But ideas are beginning to flow the other way. A group of independent schools has followed the lead of state schools by adopting a method for analysing national test results to help improve their performance.
The United Church Schools Trust, which runs eight independent schools, has commissioned Professor David Jesson, of York university, to compare their pupils' key stage 2 results with their achievements at GCSE.
"We are the first independent schools to do this," said Charlotte Rendle-Short, the trust's deputy chief executive. "We believe it is a powerful tool for asking questions about performance, and essential if we are to keep raising standards."
Like many fee-paying schools, the trust has already signed up to a Durham university analysis, which compares pupils' ability in special cognitive tests with their GCSE results. But Ms Rendle-Short said that Professor Jesson's approach, which he pioneered in state schools, gave them a broader picture because it began by examining previous national test scores.
The UCST learnt about the analysis through the Specialist Schools and Academies Trust, because it runs nine academies through its subsidiary, the United Learning Trust.
But the annual conference of the Society of Headmasters and Headmistresses of Independent Schools heard this week that a focus on test results could damage private education.
Dr Peter Bodkin, society chairman and headmaster of Tettenhall college in Wolverhampton, said exam success did not reflect the broad teaching on offer in independent schools.
"Those who are more obsessed with targets than the National Rifle Association miss the point completely," he said.
"Performance tables have produced a skewing of potential and the curriculum, to the detriment of the educational provision for pupils in the country's schools."