A new Stanford University study has documented for the first time at the national level a direct link between unequal rates of achievement and unequal rates of discipline for black and white students: as one disparity grows or shrinks, so does the other, researchers found.

"The black-white achievement gap and the black-white discipline gap are in fact two sides of the same coin," said Francis Pearman, an assistant professor at Stanford Graduate School of Education and lead author of the study.

Previously, the connection between racial disparities in academic performance and discipline was largely theoretical or studied at the local level, within a single school district. Establishing a correlation between the two has important implications for school districts, teachers and parents, the researchers said.

"If your district has higher suspension rates for students of color than it does for white students, it's likely that it is also failing to meet the academic needs of its students of color as well as it does its white students," Pearman said. "Similarly, if your district is struggling to meet the academic needs of students of color, then it will likely have a racial discipline problem."

The study analyzed disciplinary and achievement data for students in third through eighth grade in school districts across the country from the 2011-12 and 2013-14 school years. The researchers found that a 10 percentage point increase in the black-white discipline gap in a school district predicts an achievement gap that is 17% larger than the average black-white achievement gap.

The relationship goes both ways, the researchers found. As the achievement gap between black and white students widens, so does the discipline gap. According to an announcement, this study, which was published earlier this month in a peer-reviewed journal of the American Educational Research Association, is the first to examine this relationship in both directions.

In the Palo Alto Unified School District, black, Hispanic, Pacific Islander, low-income and special-needs students are suspended at higher rates, according to California School Dashboard data. They also lag behind their peers academically, a chronic gap the district is working to address.

While the study also found a "significant association" between achievement and discipline gaps between Hispanic and white students, other factors, such as poverty and education levels, were the root causes. Once the researchers controlled for these differences at the local level, the relationship between the two gaps went away.

"This suggests that the mechanisms connecting the achievement gap to the discipline gap, such as teacher biases and feeling isolated at school, may be most salient for black students," Pearman said.

School leaders, teachers and parents should pay attention to the findings, the researchers said. The announcement notes that last year, the federal government rescinded guidelines put in place in 2014 to address racial disparities in school discipline, which could cause districts to focus less on these efforts.

"Our findings should caution against such moves," Pearman said.

Other remedies could include adopting ethnic studies programs and culturally relevant teaching to close the achievement gap and using non-punitive discipline practices instead of ones that exclude students from school. Efforts focused on closing one gap could have "crossover effects" on the other, Pearman said.