Public schools have struggled during the long, slow economic recovery. On Tuesday, I noted that urban districts — especially big-city districts — have been hit particularly hard. But there’s also tremendous variation by state.

Idaho, for example, spent 12 percent less per student in the 2011-2012 school year than in 2008-2009, after adjusting for inflation. More than 80 percent of Idaho’s school districts experienced cuts. North Carolina’s cuts were slightly smaller (11 percent on average) but even more widespread: Nearly all its districts reduced spending.

Compare those states to North Dakota, where per-student spending is up 8 percent since 2009, or New Hampshire, where it’s up 6 percent.

What’s going on? Given the disproportionate impact on urban districts, you might think the hardest-hit states would be those where the highest proportion of students live in cities. But it turns out there’s no clear relationship there: City-heavy California has experienced big school funding cuts, but even more urban New York has seen per-student spending increase.

There’s a similar story when it comes to federal spending: Federal budget cuts have accounted for the bulk of schools’ recent funding woes. But states that rely most heavily on federal funding have cut spending only modestly more than more self-sufficient states.

What turns out to make a difference is actual spending levels. States that spend less per-student, such as Idaho, Utah and many Southern states, have made significantly bigger cuts (on a percentage basis) than states, such as New York and Connecticut, that spend more. The relationship isn’t perfect: Arkansas, a low-spending state, has increased funding, while big-spending Hawaii has made big cuts. But as the chart above shows, there’s a clear relationship.

One important note: These figures are adjusted for inflation, but not for the cost of living in each state. The Census Bureau provides school-spending data adjusted for personal income (see Table 12 here). Washington, D.C., for example, is one of the biggest spenders on a per-student basis, but it actually spends the least as a share of its residents’ income.

How does your state rank? See the table below.