The Georgia analysis looked at 2009 test results from more than 125,000 students taking the state’s Criterion-Referenced Competency Test, given in first through eighth grades in reading, language and math. The test is used primarily to measure school progress under the federal No Child Left Behind law. Students in some grades must pass the test before they can be promoted.

Image Kathleen B. Mathers's agency conducted the statewide inquiry. Credit... Elissa Eubanks/Atlanta Journal-Constitution

Principals and teachers are under intense pressure to improve scores. If schools fail under No Child Left Behind, they are placed in a “needs improvement” category and must offer extra tutoring and allow parents to transfer their children to higher performing schools.

The erasure analysis used the same scanners that score tests to count the erasures in which answers were changed from wrong to right. “It’s not any sort of crazy technology,” Ms. Mathers said. “You just beef up the scanner so it can read varying degrees of gray scale.”

The study determined the average number of wrong-to-right erasures statewide for each grade and subject, and flagged any classroom with an unusually high number. For example, in fourth-grade math, students on average changed 1.8 answers from wrong to right, while one classroom that was flagged as suspicious had more than 6 such changes per student.

Four percent of schools were placed in the “severe concern” category, which meant that 25 percent or more of a school’s classes were flagged. Six percent were in the “moderate concern” category, which meant that 11 percent to 25 percent of its classes were flagged, and 10 percent raised “minimal concern,” meaning 6 percent to 10 percent of its classes were flagged.

At 27 schools, 21 of which were in the Atlanta district, more than half the classes were flagged, and at four Atlanta schools more than 80 percent of the classes were flagged.

On Thursday, the state Board of Education ordered districts to investigate schools in the severe- and moderate-concern categories, and put in place new testing procedures.