Given that the SAT strives to be a well constructed measurement of achievement and is used by colleges as a measure of preparedness for college-level work, these scores suggest that homeschool students are being very adequately prepared academically. Add to this short list of studies the number of smaller studies cited by Brian Ray (Ray, B.D. (2000) "Home Schooling: The Amelioration of Negative Influences on Learning?" Peabody Journal of Education. Vol 75, Num. 1&2, 71-106.), including the works of J. Wartes and the results of testing done by the Alaska, Tennessee, and Oregon Departments of Education. Study after study shows that homeschooling stands up exceedingly well on standardized tests, particularly in comparison to public schooling. One other interesting note is that there is a complete lack of studies showing that public school students outperform homeschool students. With that said, it is clear that homeschooling is more than adequately preparing students--it is doing an outstanding job.