The Well-Adjusted Child: The Social Benefits of Homeschooling by Rachel Gathercole
I've been ruminating about this book for a while, so long, in fact, that I recently had to return the book to the library with my thoughts not quite coalesced. If you are having trouble answering the socialization question of homeschooling (to others, or to yourself), this book is an excellent place to start. In a conversational style, Rachel Gathercole provides a multitude of reasons homeschooling students are well prepared to function in the world and interact with other people of all ages. The book is full of quotes from homeschooling students and their parents, almost too many quotes. They all started to sound the same after a while.
It should not be surprising that this little book does not provide research to prove homeschooling produces well-socialized children. In the first place, Ms. Gathercole spends a great amount of time explaining that "socialization" means different things to different people. Also, almost by definition, all homeschooling families approaching homeschooling differently. Some will provide ample opportunities for "socialization" and others will provide almost none at all.
It seems unlikely to me that any research will show benefits of homeschooling because of the vast differences in styles and priorities. I believe studies could show certain homeschooling behaviors are beneficial in the same way certain parenting behaviors are beneficial (though the research on that is not always adequately shared with the public). (The difficulties in such research on homeschooling is nearly overwhelming, beginning with the fact that our goals for the education of our youth may differ dramatically from what any researchers might identify and are probably the most difficult of ideas to measure in a quantitative sense.)
My family and friends are nearly all supportive of homeschooling. (Many are homeschooling families that helped bring us to this way of life.) Even so, I have received my share of questions on socialization (I can't speak for Kansas Dad.) and this book provides a wealth of answers to that question for the casual questioner.
We are responsible for teaching our children how to kindly and respectfully interact with other people of all ages and variations. As with other educational goals, social behavior can be taught by parents in a homeschooling environment as well as or better than in a traditional school. This book may help you find words to express what you've already felt to be true. It may also provide some ideas for homeschooling families who need more encouragement to get out of the house.
You can read some of the quotes I particularly liked here, here and here. It's not a difficult book to read and worth a bit of your time.