Public and Private are Apples and Oranges

    So, there's a host of reasons why it is difficult to compare the performances of students in private schools with those in public schools.

   Private schools sometimes spend more per student, so it follows that those schools should be expected to have higher-performing students. 

  Private schools generally attract higher-income families, which often translates into more "gifted" as opposed to "slow" students. 

  Private schools can accept the bright students, while rejecting those they don't want, perhaps sometimes saying the "slow" students will not be able to keep up with the classwork.

  Private schools are not required to provide the same resources as those with disabilities, which further screens out some of the lower-performing students. 

  Private schools are more likely to attract students motivated to enjoy learning. That is usually why the students go to the private schools -- because they are attracted by the promise of having better schooling. Public schools are more likely to be packed with students just there because they have to go to school.

   Private schools are more inclined to offer specialized subjects that are attractive to students, and that cater to the talents and aspirations of those students. So, since the student is studying a topic he or she enjoys, there is more of a desire to do well.

   Parents of private schools possibly tend to be more involved with their students' learning.  

  Students in private schools often are less timid, and more socially skilled, so they tend to be more engaging in classroom discussions, which engenders better learning. 

  Private schools usually do not require their teachers to be state certified, so it can be argued teachers are better qualified in public schools.

  Teachers in public schools generally are better paid than those in private schools, so it can be suggested public schools will attract the better teachers.

   Private schools tend to offer their teachers more freedom in what they teach, so the teachers themselves might enjoy the topic more and be more enthusiastic in their presentations.

   Private schools are not limited by public funding,so they often have access to more resources.

   Class sizes are often smaller in private schools.

   Public school teachers perhaps are tasked more with disciplining, since more of their students are inclined to be disruptive. This distracts from the focus of learning and occupies the teacher with more time being spent on things other than the lesson.