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A construction site in New York. Employment data is compiled by career civil servants who have worked for both Republican and Democratic administrations. Credit George Etheredge/The New York Times

Talk about an October surprise. The post on Twitter warning of a government conspiracy to swing the presidential election in the Democrats’ favor popped up just moments after the Labor Department reported the biggest monthly decline in the unemployment rate in nine years.

“Unbelievable jobs numbers..these Chicago guys will do anything,” it said, referring to the Obama administration’s crew. “Can’t debate so change numbers.”

The author of the Oct. 5 post was not Donald J. Trump, the Republican presidential nominee and irrepressible Twitter user. It was Jack Welch, the legendary retired chief executive of General Electric, reacting to good economic news in the weeks running up to the 2012 face-off between President Obama and his Republican challenger, Mitt Romney.

Mr. Welch later admitted that he had no evidence that any numbers had been cooked — only that the reported improvements did not match his own observations of the economy.

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Such suspicions about even the routine, day-in and day-out economic statistics produced by the federal government, voiced by a scattershot of skeptics in previous years, have turned into a steady roar this campaign season.

With Mr. Trump insisting, wrongly, that the United States is “losing jobs to other countries at a higher rate than ever,” it may not be a surprise that nearly half of Mr. Trump’s supporters “completely distrust the economic data reported by the federal government,” according to a recent Marketplace-Edison Research survey. (By contrast, 5 percent of those planning to vote for Hillary Clinton say they distrust the government information.)

Decades of psychological research have shown that people, regardless of political affinity, tend to embrace information that confirms their existing beliefs and disregard data that contradicts them.

“Partisans tend to credit the information when it reflects well on their leaders and dismiss it when it doesn’t,” said Dan M. Kahan, a law and psychology professor at Yale University.

“People don’t know where these figures come from, they don’t know what they mean,” Professor Kahan said. “They just have an emotional ‘yay’ or ‘boo’ response to them and anything else that they recognize as having a political significance.”

Earlier this year, Mr. Trump said, “Don’t believe those phony numbers,” contending that the jobless rate was “probably 28, 29, as high as 35. In fact, I even heard recently 42 percent.” More recently, he declared the official 5 percent jobless rate “one of the biggest hoaxes in American modern politics.”

By affirming that view, Trump supporters are in effect signaling: “I’m with him.”

So how reliable is the government data on employment, which will be reported again on Friday? Like all statistical measurements, it can be both honest and imprecise; a best estimate given the available tools but nonetheless subject to ambiguity, misinterpretation and error.

“Every data collection comes with a set of strengths and weaknesses,” said Karen Kosanovich, an economist and 24-year veteran of the Bureau of Labor Statistics. “That’s part of the business of collecting information.”

There are some basic ground rules, however, that prevent the process from spitting out any answers you please and undermine claims that the results are rigged for a political purpose.

For starters, the people who generate the numbers are all career civil servants who have churned out reports for both Republicans and Democrats. And their basic methods do not swerve from one administration to the next. If the figures are biased, they are consistently biased in the same way regardless of what party is in office.

“I’ve never had any outside influence that tells me what to do or how to collect and interpret information,” Ms. Kosanovich said. “Our approach is based on methodologies that have been proven over time and approved statistical practices. They are not based on political influence.”

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Jack Welch, the former chief of General Electric, caused a stir in 2012 by questioning favorable jobs data that did not match his personal observations. Credit Richard Drew/Associated Press

The monthly employment report is derived from two separate surveys that serve different purposes. The first, collected by the Census Bureau since 1942, allows the government to estimate the number of people who are employed and calculate the unemployment rate.

The most common misconception among the public, Ms. Kosanovich said, is that the unemployment rate is determined solely by counting people who are receiving unemployment insurance benefits. That is not the case.

Rather, it is based on what is known as the Current Population Survey, a monthly survey of 60,000 households, or about 110,000 individuals from all around the country. (By comparison, most respected public opinion polls depend on a random sample of 1,000 to 2,000 people).

In general, anyone who reports working for pay — even just an hour — during the previous week is considered employed. Anyone who was laid off or actively looked for work (sending out résumés, responding to help-wanted ads) during the previous four weeks, regardless of whether they received any government benefits, is considered unemployed. People who are not looking — this includes millions of students enrolled in college, plenty of parents who are happy to stay home with young children, and millions more retirees — are not counted as being in the labor force.

The second survey is designed to measure something else: employment changes over time. This payroll survey focuses solely on jobs, rather than individuals. Thus, a single person working two jobs would be counted once by the household survey (one individual is employed) and twice by the payroll survey (two jobs exist).

To estimate how many jobs were created and lost, the labor bureau each month gathers data from 146,000 private business and government agencies covering about 623,000 work sites throughout the country.

So what gives the best picture of the job market? That depends. The survey of employers, started in a bare-bones form more than a century ago, is considered a more reliable measure than the household survey, in part because the sample size is much larger. But it does not pick up all the types of jobs (the self-employed, unpaid family workers, domestic help and agricultural workers) or answer questions about workers’ race, ethnicity, age and educational level. The household survey helps fill in those gaps.

The official jobless rate comes from the household survey and represents the number of people who are 1) in the labor force, and 2) unemployed. In September that was 7.9 million Americans out of the 160 million in the labor force, or 5 percent.

Many economists, however, consider the official unemployment rate to be an inadequate gauge of what people are experiencing. It does not take into account people who are working only part time because they cannot find a full-time job. Or the former steelworker who, after years of fruitless searching, has given up looking but would take a job if he could find one.

The bureau publishes alternative measures of unemployment to help capture this reality. The broadest one, which includes both discouraged and underemployed workers, tends to rise and fall with the official rate but is always larger. In September, the measure, known as U-6, was 9.7 percent.

Even that broader figure does not capture the full picture. In 2003, for example, Austan Goolsbee, who later went on to serve as a top economic adviser in the Obama White House, complained that the jobless rate was understated because of government programs. Social Security disability, in particular, he argued, had “effectively been buying people off the unemployment rolls and reclassifying them as ‘not in the labor force.’ ”

Mr. Goolsbee called this “a kind of invisible unemployment” and noted that “underreporting unemployment has served the interests of both political parties.”

Since then, concerns about the shrinking size of the labor force have sharpened. The proportion of Americans officially in the labor force has failed to recover significantly after taking a steep dive during the recession. In 2008, about 66 percent of the population was actively looking or working; now less than 63 percent is.

Some people have willingly made the choice to stop working. But many, particularly those in their prime working years, are missing from the labor force. Recent research by Alan B. Krueger, a Princeton economist and former Obama administration adviser, found that nearly half of the seven million men between 25 and 54 not in the labor force were on daily painkillers or disabled.

“Just because people left the work force out of discouragement, doesn’t mean they’re not available for work,” said Patrick J. O’Keefe, director of economic policy at CohnReznick and a former deputy assistant secretary in the Labor Department. “It just means the economy is not generating sufficient jobs at sufficient pay levels to get them back in.”

Positive or negative spin, however, is not part of the Labor Department’s brief, Ms. Kosanovich said. She repeated a comment made by Kathleen Utgoff, a former Bureau of Labor Statistics commissioner appointed by George W. Bush, that serves as the agency’s unofficial motto: When asked whether the glass is half full or half empty, the bureau’s response is, It’s an eight-ounce glass with four ounces of liquid.

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