For many parents, judging a local public school comes down to average test scores and the amount of money going into that school.

However, a new Stanford University study of test scores from 45 million students upends that set of assumptions.

The study found no correlation between a given district's socioeconomic status and the average test scores of its students.

According to Stanford sociologist Sean Reardon, the smartest way to measure a school's effectiveness was to instead look at the students' rate of improvement over time, as measured by their standardized tests.

In many cases, students in poor communities started with low test scores, but their scores rose much faster over the years than kids in wealthier areas.

Parents can use the information to better select schools for their kids. Instead of focusing on how high the test scores are or how big the school's budget is, they can focus on the test score improvement rate — the students' trajectory — to gauge whether a school is effective.

Read more about students success in public and private schools by Chris Weller at businessinsider.com.