Washington ? IRS centers established to help people prepare their tax returns gave incorrect answers — or no answer at all — to 43 percent of the questions asked by Treasury Department investigators posing as taxpayers.

The investigators concluded that half a million taxpayers may have been given wrong information between July and December 2002.

Service varied widely by state, with some of the best in the Northeast and some of the worst in the Midwest and Plains.

Auditors were given correct answers to 57 percent of their tax law questions during the course of the study. Less than half, or 45 percent, of the questions were answered correctly and completely. In 12 percent of the cases, the answer was correct but incomplete.

Internal Revenue Service employees gave wrong answers to 28 percent of the questions. Twelve percent went unanswered, as taxpayers were told to do their own research in IRS publications. In 3 percent of the attempts to get questions answered, the auditor could not get any service at the center.

The IRS disputed the results. Using the raw numbers gathered by Treasury investigators, the IRS recalculated the error rate and ignored any instance when a taxpayer was denied service or told to do his own research. Of the questions answered, they calculated that 67 percent were answered accurately.

“We recognize that an accuracy rate of 67 percent for tax law service is inadequate,” Henry O. Lamar, the IRS commissioner overseeing individual tax returns, wrote to the investigators.

The auditors said they had a better chance of getting a correct answer when IRS employees walked them through relevant material and asked probing questions.

The questions most commonly answered incorrectly dealt with the earned income tax credit, education credit and dependents.