In fact results of specialists were already better before they acquired their new status, says Professor Stephen Gorard at Cardiff University. And results of both specialists and non-specialists have risen in equal proportion over a six-year period.

In a report published this week, Professor David Jesson of York University shows that pupils entering specialist schools perform only marginally better in national tests at 11 but significantly better at GCSE.

But Professor Gorard says the difference can be explained simply: better schools have more chance of becoming specialist. He compared GCSE results between 1994 and 2000 for schools that became specialist in that period, and those that did not. He excluded schools whose intake was affected by selection.

His results show that the future specialist schools started off with 45 per cent of pupils getting five A*-C grades compared with 42.3 percent at the non-specialist schools.

Over the next six years, this figure at specialists rose to 52.5 per cent, and at non-specialists to 49.2 per cent - a similar improvement.

He says “value-added” analysis is needed to decide whether specialism really leads to improvement. “Specialist schools were already doing better before they became specialist,” he said. “We have no reason to believe they are doing extra-specially better now.”

Professor Gorard says Profesor Jesson’s previous research excluded grammar schools from his data but not secondary moderns, which are more likely to be non-specialist so his analysis favoured specialists.