Both Southern states also rank among the most conservative, according to Gallup's latest ranking: Mississippi was first, and Louisiana ranked third.

The relationship is loose, although the overlap is real: Five states are among both the 10 most conservative and the 10 most reliant on federal funds. Four states are among both the 10 most liberal and the 10 least reliant on federal funds.

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The Tax Foundation's analysis is based on a crude calculation of Census revenue data: Divide each state's "intergovernmental revenue" (i.e. revenue from other governments) by its "general revenues," a category that includes most — though not all — state revenues. That federally sourced revenue comes in many forms, including Medicaid payments, education funding assistance and infrastructure financing.

A rough pattern emerges by region, too.

The South is home to five of the 10 most reliant states. The West and Midwest are each home to two, and the Northeast is home to one.

The most reliant states tend to collect less revenue on their own and house larger poor populations, the Tax Foundation notes.

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Of the 10 states least reliant on federal revenue, four are in the West, three are in the Northeast, two are in the Midwest and one is in the South.

North Dakota is the least reliant state, with federal revenue accounting for just 19 percent of its fiscal 2013 revenue, according to the analysis.