ANCHORAGE -- This is the time of year when the 9 a.m. darkness begins to eat into the soul. The cold adds genuine agony to even short walks over iced concrete to the federal offices that tend to this remote corner of the American empire.

Nobody drawing a federal pay check in this grimy Arctic metropolis was in a mood for bad news, but it came anyway. Statisticians in Wisconsin, under contract to the Office of Personnel Management (OPM), announced that it now costs less to live in Anchorage than in Washington, D.C., and the cries of pain and outrage are echoing across the tundra.

The immediate problem is the threat to the 25 percent cost-of-living allowance paid to about 10,000 federal workers in Alaska. Such allowances, also paid to federal employees in Hawaii, Puerto Rico and the Virgin Islands, were established decades ago to lure people to out-of-the-way places and naturally will be missed by their recipients.

But much of the strong language heard here about the OPM report extends to a much wider circle because it punctures a favorite defense of the Alaskan life style. It also is likely to provoke heated arguments the next time anybody here heads south to see friends and relatives in the "Lower 48," as the continental United States is known here.

For years, Alaskans have enjoyed some of the highest family and per capita incomes in the country. On hearing envious comments about this good fortune, the alert Alaskan always had an airtight response: "You know, the cost of living is murder up here."

Not so, says Runzheimer International, a family-owned management consulting firm in Rochester, Wis., which has made a good living keeping track of the cost of bread and bungalows in assorted American cities. Its calculations are somewhat complex, with cigarettes 26 percent more expensive in Anchorage than Washington and low-income apartments 26 percent less expensive. But the conclusion is simple: The annual cost of living in Anchorage is 1 percent less than in Washington.

This was front-page news in Anchorage newspapers and a leading item on television. The state's representatives in Congress rushed to warn against panic and suggested that OPM recheck its figures, but the psychological damage had been done.

"Yeah, okay, I do make more money here," said Terre Sweeting, an energetic Anchorage resident who works as both insurance and rental-car agent. "And I think the environment here is nicer. Anchorage is a very clean city, and it has a lower crime problem."

The myth of the rugged life of the north, fighting off polar bears with one hand and the Consumer Price Index with the other, appears doomed. What is to become of Alaska's image when the rest of the country learns that Anchorage residents not only pay no state income tax and receive about $900 a year from the state's oil largesse but also pay less for split-level homes and babysitters than their cousins in Bethesda?

Thomas Peiffer, executive vice president of Runzheimer's living costs division, said Washington is as much to blame for this turn of events as Anchorage.

Food and medical care remain more expensive in Alaska because of transportation costs and shortage of some key skills. But the churning Washington real estate market has more than made up the difference, particularly since the oil slump, now at least temporarily relieved, depressed Alaskan housing prices.

A new international oil shortage would push Anchorage prices up again, and so OPM is being asked to wait before cutting anyone's allowance. "The thing is skewed," said Sen. Ted Stevens (R-Alaska).

Jeff Smith, a spokesman for Rep. Don Young (R-Alaska), said "we're hoping that OPM can achieve a freeze or a bureaucratic delay" while new numbers are pushed through the Runzheimer computers.

Peiffer, in a meeting with Stevens, tried to discard his villain's cloak and portray Wisconsin, like Alaska, as just one more distant part of the country not well understood on Connecticut Avenue.

But Stevens, his state's reputation at stake, was unmoved. "He didn't even chuckle at that one," Peiffer said.