Intellectual Method

Some people you meet are very logical and need to be reasoned with to change their minds.  This is what we would call the Intellectual Method of reaching people.  We read in Acts 17 how Paul reasoned with the people of Athens, because they were a very logical group.  Verse ²¹(All the Athenians and the foreigners who lived there spent their time doing nothing but talking about and listening to the latest ideas.) Arguing with them would not have done anything, but reasoned discussion caused many to believe in Christ.

We can use this same method when discussing Homeschooling.  There are many studies that show that Homeschoolers test well, are socialized, do well as adults, and overall become good citizens when they are adults.  The National Home Education Research Institute has many of these studies available.

Also, there are many White Papers listed under Google's Scholar section, which is a compilation of research paper published in University archives.

This is not a quick and easy method of convincing people about homeschooling.  It usually works best over time, and in conjunction with the Relational Method as they watch homeschooling work in your family. 

So do your research, become well versed in the studies and when you come across someone who needs to be convinced with statistics, you will be ready.