Many teachers believe that a “few bad apples” can spoil a whole classroom, reducing the learning of everyone in the room. While this is part of the folk wisdom of teaching, it has been surprisingly difficult to find these effects in the data.

But a very convincing new paper, by Scott Carrell of U.C. Davis and Mark Hoekstra of U.Pitt, “Externalities in the Classroom: How Children Exposed to Domestic Violence Affect Everyone’s Kids” (available here), suggests that these effects can be pretty big.

The real difficulty in this style of research is to find a useful proxy for whether or not a classroom is affected by a disruptive student. Previously researchers have used indicators like whether a student has low standardized test scores, but as any teacher knows, the under-performing kids may not be the disruptive ones. And if you analyze only a weak statistical proxy for classroom disruption, you get weak estimates, even when the true effects are large.

The truly innovative part of the Carrell and Hoekstra study begins with their search for potentially disruptive kids: they looked for those coming from particularly difficult family situations. In particular, they combed through court records and linked every domestic violence charge in Alachua County, Florida to the county schooling records of kids living in those households.

It’s a sad story: nearly 5 percent of the kids in their sample could be linked to a household with a reported domestic violence incident. (And given under-reporting, the true number may be much larger.)

The costs of this dysfunction are even more profound. Kids exposed to domestic violence definitely do have lower reading and math scores and greater disciplinary problems. But the effects of this dysfunction are not limited to the direct victims of this violence: kids exposed to kids exposed to domestic violence also have lower test scores and more disciplinary infractions.

Around 70 percent of the classes in their sample have at least one kid exposed to domestic violence. The authors compare the outcomes of that kid’s classmates with their counterparts in the same school and the same grade in a previous or subsequent year — when there were no kids exposed to family violence — finding large negative effects.

Adding even more credibility to their estimates, they show that when a kid shares a classroom with a victim of family violence, she or he will tend to under-perform relative to a sibling who attended the same school but whose classroom had fewer kids exposed to violence. These comparisons underline the fact that the authors are isolating the causal effects of being in a classroom with a potentially disruptive kid, and not some broader socio-economic pattern linking test scores and the amount of family violence in the community.

You likely already believe there is an equity rationale for trying to help those kids subject to difficult family situations. This research also suggests a compelling efficiency rationale, as the effects radiate well beyond the dysfunctional household.