Following on from RedOrangeGoldLeaf's link above, here is the original research write up for anyone who is interested in a bit more info. etheses.dur.ac.uk/1005/1/1005.pdf
From 2007, a study commissioned by the Department of Education & Skills (downloadable from UCL link here) references the Rothermel research and includes the following statement:
4.16 There have been few systematic studies on the achievement and attainmentof home educated children. A study of home educated primary childrenconducted in 2002 found that 64% of home educated reception-aged children scored over 75% on the Performance Indicators of Primary Schools (PIPS) baseline assessment, compared to 5.1% of children nationally. Alternatively, a small-scale recent study concerning home educated Gypsy, Roma and Traveller children reported real anxiety regarding the adequacy of the education provided for these children. This was because of concerns regarding parents’ capability in the areas of literacy and numeracy.
More recently, a US study published in the Journal of College Admission, n208 p18-25 Sum 2010 titled "Exploring Academic Outcomes of Homeschooled Students" abstract linked to link here with full text link here Extract:
This exploratory study examines the academic outcomes of homeschooled students who enter a medium size doctoral institution located in the Midwest. Descriptive analysis reveals homeschool students possess higher ACT scores, grade point averages (GPAs) and graduation rates when compared to traditionally-educated students. In addition, multiple regression analysis results reveal that students who are homeschooled earn higher first-year and fourth-year GPAs when controlling for demographic, pre-college, engagement, and first-term academic factors. Further, binary logistic regression results indicate there is no significant difference between homeschooled student’s fall-tofall retention and four-year graduation rates when compared to traditionally-educated students while controlling for these same factors.