He said some states did not ask their testing contractors to generate an erasure analysis, while others did receive them but did not use them.

One problem, experts said, was asking school systems to police themselves, which often requires the kind of independent oversight set up in Georgia. The state Department of Education is led by an elected superintendent, Kathy Cox, but the governor, Sonny Perdue, controls a separate Office of Student Achievement, which has auditing powers.

It was the Office of Student Achievement that conducted the erasure study, not the Education Department.

Even states that have weathered widespread cheating scandals do not necessarily follow up with regular statistical monitoring. In 2005, after an investigation by The Dallas Morning News pointed to extensive cheating in Texas, the state hired Caveon Test Security, a Utah company that improves testing procedures, to conduct what the company calls “forensics analyses” of answer forms. But the company was not retained to do yearly monitoring, said John Fremer, Caveon’s president.

Caveon’s forensics analyses use several methods of detecting cheating, screening not only for erasures but improbable increases or decreases in scores, individual students whose performance swings widely from year to year, patterns where multiple students share the same wrong answers and other anomalies.

Erasures alone only indicate certain types of misconduct, as when answers are changed after a test. Other methods, Mr. Fremer said, flag other types of cheating, like filling in the remaining answers on an incomplete form.

States that are not checking answers with such forensic measures cannot use the excuse that they are new, said Walt Haney, a senior researcher at the Center for the Study of Testing, Evaluation and Educational Policy at Boston College. Using statistics to detect cheating on standardized tests dates back to the 1920s, and erasure analyses are practically as old as filling in bubbles on answer forms with a No. 2 pencil.