Homeschool academic achievement -- as measured by standardized tests -- is normally distributed, just like public school academic achievement. Not only is the homeschool curve the same shape as the public school curve, it is also the same width.
National homeschool test scores are normally distributed
Data source: Test scores from 11,739 students sampled nationally
Oregon homeschool test scores are normally distributed
Source: The Homeschool Effect
The width of these normal curves reflects the amount of variability in student achievement outcomes. The variability is the same for both public schools and homeschools.
This means that homeschooled students are as consistently (equitably) educated as public school students. There are proportionately just as many well-served homeschool students as there are well-served public school students. And there are proportionately just as many ill-served public school students as there are ill-served homeschool students.
Homeschool critics talk about homeschooled students falling through the cracks, though they ignore public school students falling through the cracks. The assumption is that public school students are not ill-served because the system assures a level of uniform treatment.
But the data contradicts that assumption by showing that public schooled students and homeschooled students experience the same variability in outcomes. Homeschool academic results are just as consistent as public school results.