The size of a school does impact the quality of education. When a student attends a larger school, he has a better selection of teachers and subjects that he can learn from. This greater variety often leads to increased levels of academic success, and while many students feel more pressure in these large environments, they get a better education.
I believe their is definitely a connection between school size and education quality. I speak from personal experience on this issue. When I was in school, there was little funding for our district so some schools closed and the rest were consolidated. This made for overcrowded classrooms. When classrooms are too big, many students slip through the cracks. It is harder for the teacher to ensure everyone is learning what they should be for the current grade. It may also be harder for the teacher to control larger classrooms. I know many friends that barely learned anything but were passed to higher grades, simply because the teacher did not have the time to make sure they were where they should be. Smaller classrooms are the key to better quality education but enable for schools to have smaller classes, the districts need better funding, whether it be through government or their local communities.
When there are more students, that means bigger class rooms, and bigger class rooms almost always means a lower quality of teaching. Students require individual attention, motivation, and some acknowledgement, and big classrooms rarely provide that. It becomes an every student for himself mentality, and most students would rather defer from school than take the challenging road.
How much time a teacher can spend with a student is vital to a quality education. Smaller schools, with less students and more teachers, offer a better education that can be tailored to an individual. The ideal setting is to have a one-on-one ratio of students to teachers. While that number is impossible without a personal tutor, smaller schools can lead to better students.
Smaller schools generally have lower student:teacher ratios, which allows each student to get more attention from the teacher. This generally results in a higher quality of education than a very large school where the students will receive a completely impersonal education. Of course, the issue can go the other way, too: a school that is too small to have the resources to properly educate the students will not do well either.
I believe the size of a school has an impact on the quality of education because there have been multiple studies that have concluded that smaller classroom sizes most often result in a better learning environment, where each student gets more face time and interaction with their teachers. Smaller classrooms allow teachers to provide more attention to each individual student.