The statistics show that you are wrong.
1. In 1997, a study of 5,402 homeschool students from 1,657 families was released. It was entitled, "Strengths of Their Own: Home Schoolers Across America." The study demonstrated that homeschoolers, on the average, out-performed their counterparts in the public schools by 30 to 37 percentile points in all subjects. A significant finding when analyzing the data for 8th graders was the evidence that homeschoolers who are homeschooled two or more years score substantially higher than students who have been homeschooled one year or less. The new homeschoolers were scoring on the average in the 59th percentile compared to students homeschooled the last two or more years who scored between 86th and 92nd percentile.
2. in another study by Dr. Lawrence Rudner of 20,760 homeschooled students which found the homeschoolers who have homeschooled all their school aged years had the highest academic achievement. This was especially apparent in the higher grades. ii This is a good encouragement to families catch the long-range vision and homeschool through high school.
3. In 1991, a survey of standardized test scores was performed by the Home School Legal Defense Association in cooperation with the Psychological Corporation, which publishes the Stanford Achievement Test. The study involved the administering of the Stanford Achievement Test (8th Edition, Form J) to 5,124 homeschooled students. These students represented all 50 states and their grades ranged from K-12. This testing was administered in Spring 1991 under controlled test conditions in accordance with the test publisher's standards. All test administers were screened, trained, and approved pursuant to the publisher's requirements. All tests were machine-scored by the Psychological Corporation.
These 5,124 homeschoolers' composite scores on the basic battery of tests in reading, math, and language arts ranked 18 to 28 percentile points above public school averages. For instance, 692 homeschooled 4th graders averaged in the 77th percentile in reading, the 63rd percentile in math, and the 70th percentile in language arts. Sixth-grade homeschoolers, of 505 tested, scored in the 76th percentile in reading, the 65th percentile in math, and the 72nd percentile in language arts.
4. Statistics also demonstrate that homeschoolers tend to score above the national average on both their SAT and ACT scores.
For example, the 2,219 students reporting their homeschool status on the SAT in 1999 scored an average of 1083 (verbal 548, math 535), 67 points above the national average of 1016. In 2004 the 7,858 homeschool students taking the ACT scored an average of 22.6, compared to the national average of 20.9.
According to the 1998 ACT High School Profile Report, 2,610 graduating homeschoolers took the ACT and scored an average of 22.8 out of a possible 36 points. This score is slightly higher that the 1997 report released on the results of 1,926 homeschool graduates and founding homeschoolers maintained the average of 22.5. This is higher than the national average, which was 21.0 in both 1997 and 1998.
from:
http://www.hslda.org/docs/nche/000010/200410250.asp5.Test score data from states requiring testing or from homeschooling associations, while not totally representative, suggest that tested homeschooled children are above average (Lines 2001). According to two Time reporters (Cloud and Morse 2001), "the average SAT score for home schoolers in 2000 was 1100, compared with 1019 for the general population."
Ray's report shows that "home-schooled pupils who took the Iowa Test of Basic Skills outscored public school students by 37 percentile points" (Viadero, March 19, 1997). On the Stanford Achievement Test, the advantage was 30 percentile points. The longer kids had been educated at home, the better their test scores. Also, "students whose parents had teaching certificates scored only slightly higher than the children of nonteachers" (Viadero, March 19, 1997).
6.Results were similar in Lawrence Rudner's (1999) large-scale, noncontrolled study of 20,760 K-12 homeschoolers from 11,900 families who subscribe to Bob Jones University's Testing and Evaluation Service. Students' median scores on the Iowa Tests of Basic Skills or Tests of Achievement Proficiency (TAP) fell between the 70th and 80th percentiles. While urging caution in interpreting results (especially in light of participating families' white, middle-class demographics), Rudner concludes that a homeschool setting has proved academically beneficial for these kids. This observation holds true even though "not all home schoolers take standardized tests" and not all homeschools have well-structured curricula and dedicated parents (Cloud and Morse 2001).
http://eric.uoregon.edu/trends_issues/choice/home_schooling.htmlAnd from wikipedia:
Academic findings
Some studies have suggested the academic integrity of home education programs, demonstrating that on average, home-educated students outperform their publicly-run school peers by 30 to 37 percentile points across all subjects. Moreover, the performance gaps between minorities and gender that plague publicly-run schools are virtually non-existent amongst home-educated students.<19>
Some critics argue that while home-educated students generally do extremely well on standardized tests<20>, such students are a self-selected group whose parents care strongly about their education and would also do well in a conventional school environment.
Some opponents argue that parents with little training in education are less effective in teaching. However, some studies do indicate that parental income and education level affect home-educated student performance on standardized tests very little.
Home-educated student curricula often include many subjects not included in traditional curricula. Some colleges find this an advantage in creating a more academically diverse student body, and proponents argue this creates a more well-rounded and self-sufficient adult. Increasingly, colleges are recruiting home-educated students; many colleges accept equivalency diplomas as well as parent statements and portfolios of student work as admission criteria; others also require SATs or other standardized tests. Some opponents argue that home education curricula often exclude critical subjects and isolate the student from the rest of society, or presents them with their parents' ideological world views - especially religious ones - rather than the publicly sanctioned worldviews taught at state schools.
The results of home education with gifted and learning-disabled children have not been as thoroughly studied.