For the school system in Gary, Ind., the results were especially troubling when the state checked for irregularities in standardized testing two years ago. Of Gary’s 12 elementary and middle schools, eight had so many erased and corrected answers as to defy all statistical probabilities.

But Indiana’s state education department didn’t investigate the Gary schools or the 82 others it flagged for excessive erasures. It didn’t announce the findings in public. It didn’t even notify the parents of students in the suspect schools.

“This information will not be released to the public,” Wes Bruce, Indiana’s chief assessment officer, told Gary’s superintendent in a letter recently obtained by The Atlanta Journal-Constitution. The education department, Bruce added, “will not investigate this issue further nor institute any consequences.”

Indiana’s handling of its erasure data mirrors that of several other states, where gathering evidence of suspicious test scores — evidence of possible cheating — does not necessarily translate into acting on those suspicions, the Journal-Constitution found. New Jersey kept erasure analyses secret until a newspaper won a lawsuit forcing disclosure of the information. Pennsylvania did not publicly acknowledge it had erasure data until a new state administration released material that reflected poorly on its predecessor.

“There is a long tradition of not following up on various types of data,” said John Fremer, president of Caveon Test Security, the consulting firm that initially investigated cheating for the Atlanta Public Schools in 2010. “There is no established pathway of, ‘This is how we handle this kind of problem.’ ”

In Indiana, Bruce and other officials did not respond to requests for interviews. A spokeswoman for the state education department wrote in an email: “Indiana takes test security very seriously, and we are extremely careful about the information we share with outside parties regarding potential security breaches.”

The newly installed school superintendent in Gary, Cheryl Pruitt, said in an interview that she was only vaguely aware of the erasure analysis and other suggestions of test tampering. “I can’t really respond to what I haven’t seen,” Pruitt said. “I can only comment on the future.” If cheating occurs, she said, “I can tell you it won’t be tolerated.”

Indiana’s review of test results, known as an erasure analysis, came to light after the Journal-Constitution reported Sunday that many school districts and state education agencies treat cheating cases as one-time, isolated occurrences, often ignoring patterns that indicate systemic wrongdoing. This was the case in several districts among the 196 the newspaper identified earlier this year as having extreme concentrations of suspicious test scores. One of the districts with the unlikeliest scores: Gary, where nearly a third of classes were flagged each year from 2008 to 2010.

Indiana officials refused to provide the newspaper with records of cheating investigations or erasure analyses, contending those files were not subject to the state’s freedom of information laws. A lawyer for the Gary school district also denied a request from the newspaper, but it was unclear whether she meant that no relevant documents existed or that the law didn’t require the district to release them.

This week, however, the Journal-Constitution obtained documents describing Indiana’s 2010 erasure analysis, along with internal memos from Gary about that analysis.

The documents do not identify other districts — known in Indiana as “community school corporations” — where the analysis found suspicious numbers of erasures that turned mistakes into correct answers. But Gary had the unfortunate distinction of leading the state on suspicious changes, the records show.

“Gary was the No. 1 corporation with this problem,” the school district’s assessment director wrote in an October 2010 memo to the superintendent, referring to the state’s analysis.

For at least one Gary school, the documents show, the odds of the wrong-to-right changes occurring without tampering or other intervention literally were incalculable: one in infinity.

In a third-grade classroom at that school, Beveridge Elementary, the erasure analysis detected 122 changes on both the math and language-arts tests. Of those, 95 of the language-arts changes and 96 of those in math were wrong-to-right erasures.

Those numbers defy logic and warranted a state investigation, said Scott Marion, associate director of the Center for Assessment, a nonprofit consulting firm that helps states develop tests and teacher accountability systems. Typically, Marion said, the first answer a student selects is correct, so right-to-wrong erasures would be more likely.

“They’re clearly doing something that doesn’t pass the smell test,” Marion said.

In his letter to the district, Bruce, the state’s assessment officer, told Gary officials, “I expect you to look into each instance listed to determine the reasons behind the high rate of answer changes in these classrooms.”

Correspondence from the principals of the eight schools to the district headquarters indicates that principals did speak with teachers in the classes involved.

In a memo to the school district headquarters, Beveridge’s principal, Stephanie Billups, wrote that a teacher had “cleaned her students’ [test] books by erasing stray marks and darkening some circles because they were so light.”

“She didn’t recall anything else unusual taking place,” Billups wrote. Billups declined to comment this week.

Billups also reported a claim that two staff members were seen erasing students’ answers in the school library. The report was made by a teacher, who said she heard it from another school employee. Billups said she tried three times to get the teacher to reveal her source, but the teacher refused. The third time, Billups wrote, the teacher “indicated to me that this wasn’t going any further with her and as far as she is concerned, it’s a dead issue.”

Other principals in Gary also wrote reports to the district in response to the state’s findings. Many of the reports ran no more than a few sentences. Some echoed the early days of Atlanta’s cheating scandal, when administrators and district officials claimed that excessive erasures resulted from experimental test-taking strategies. One principal said he would address the problem by having his teachers “reduce unnecessary erasering.” Students, he said, would “practice strategies of using pencils without erasers.”

After the principals responded, a testing official at the district headquarters drafted “talking points” for the superintendent — including a warning that if the district didn’t rein in erasures, the state “will launch a ‘real’ investigation.”

The documents contain nothing to indicate that state or local officials examined students’ test scores or looked for other statistical indicators of cheating following the 2010 erasure analysis.

But examples of unusual score increases abounded. At Beveridge, for example, the pass rate on the third-grade language-arts test increased by 44 percentage points from 2009 to 2010; on the math test, by 35 points.

Questions about Gary’s test scores follow decades of struggles for the city and its schools: long-term depopulation, the rise of charter schools that siphon away top students, financial problems so severe that most bus service was discontinued to neighborhood elementary schools. And questions did not end with the 2010 erasure study.

Last March, Gary notified the state education department of three possible irregularities during the 2012 tests — all at Beveridge Elementary.

In one incident, a teacher gave the wrong exam on the wrong day. Another teacher allegedly let students take extra time to finish a test, and a third was accused of telling a student to change an incorrect answer.

After the teachers denied wrongdoing, a Gary official wrote to the state, “It is our belief that no testing improprieties took place.”