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At a time when Wisconsin's jobs statistics are under scrutiny as never before, preliminary data released Thursday showed that Wisconsin lost an estimated 6,200 private-sector jobs in April.

This is the second consecutive month of private-sector job losses in the state, according to the report from the state Department of Workforce Development.

Wisconsin's state government added 500 jobs, according to the data, while the state's cities and counties shed jobs. Adding slight net gains in the government sector to the net losses in the private sector, the state lost an estimated total of 5,900 total non-farm jobs in April from March.

The state's unemployment rate, which comes from a separate monthly survey of households rather than employers, declined to 6.7% in April from 6.8% in March, the lowest since 2008, the preliminary data show.

Thursday's numbers come amid an unprecedented level of skepticism about the validity and reliability of the monthly state jobs report.

Earlier in the week, Gov. Scott Walker released new employment data for the fourth quarter of 2011 - not due for formal release until June 28 - showing that Wisconsin added more than 23,000 public and private sector jobs last year.

It was an unusual step for Walker because the numbers had not been fully vetted by federal authorities at the U.S. Bureau of Labor Statistics. The new figures from the Quarterly Census of Employment and Wages - which is collected from 95% of the state's private and public sector employers - contrast sharply with more than a year's worth of monthly employment surveys, which suggested that Wisconsin lost 33,900 jobs last year, ranking it last among the 50 states.

The census figures cited by Walker are considered by economists the more reliable of the two data sets. Unlike Quarterly Census figures, the monthly estimates released Thursday are based on surveys of only about 4% of the state's businesses each month and then extrapolated statewide under a mathematical model that's routinely prone to error. While the accuracy of the monthly data has been called into question in the past, they were never shown to be off by a magnitude of 57,200 in a single year.

"State data from the BLS monthly employment surveys is not highly reliable," said Thomas Kochan, a professor at the Massachusetts Institute of Technology and co-director of the MIT Institute for Work and Employment Research. "There are big margins of error, and that's well known."

The monthly employment survey can be off by as many as 9,340 jobs in either direction, according to the bureau, which compiles the figures for the nation and each of the 50 states.

'A right to be confused'

If not for the dispute over the accuracy of the numbers, the same jobs report in any other month would have ignited renewed debate about the sluggish recovery. It was the second consecutive month of private-sector job losses, which were spread over multiple sectors of the state economy: construction, manufacturing, services, hospitality.

The numbers were not a surprise; they had expected to be weak after a disappointing set of national jobs data for the same month, which were released two weeks earlier.

Kochan at MIT, a Wisconsin native who earned his graduate and undergraduate degrees at the University of Wisconsin-Madison, said jobs data ultimately is not what will sway voters.

"The public has a right to be confused" by the welter of conflicting job data, Kochan said. "But the public is going to be convinced by the reality they see in their families and their communities and what they see their firms doing. When I go back to Two Rivers and Manitowoc, they are depressed. That's the reality people are experiencing and that's what's going to influence their judgment."

Thursday's report confirmed that the monthly state employment numbers are "murky," said Dale Knapp, research director at the Wisconsin Taxpayer Alliance, a nonprofit fiscal watchdog organization based in Madison.

Knapp pointed to the major revisions for the previous month in March, which continued to show a loss of private-sector jobs while at the same time showed an increase of 7,900 new jobs in state government. That apparent hiring spree followed a gain of 4,300 in state government in February, but a plunge of over 9,000 state jobs in January. Such a hard-to-believe roller-coaster of state hiring and firing data made Knapp "more and more leery" of the monthly jobs survey.

The problem, Knapp said, is that the April numbers could be accurate but no one can know with certainty.

At the root of the statistical problem is an approach to data collection that works at the national level - because the national sample sizes are big enough to shrink the margin of error - but that begin to deteriorate at the state and local level, Bureau of Labor statisticians concur.

"This isn't just a Wisconsin problem," Knapp said. Other states like Illinois and North Dakota show divergence in their jobs data as well.

In the end, how the numbers are used often depends on who is using them - and why.

"Every politician uses the numbers to their advantage wherever they can," said Kochen at MIT. "There's a long history of this."