Until about 19 months ago, Martha Davis, 31, seemed a hopeless welfare statistic. Dependent on public assistance all her adult life, she dropped out of the 11th grade, had two children, and moved from North Carolina to this northern industrial city.

Then something happened to change all that. For the past year, she has been employed as a bench mechanic at a local aircraft engine plant. She wields a handtool to clean engine parts on the midnight shift. Completely off welfare, she earns around $9 an hour.

"It's a good feeling to get up and go to work," she said. "I know you got to start at the bottom. But you got a chance to do better later on."

How many of the nation's poor have become so debilitated that they cannot be helped out of their cycle of dependency? Do they "Just want a free ride?" Or will they respond to the right kind of opportunity?

A major five-year social experiment, sponsored by four federal departmentss and the Ford Foundation, set out to address such questions and has produced some dramatic answers. Martha Davis represents one of them.

The Ford-federal study found, for instance, that twice as many women on welfare like Davis make the transition to self-sufficient employment if the government subsidized transition jobs for them, instead of merely distributing welfare checks.

It also found that crime rates among drug addicts drop by about one third under the same program.

It found as well that the public treasury saves money -- about $8,150 per person -- by subsidizing improved jobs for the welfare mothers instead of simply paying them welfare.

The National Supported Work Demonstration, as the $82 million study was called, provided transitional work experience to 3,200 of society's least-employable people, all volunteers. It operated at locally run sites in Hartford and 14 other cities initially.

Of 1,500 welfare mothers followed for research purposes, one third got off of welfare to self-supporting jobs.

For each person selected to work, another hard-to-employ jobseeker was rejected but was kept track of by researchers for comparison as a control group.

To the surprise of some experts, the most desperate, least educated welfare mothers -- women receiving Aid to Families with Dependent Children (AFDC) -- responded more dramatically than any of the other hardcore unemployable groups that were targets of the experiment, drug addicts and out-of-school teenagers.

Many of the women "sought and obtained jobs and remained employed even though their earnings were substantially offset by the loss of welfare benefits," the report concluded.It was released yesterday in New York City.

But the program didn't work at all with its contingent of young high school dropouts, many of whom have records of delinquency or criminality.

The complex experiment, which provided jobs for 10,000 people overall, was hailed as a rare attempt to assess scientifically the impact of a social program on peoples' lives before public policy and dollars are committed to it on a massive scale.

The welfare mothers who went through the program not only achieved a higher rate of employment, but worked more hours and earned higher wages, the study reported. By months 19 through 27 of the program, after the women had left the supported work program and many had been placed in regular jobs, about twice as many of them had left the welfare rolls as those who were not in the program.

These women had the best work attendance rates, stayed the longest average time in the subsidized program, had the highest rate of departures to a regular job (about 35 percent) and the lowest rate of firings, compared with the other workers.

The transition jobs paid about the minimum wage and taught the women to fill out forms, to show up on time and other disciplines of regular employment.

They went to work building bunk beds in a sawdusty furniture factory, recapping tires, cleaning machine parts, demolishing interiors of old buildings and shoveling trash, working on construction projects and running parks or day care centers.

Ex-drug addicts showed positive results, though much less dramatic than those of the welfare mothers. They improved their job-getting and earning ability, and also cut down significantly on drug-related and other criminal activity thus suggesting that they substitute "legitimate for illegitimate income for the purchase of drugs," the study said.

The ex-convicts category, like the high school dropouts, showed no significant longterm benefit from the program.

Because the response by school dropouts was so poor, officials said, the study calls into question the value of government programs that emphasize some type of work experience to deal with the explosive and persistent youth unemployment problem.

Such training programs have been a major element in efforts to deal with unemployment and welfare dependence and are a component of the Carter administration's new $2 billion proposal to attack youth unemployment.

"We were not committed to make the program work," said manpower specialist Eli Ginsberg, who served as chairman of the board of the independent corporation created to run the project and minimize bureaucratic infighting. "We were committed to understand where it works and where it doesn't. So in that sense the negative findings were not a failure" he said.

Most participants were black or Hispanic, less than a third had been graduated from high school, and less than a quarter were married. They had worked an average of only three to 10 weeks during the preceding 12 months and, except in the welfare mothers category, the arrest rates ranged from 54 to 100 percent, with heavy drug use (heroin) among the ex-convicts as well as the ex-addicts.

Program manager William Dowdy in Hartford said the women not only had a high success rate for themselves but they had "a profound impact on the other workers."

"These ladies had some maturity, responsibility and stability before they came here, even though they were on welfare," he said. "Maybe because of the children at home. . . . They made the others cut down on profanity, fights, things like that."

The project was sponsored by the U.S. departments of Labor, Health, Education and Welfare, Justice, Housing and Urban Development, along with the Ford Foundation.