In 2011, a 17,000-square-foot supermarket opened, aided by city money that paid some 40 percent of the costs of its construction. The neighborhood welcomed the addition, and perceived access to healthy food improved. But the diets of the neighborhood’s residents did not.

This verdict comes from a study that compared shopping behavior in Morrisania with a neighborhood a mile away with similar demographic characteristics. “There were not a lot of things that really changed,” said Brian Elbel, an author and an associate professor of medicine at New York University. “Consumption didn’t really change. Purchasing didn’t really change.”

The work adds to a growing body of evidence that merely fixing food deserts will not do nearly as much to improve the health of poor neighborhoods as policy makers had hoped. It seems intuitive that a lack of nearby healthy food can contribute to a poor diet. But merely adding a grocery store to a poor neighborhood, it appears, doesn’t make a very big difference. The cost of food — and people’s habits of shopping and eating — appear to be much more powerful than just convenience.

Another study, published this week as a working paper by the National Bureau of Economic Research, looked across the country and found that no more than a tenth of the variation in the food people bought could be explained by the availability of a nearby grocery store. The education level of the shoppers, for example, was far more predictive.