Students are randomly chosen and there are equally likely chance of being selected under different class sizes. Every student’s probability of being selected is same. They are not being categorized according to their ability and background.

Negative correlation means two variables have inverse relation. So, a class of smaller class is associated to higher performance. For example, children from rich families might be more expected to attend the schools having smaller class sizes, and rich children generally score better than others on the standardized tests. Another possible situation might be that a school principal assigns well students to minor classes.

There is a strong evidence that smaller class size causes better performance. One of the possibility is that some parents might insist their children to be seated in the smaller classes and thus such parents are likely to be extra involved in their children’s education.