Indeed, the survey measured a number of other basic health indicators, but only one of them registered any real change: About 2.9 percent of respondents said they had experienced a “serious psychological stress during the past 30 days,” down from 3.7 percent in 2013.

That finding resembled a pattern in one of the most revealing studies of the effects of health insurance on a population in which researchers found that Medicaid coverage for poor people in Oregon improved mental health and financial security, but not physical health.

The nation’s uninsured rate stood at about 13 percent at the time of the survey, and has declined gradually from about 16 percent in 2010, the highest share of uninsured since the National Health Interview Survey began tracking it in 1997. Many experts attribute the changes to the health care law, but there is not definitive proof that the law was the driver.

The most significant decline in the share of the uninsured was among 19- to 25-year-olds, 21 percent of whom were uninsured in the first quarter, down from 27 percent in 2013. The share of uninsured for that age group has been declining since 2010, when a provision in the law began allowing dependents to stay on their parents’ insurance policies until their 26th birthday. Experts are also looking at how much Americans are using the health care system as a measure of the law’s progress.

In an analysis of data from the National Association of Insurance Commissioners, which receives information on hundreds of health insurance plans across the country, the Robert Wood Johnson Foundation, which funds research and programs to improve health, found a 20 percent increase in the rate of hospital admissions among people in the individual market — the place where many of the newly insured are covered — in the second quarter compared with the second quarter of 2013. (The data did not measure public insurance programs like Medicaid, which is also playing a big role in the overhaul.) There were also small increases in outpatient care (5.3 percent) and physician visits (1.9 percent) among that population.

Katherine Hempstead, who directs research on health insurance coverage at the foundation and who analyzed the data, said the rise appeared to indicate that some of the newly insured — many of whom did not previously have insurance because they could not afford it or because they had pre-existing conditions — were starting to use the health care system.