Now we know who did it. D.C. Inspector General Charles J. Willoughby wrapped up a 16-month probe of cheating on standardized tests in city schools, and he concluded that kids, not adults, made the astonishing number of wrong-to-right changes found on answer sheets.

Never mind that testing companies, academic experts and veteran teachers say students almost never make more than one or two wrong-to-right erasures per test. Ignore the fact that in Atlanta, where there were similar volumes of erasures on 2009 tests, state investigators with subpoena power found 178 teachers and principals had changed the answers.

After his investigators visited only one school, Crosby S. Noyes Education Campus, Willoughby endorsed their conclusion that because the adults at that school seemed innocent of changing answers, none of the adults at dozens of other schools with massive erasures could be guilty either.

I had hoped Willoughby’s report would be thorough and independent. This thin, biased 14-page document fails egregiously on both counts.

Deputy Inspector General Blanche L. Bruce told me, “Your assumptions and conclusions are incorrect.” She said her office’s conclusions relied “on the totality of all the evidence.”

At Noyes, the only school investigated, 75 percent of the classrooms were flagged by the testing company, CTB/McGraw-Hill, for unusual numbers of wrong-to-right erasures on the D.C. Comprehensive Assessment System tests in 2008. The percentage flagged was 81 percent in 2009 and 80 percent in 2010. At least five Noyes classrooms during that period had wrong-to-right erasure rates of more than 10 per child, while the D.C. average was less than two. (Disclosure: my wife, Linda Mathews, conceived and supervised a USA Today investigation that revealed that 103 D.C. schools had abnormally high erasure rates at least once from 2008 to 2010.)

Gregory Cizek, a testing expert at the University of North Carolina at Chapel Hill and a consultant to the Atlanta investigation, told me that “nothing we know of” has ever caused such large groups of students to change so many wrong answers to right. Massive erasing only occurs when “others do it for them,” he said.

Yet the inspector general’s report, quoting no experts on test erasures, concludes that the D.C. data, without “specific evidence of impropriety . . . was not a sufficient basis to conclude the erasures resulted from cheating.” His investigators interviewed 32 current and former staffers at Noyes, and they found just one former teacher willing to admit that he or she helped some kids get the right answers on one test.

At that point, Willoughby let himself be swayed by an official with a vested interest in his conclusions. His investigators could have looked at J.O. Wilson Elementary School, where 93 percent of classrooms were flagged for unusual erasures in 2008, 83 percent in 2009 and 100 percent in 2010. But the report says the investigators discounted those numbers because D.C. Schools Chancellor Kaya Henderson told them that Wilson was a great school and that “she does not consider a high number of erasures to be an indication of a problem.”

No other schools were visited, the report says, in part because Henderson “revealed no additional evidence to corroborate the allegations.” Was gathering evidence Henderson’s job or Willoughby’s? Henderson did not respond to my questions.

D.C. administrators and teachers had an incentive to cheat. They won big bonuses for high test scores. Some were dismissed when scores failed to climb. Still, the inspector general found that students, who got nothing for a good score, made all those answer sheet changes on their own. No doubt some changes were legitimate. But all of them?

The investigators didn’t bother to ask any students whether they made the many changes that were found when their answer sheets were scored. Investigators did not check Noyes students’ test scores in subsequent years to see whether they continued to perform at high levels when test security was tightened and erasures declined.

That is what a real investigator who wanted to get at the truth would have done.