Here's one reason why some food desert interventions don't show results: Most people do not shop where they live.

That's the conclusion of a new study from the University of Washington's Adam Drewnowski. It's the first to look at both which supermarkets individuals live near and where they actually shop. And it finds surprisingly little overlap between the two: In his survey of 1,682 Seattle residents, he found only 14 percent shopped at the supermarket nearest to them.

“In the present study, proximity to the nearest supermarket had no impact on obesity rates,” the study finds. “These findings ran counter to previous research consensus that physical proximity to supermarkets had a major influence on diets.”

What did matter, however, was price: The patrons of the lower-priced grocery store (like Safeway) tended to have a higher rate of obesity than those who shopped at the higher-priced grocery stores in the study (think Whole Foods). That relationship held true after adjusting for variables like education and income. It makes Drewnowski think that “choice of primary food source was driven by price.”

It’s worth mentioning that food desert interventions being worked on right now aren't all about proximity. They work on price, too: The point is not just to reduce the distance to healthy foods, but also bring down economic barriers. The Philadelphia-based Food Trust, for example, works with local corner stores to help price foods at reasonable prices. Drewnowski’s research suggests it might be worth putting more focus on that element of the intervention, and paying less attention to proximity.