The new records show that on at least one day during the last three months of 2017 — the most recent period for which data were available — a quarter of facilities reported no registered nurses at work.

The Centers for Medicare & Medicaid Services discouraged comparison of staffing under the two methods and said no one should expect them to “exactly match.” The agency said the methods measure different time periods and have different criteria for how to record hours that nurses worked. The nursing home industry also objected, with Mr. Gifford saying it was like comparing Fahrenheit and Celsius temperatures.

But several prominent researchers said the contrast was not only fair but also warranted, since Medicare is using the new data for the same purpose as the old: to rate nursing homes on its website. “It’s a worthwhile comparison,” said David Grabowski, a professor of health care policy at Harvard Medical School.

Of the more than 14,000 nursing homes submitting payroll records, seven in 10 had lower staffing using the new method, with a 12 percent average decrease, the data show. And as numerous studies have found, homes with lower staffing tended to have more health code violations — another crucial measure of quality.

Even with more reliable data, Medicare’s five-star rating system still has shortcomings. Medicare still assigns stars by comparing a home to other facilities, essentially grading on a curve. As a result, many homes have kept their rating even though their payroll records showed lower staffing than before. Also, Medicare did not rate more than 1,000 facilities, either because of data anomalies or because they were too new to have a staffing history.

There is no consensus on optimal staffing levels. Medicare has rebuffed requests to set specific minimums, declaring in 2016 that it preferred that facilities “make thoughtful, informed staffing plans” based on the needs of residents.

Still, since 2014, health inspectors have cited one of every eight nursing homes for having too few nurses, federal records show.