Every year newspapers and magazines list the top schools in Illinois, and every year many of the same schools make the cut, selected for their high scores on state tests.

Those “top” schools often have one thing in common - very few poor students.

A WBEZ/Daily Herald analysis of Illinois State Report Card data presents a new way to view schools’ performance — through the lens of income.

We’re calling it the Poverty-Achievement Index.

It takes into account the challenge of educating low-income students, and assigns schools a score based on how they compare to other schools educating similar percentages of low-income kids. A positive score on the Poverty-Achievement Index means the school performs better than the average for schools with a similar level of poverty. A negative score means the school performs worse.

(For the statisticians out there — the scores are measured in standard deviations from the mean. Here’s more about our methodology.)

READ MORE: Poverty’s enduring hold on school success

FIND YOUR SCHOOL: The Poverty-Achievement Index

Our goal was to find overachieving schools that might otherwise be overlooked — schools that are scoring much higher than might be expected given the percentage of poor students they serve.

One example is John Jay Elementary School in Mount Prospect, where 80 percent of students are low-income. Fifty-five percent of kids at the school met or exceeded state standards on the 2014 ISAT — which is below the statewide average on that exam. But John Jay scored 1.13 on our Poverty-Achievement Index, meaning the school is performing significantly better than peer schools with similar levels of low-income students.

The Poverty-Achievement Index doesn’t only highlight the performance of high-poverty schools.

For example, just 8.5 percent of students at Lake Zurich Middle School South are considered low-income. As might be expected, the school scored well above the state average on ISAT in 2014, with 75 percent of students meeting or exceeding state standards. But a Poverty-Achievement Index of -1.47 shows that students there are performing below what could be expected from a school with such a low poverty level, and lower than peers with a similar poverty level. And looking back, our analysis shows that Lake Zurich Middle School South has consistently scored lower than could be expected on the Poverty-Achievement Index, posting a negative score 7 times in the last 11 years.

At John Jay — with the lower overall test scores — the school has consistently outperformed peer schools with similar poverty rates. The school has had a positive score on the Poverty- Achievement Index 7 of the last 11 years.

Chicago schools are strong performers given high poverty rates

The WBEZ/Daily Herald  analysis found hundreds of schools statewide that - even taking into account the percentage of low-income students they enroll - are falling behind. Year after year these schools turn in scores that are lower than could be expected. In some cases, entire districts are underperforming.

And we  found dozens of high-poverty schools that are consistently performing much better than the average for their income level. Among them are many Chicago schools. Two-thirds of city elementary schools in 2014 had a positive score on the Poverty-Achievement Index, beating the odds when it comes to poverty by doing better than would be expected given the percent of low-income students enrolled. CPS has gotten better vis-a-vis the rest of the schools in the state, our analysis shows. A decade ago, just half of city grammar schools had positive scores on the Poverty- Achievement Index.

And looking over time, of the 100 elementary schools in the state with the best cumulative Poverty-Achievement Index scores — schools that year after year do better than expected given their poverty rate — 55 are in Chicago Public Schools, a wildly disproportionate number.

Researchers say that looking at school performance through the lens of poverty is a fairer way to judge schools than simply looking at raw achievement. But some caution this method still doesn’t capture all that schools may be accomplishing, particularly those with high percentages of low-income students. They say the best methods look at individual student growth. “It’s probably more important to know about how much that school is able to boost the achievement levels over the course of a year,” says Greg Duncan, professor of education and economics at University of California-Irvine.

And researchers caution that two schools could have the same percentage of low-income students, but educate students with wildly different challenges. “Those students may have other characteristics that make them high- or low-achieving, such as being in a particularly impoverished neighborhood with a very high crime rate, or being a school you test into,” says Elaine Allensworth of the Consortium on Chicago School Research at the University of Chicago. The Consortium has found that degrees of poverty matter; the more extremely poor a school’s community is, the more difficult improvement.

“The schools with high test scores like to attribute those high scores to the quality of the schools. But you have to keep in mind that it has a lot to do with who the students are and the families they come from,” says Larry Joseph, director of research at Voices for Illinois Children.

Click to see Poverty-Achievement Index scores for every school in the state for 2004 through 2014.