One leading public employees union with a definite dog in this fight believes just the opposite: There is a definitive way to compare federal- and private-employee pay. And that’s a simple measure of what the job is.

“We’ve always stood by a jobs-to-jobs comparison,” Colleen M. Kelley, president of the National Treasury Employees Union, said in an interview Tuesday. “That’s what the government’s method is driven by.” And in that scenario, federal workers come out behind — by 24 percent on average last year.

The GAO study looked at several approaches to comparing federal and private-sector pay. One approach compares pay for similar jobs based on job-related attributes such as occupation and level of work. Another looks at trends in pay for certain occupations and jobs over time.

The third, “jobs-to-jobs” approach, compares the duties of the worker. For example, if we compare a government attorney who oversees $3 billion in stimulus projects to an attorney who handles wills and estates for a private law firm, the federal attorney will make less, even though he or she has more responsibility in the view of many.

The GAO concluded that each approach uses different methodologies, proof that no one measure is best.

Conservative and libertarian think tanks and budget watchdog group Project on Government Oversight (POGO), have found that the shortfall runs in the other direction. The Congressional Budget Office (CBO) split the difference this year with a report finding federal employees ahead by 2 percent on average.

The think tanks try to compare pay for individuals taking into account education and job experience, as well as other attributes such as occupation, locality and size of employer. Cato, for example, has focused on trends in pay over time without controlling for attributes of the workers or jobs, it said.

But Kelley, who serves on the council that makes recommendations on federal pay matters to a panel made up of the directors of the Office of Management and Budget, the Office of Personnel Management and the Secretary of Labor, said the job-to-job comparison is best. It is also the method used by the government, for now at least.