This statistic is giving people a glimmer of hope about the Massachusetts coronavirus pandemic

A coronavirus test site was set up in the parking lot of a Somerville hospital. The percentage of tests coming back positive is getting smaller.Steven Senne/Associated Press

A little-noticed number is offering a glimmer of hope about Massachusetts’ fight against the coronavirus pandemic.

The number is the percentage of coronavirus infection tests being given that come back positive. And it has been dropping in recent weeks, even as other stats have only recently started to edge downward.

Governor Charlie Baker said Monday that thousands of people are still in the hospital with the deadly virus but the “numbers have started to trend in the right direction” in the past few days, with decreasing hospitalizations and “very few spikes in new admissions.”

The positive-tests percentage has been sending signals since mid-April.

Baker noted last week the number was “an important piece of the data that we monitor” and he called the declines in it “a good sign.”

“Even as we’ve been testing more and typically been testing in places where we felt it was important to test, we’ve still seen a pretty decent sort of gradual trend down with respect to the number of positives,” Baker said at his Thursday briefing.

The seven-day rolling average of positive tests peaked in mid-April at about 29 percent and it has been trending down ever since, falling to about 17 percent as of data released by the state on Sunday.

Here is the percentage of people testing positive for the coronavirus over time.Matt Rocheleau

Samuel Scarpino, a mathematical epidemiologist at Northeastern University, said the stat is something that he looks at – and it jibes with other data.

“I think it’s certainly consistent with the models and the other pieces of data that we’re seeing -- that the peak in symptomatic cases has probably happened and we’re now in the peak of ICU occupancy and mortalities,” he said.

He noted that using the percentage of tests that come back positive as an indication of the intensity of the epidemic relies on the assumption that the state isn’t somehow getting worse at finding positive cases.

The number of tests reported by the state has been steadily increasing and as of Sunday was more than 11,000 a day on average over the past seven days. Baker highlighted on Monday the more than 15,000 tests that were reported Sunday. The state’s testing performance per capita has been touted by Baker, who has called the state a “Top 5 player” in the world.

“If anything, the evidence suggests we’re getting better at finding positive cases," Scarpino said. “As the percent-positive drops, we feel better and better.”

Scarpino cautioned that while the stat suggests that the epidemic may be on the wane in the state as a whole, there could still be hot spots.

Boston Mayor Martin J. Walsh said Monday, “Our positive rate is at 32 percent and trending down. When I say trending down, I think it was at 34 percent last week. So it’s a small trend, but it’s going down. It’s going down, regardless.”

Scarpino warned that a little bit of good news is not enough to warrant easing up on social distancing measures that have been taken to stop the spread of the pandemic, which, as of Sunday, had killed 4,004 people in the state (though some experts say the real toll was likely higher) and has put thousands of people in the hospital.

“We’ve seen in other states that if you relax measures too early, the number of cases shoots back up, meaning we need to keep these measures in place until the numbers come way down,” he said. “Simultaneously, we need to make sure contact tracers are trained and in place, that we’ve got the test capacity, including the antibody tests we need."

The state needs to be “running at full speed with our prevention measures before we start to relax," he said.

Jaclyn Reiss and Matt Rocheleau of the Globe staff contributed to this report.