The bold social experiment, called Moving to Opportunity , was intended to put a theory about poverty to the test, using the same kind of rigorous study that is the gold standard in medicine.

Now, a new analysis by a team of social scientists suggests that while the $80 million program did not lift people out of poverty, it made a profound improvement in their happiness.

For every 13-percentage-point decrease in the neighborhood poverty rate, people reported an increase in their well-being equivalent to how they would feel if they had a  $13,000 increase in annual income, the authors calculated.

People given vouchers to move to neighborhoods with less poverty also experienced improvements in mental health and a strong suggestion of benefits to physical health.

Their household incomes did not improve, however.

Surprisingly, the level of racial integration in a neighborhood did not matter nearly as much as the rate of poverty when it came to residents’ happiness.

“The bigger the change in poverty that you got through a move, the bigger the improvement in well-being and health,” said Lawrence Katz, an economics professor at Harvard University who leads the long-term evaluation of Moving to Opportunity.

“If you stay in a poor neighborhood, but it’s more racially integrated, it doesn’t seem to have big effects. . . . Being in a really poor neighborhood has adverse effects, regardless of the racial composition.”

The 15-year study, sponsored by the US Department of Housing and Urban Development, began in the early 1990s at a time when urban issues and neighborhoods were a national focus, driven in part by the Rodney King riots in Los Angeles.

It also presented an opportunity to answer scientific and policy questions that had been mounting since the Victorian era:

Does living in a distressed neighborhood cause residents to have lower education, a greater likelihood of being involved in crime, worse health, and lower economic achievement?

Or do the greater rates of those outcomes reflect something about the people who are drawn to those neighborhoods?

In 1994, families living in public housing in areas where more than 40 percent of residents were below the federal poverty threshold were given the opportunity to enter a lottery. Over four years, 4,600 families from Baltimore, Boston, Chicago, New York, and Los Angeles enrolled and were randomly assigned to three groups.

Some received vouchers, which could be used to subsidize rents at private apartments, and were required to move to neighborhoods where the poverty rate was below 10 percent.

Others received traditional vouchers that allowed them to move unrestricted.

A third group stayed in public housing.

The Boston participants were living in housing projects in East Boston, Mission Hill, and South Boston.

Previously published findings from the long-running study were mixed. There was no clear difference in income for those who moved to better neighborhoods, as many had hoped they would see. Still, moving to a less-poor neighborhood was associated with reductions in extreme obesity and diabetes. Among children, girls experienced less harassment and pressure to have sex, but boys seemed to stay in the same social networks.

But the authors and outside researchers said the newest analysis of the study, published in the journal Science, showed clear and quantifiable benefits from moving to less impoverished communities.

“The finding is important because it provides rigorous scientific evidence for the theoretical assumptions we’ve had about the effects of neighborhoods on well-being,” said William Julius Wilson, a Harvard sociologist whose 1987 book “The Truly Disadvantaged” argued that increasing poverty concentration in cities had harmful effects. “It’s good to see increasing attention to the adverse effects of growing income segregation, because this has not been high on [receiving] public policy attention.”

To assess the well-being of residents, the study used their responses to questions such as: “Taken all together, how would you say things are these days — would you say that you are very happy, pretty happy, or not too happy?”