An investigation by The Atlanta Journal-Constitution has identified about 200 school districts, including four in Washington state, that recently reported test-score gains the article describes as extremely improbable.

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A recent national news article raised questions about the reliability of student test scores across the country, but administrators in Washington state schools say they are confident the scores they’re reporting are accurate.

The investigative article, published March 25 in The Atlanta Journal-Constitution, appeared under the headline “Cheating our Children.” It identified about 200 school districts — including four in Washington state — that recently reported test-score gains the article described as extremely improbable to have actually occurred.

The four Washington school districts were Mukilteo, Sumner, Tahoma and Kennewick.

The methodology used in reporting “Cheating our Children” has been widely debated since the article’s publication; many have pointed out serious flaws in it.

To identify districts with test results the newspaper concluded were suspicious, a team of reporters and database specialists obtained scores from 2008-2011 from every state and separated the scores into “classes” made up of all students in a given grade at a given school.

They then used a mathematical formula to predict what each class’s average test score should have been each year. If a class’s actual scores were far off from the prediction, the class was “flagged.”

In each of the 200 identified districts, more than 10 percent of classes were flagged. Even more troubling, according to the article, the districts included a significant number of classes that performed unusually well one year then did much worse in subsequent years.

In each case, the newspaper reported, the odds of that happening “by chance alone” were less than 1 in 1,000.

Tahoma School District spokesman Kevin Patterson had a simple response to the newspaper’s conclusions: “We’re not cheating.”

“We have had some big gains over the years, yes, … (But) we’ve never had any difficulty with any test security,” he said. “That’s just not how we do business. And we’re pretty vigilant about making sure the tests are secure.”

A spokesman for Mukilteo School District offered a similar sentiment.

“We place the credit for our improved test scores on hard work both by teachers and students,” Andy Muntz wrote in a statement, citing increased professional development, new technologies and an effort to maintain small class sizes.

Spokeswomen for the Sumner and Kennewick school districts did not respond to several phone and email messages.

Larger school districts in the Puget Sound region performed better on the newspaper’s analysis, but some still had scores described as suspicious.

For 2009, 13.6 percent of Bellevue’s classes were flagged, according to the analysis. Fewer were flagged in other years.

District officials have contacted The Atlanta Journal-Constitution for more information, spokeswoman Jacque Coe said.

Washington’s state Office of the Superintendent of Public Instruction requires districts to document all testing irregularities, spokesman Nathan Olson said. That office investigates the scores, he said.

The newspaper has not gone unchallenged since it published the article.

Some critics have noted that the analysis did not account for students moving in or out of the district, or in or out of individual schools, in the middle of a school year or between school years.

In a related criticism, the newspaper has gotten flak for analyzing class-level scores as opposed to individual student scores.

Eric Celeste wrote in the alternative magazine Creative Loafing Atlanta that the conclusion in the newspaper’s article was “most likely tremendously overstated and the data used to arrive at it is deeply flawed.”

But many experts say the numbers, while not definitive evidence of cheating, should raise suspicions.

In a statement, U.S. Secretary of Education Arne Duncan called the findings concerning.

The top education official in Washington, Superintendent of Public Instruction Randy Dorn, said he read the article carefully. Dorn said his office examines suspicious scores and that he has encouraged districts to do the tests online so less cheating is possible.

Asked if the article would not make him take the issue more seriously, Dorn said no. “We’re already taking it seriously,” he said.

Brian M. Rosenthal: 206-464-3195 or brosenthal@seattletimes.com. On Twitter @brianmrosenthal.