Correction: Correction: A previous version of this story misstated the number of jobs gained in September. It was 114,000.

The September jobs report, which revealed a surprising drop in the unemployment rate, immediately provoked conspiracy theories among the Obama administration’s critics.

Former General Electric chief Jack Welch on Friday kicked off the speculation with this morning post on his Twitter account: “these Chicago guys will do anything. can’t debate so change numbers,” implying that the Obama administration had artificially inflated the figures.

Welch’s statement was quickly dismissed, even provoking a statement by a former Bureau of Labor Statistics commissioner, and there is no evidence that the numbers were tainted. But the speculation raises a broader question: How does the Bureau of Labor Statistics derive these numbers? How accurate is that process? And how susceptible is it to tampering?

The jobs report is actually a compilation of two different surveys: the Current Population Survey, which is commonly dubbed the “household survey,” and the Current Economic Statistics, or the “employer survey.” The household survey produces the unemployment rate — 7.8 percent in September — and the employer survey produces the “nonfarm payrolls” number, which is the most common measure of jobs gained or lost and was up 114,000 last month.

The monthly population survey is conducted by the Bureau of Labor of Statistics and the Census Bureau. In it, the government asks survey takers how many people in their household have worked (or were temporarily absent from the workforce) in the past week; how many have actively looked for work in the past month but did not work; and how many neither looked for work nor worked.

Unemployment in September dropped to a four-year low while job creation reported a modest gain.

The population survey includes interviews with about 66,000 households. Every month, 25 percent of the sample is changed and the response rate is very high — usually more than 90 percent. By contrast, opinion polls have a response rate of about 9 percent, and contain samples a fraction of that size.

The employer survey is also conducted by the BLS, which surveys 141,000 employers, private and public, at 486,000 work sites and asks for the number of employees, hours worked and earnings.

The BLS process for both surveys is highly confidential. Economists are put on an eight-day security lockdown in advance of the report, signing confidentiality agreements every morning. The computers they use feature heavy encryption, and data are placed in a safe even for bathroom breaks. The Wednesday before the release, the population data arrive, followed by the employment survey data a few days later.

On the day before the release, three copies of the report and a CD-ROM are placed in a safe and taken to downtown Washington from the secure location where they were prepared and presented to the few White House officials — President Obama, Vice President Biden, a handful of top government economists and the secretary of labor — who have permission to have a sneak peek. Journalists are given access to the information 30 minutes before release but have to connect to a secure network that prevents them from sending out the data ahead of the official release.

The BLS is a nonpartisan agency whose commissioners typically span administrations and political parties. The agency is headed by Jack Galvin, a career employee who ran the employment and unemployment statistics division from 1998 to 2011 and has held a variety of positions there since 1978. Prior to Galvin, Keith Hall led the agency from 2008 to 2012, following career positions at the Council of Economic Advisors and the International Trade Commission. Janet Norwood served as commissioner from 1979 to 1991, spanning the Jimmy Carter, Ronald Reagan and George H. W. Bush administrations, while her predecessor Julius Shiskin headed it under Richard Nixon, Gerald Ford and Carter.

But presidents have been known to worry about the agency. Richard M. Nixon infamously asked his aide Fred Malek to count the number of Jews working in BLS, based on his delusion that Jewish liberals were trying to sabotage him through bad jobs numbers.