The error appeared to be the first major mishap leading to the invalidation of American scores on an international test, Dr. Schneider said. But a string of similar incidents brought flawed results on other standardized exams, including the SAT’s and the state math and reading tests used to judge schools under the federal No Child Left Behind Act.

“We need to recognize that the testing industry is under immense pressure at a time when scores are being given immense importance,” said Thomas Toch, who wrote a report last year detailing the problems of the American testing industry for Education Sector, an independent policy group, where he is a co-director.

Conducted every three years, the international test focused on science literacy in 2006, but also included sections on reading and math. The problem with last fall’s test was that pages in the exam booklet were assigned incorrect numbers. As a result, questions referred students to texts, said to be “on the opposite page,” but in reality printed on a previous page.

Nobody  not officials at the testing firm, within the federal government or at the Organization for Economic Cooperation and Development  noticed the error until July 2007, Dr. Schneider said. Then O.E.C.D. experts concluded that the error had ruined the reading scores, and threw them out. The same error affected math and science scores to a lesser degree, and they were not invalidated.

The contractor that printed the tests, RTI International, based in Research Triangle Park, N.C., will repay the $500,000 it received for the reading part of the test as part of its overall $2 million contract to administer the exam. The firm has 13 active contracts with the Department of Education, worth $196 million. Patrick Gibbons, a spokesman, said that the contractor took “great care” to provide reliable research results, but that in this case quality-control procedures failed.