The Times has tried to look for an indication of the quality of teaching and learning, regardless of where a school sits or what type of students attend it. We did this with an analysis that adjusted for what schools can't control: family income.
The line: Running through the middle of each graph below, this line represents expectations. How high should my school score?
The expectations are based on the number of students who qualify for free or reduced-price lunch. If a school is above the green line, students are scoring better than expected. If below the line, they're not.
Most land close enough to the line, within a few points, that the difference is insignificant. But a small handful of schools repeatedly fall short, regardless of the subject or the grade level. And a few repeatedly exceed expectations in all areas.
The data: We included data for all three systems in Madison County. The graphs combine 2007 scores on the Stanford Achievement Test with the percentage of students who qualify for free or reduced-price lunch.
We showed the data, and the results, to two professors at the University of Alabama and a researcher at the Public Affairs Council of Alabama. Each commented on the strength of the link between poverty and test scores.
R-squared: This figure offers a way to tell the strength of correlation. For example, in third grade, socio-economic status explains about 80 percent of the difference in reading scores between schools, but only 63 percent of math scores. If the R-squared hit 1, the schools would form a perfectly straight line.
These results show that socio-economic status here better predicts success in reading than in math among elementary children. That changes by middle school.
School quality: The distance from the line leaves room for other factors in addition to socioeconomic status, including factors that schools can control, such as the quality of teaching and learning.
Cautions: Other factors could help determine socioeconomic status, such as parents' education or how hard they work. And there could be factors that fall outside socioeconomic status altogether, such as having more students who don't speak English at one school than another.
And, of course, tests scores don't directly capture some important attributes of a school, such as the cleanliness or safety of the building or warmth of the staff. However, some environmental factors have been shown to indirectly influence achievement.