Private school leaders have long been irritated by the stereotype that their pupils are toffs or posh kids. Now they are trying to prove that the most successful state schools are posher.
Earlier this month, David Lyscom, chief executive of the Independent Schools Council, said he was frustrated by the perception that his members' schools were "stuffed full of posh white kids". His comment echoed a remark made last year by the then-chair of the Headmasters' and Headmistresses' Conference, who called for an end to the perception of a "chav-snob divide" between state and private schools.
Mr Lyscom went further. Not only were the critics wrong, he said, but the figures proved it. "The proportion of ISC pupils from economically deprived backgrounds is nearly double that in the top grammar and comprehensive schools," he said.
The claim generated plentiful press coverage, with headlines such as "Private schools: we take more poor children". But the research does not back up these claims although the figures do give a fresh insight into the backgrounds of private school pupils and how they really do compare with those in the state sector.
Mr Lyscom's claim was based on figures from two separate pieces of research. One was an analysis by the ISC that looked at its member schools' pupils; the other was an earlier report by the Sutton Trust education charity examining the 200 best-performing state schools at GCSE, including grammars.
The Sutton Trust report showed that an average of only 5.3 per cent of the pupils at the top state schools were eligible for free school meals, the standard deprivation measure.
The ISC said that, in contrast, 9.5 per cent of its pupils lived in postcodes where typical local incomes were estimated to be low enough for families to be eligible for free school meals. It was those figures that led to the "twice as likely to be deprived" claim.
But the comparison is flawed: pupils who are actually deprived were compared with pupils who might be deprived because of the roads they lived on. Having a postcode in which many families have an average income of Pounds 16,000 or lower does not automatically mean that you will, too - just as living on a street where your neighbours are mostly white does not mean you cannot be black, or vice versa.
Ian Plewis, professor of social statistics at Manchester University, said: "You cannot equate neighbourhood conditions to household or family circumstances because there's a lot of variability between households within even small neighbourhoods."
The ISC's analysis was carried out with Experian, the global credit monitoring company, which uses a system called Mosaic which categorises postcodes by resident type (see graphs).
The ISC report acknowledged the system's limitations, saying that it could not "describe" precisely every household in the UK. Yet it argues, correctly, that it "does, however, show that ISC pupils come from areas where the housing and level of affluence are not those of the stereotypical independent school pupil".
Some critics of private schools would indeed be surprised to learn that 8 per cent of the ISC pupils live in postcodes associated with a household income below Pounds 7,999, while a further 9.4 per cent live in areas associated with incomes between Pounds 7,500 and Pounds 13,499.
Yet even here the report notes that the families who opt for private education are likely to differ from their neighbours. "We would expect very few households sending a pupil to an independent school to actually have an income below Pounds 7,499," the report states.
Just 1.13 per cent lived in postcodes where it was "very likely" they would be eligible for free school meals. Meanwhile nearly half were categorised as living in "symbols of success" areas, the richest of the 11 postcode types. They are defined as "people with rewarding careers who live in sought-after locations, affording luxuries and premium quality products".
This is strikingly similar to "the stereotypical perception of independent school pupils" mentioned in the report's opening line, defined as "one of a privileged rich elite, population of wealthy, upper-class families.
The urgency behind the ISC's push to debunk the "posh white kid" stereotype lies in the new public benefit tests for independent schools. The Charity Commission, which began the tests last year, has suggested that most schools will pass, but threatened to remove charitable status from those that fail, along with the accompanying tax benefits.
The ISC report notes that the stereotype of posh private school pupils "has also pervaded the debate about public benefit - clearly, evidence that access to independent schools is open to all sectors of society is required".
The main form of evidence independent schools have used in the past has been the proportion of their pupils who receive financial assistance with their fees - on average, 33 per cent. Yet while a family needs to receive welfare payments or earn less than Pounds 16,000 a year to be eligible for free school meals, families earning more than Pounds 30,000 can be eligible for some independent school bursaries.
The ISC stressed that it never claimed it knew the proportion of its pupils eligible for free school meals, and that the postcode data was the best available information. Finding equivalent free meal figures for independent schools was not possible, the ISC spokeswoman said, partly because of rules on data protection and partly because its schools provided all pupils with meals.
Despite the flaws in the ISC's comparison, it is true that some independent schools have more socially deprived intakes than certain grammars and comprehensives.
Pam Sammons, professor of education at Nottingham University, said: "I've known fairly disadvantaged ethnic minority parents who have put a great emphasis on their children's education and prioritised this by paying for private schools - despite their low income."
The cost of private education can also be more affordable than moving into the catchment area of certain maintained schools. For example, according to Ofsted only 1.15 per cent of pupils at the highly popular Tiffin Girls' School in Surrey are eligible for free meals.
In contrast, the independent Christ's Hospital in Horsham, West Sussex, believes that 31 per cent of its pupils would be eligible for free school meals, more than double the national average. More than 84 per cent of the cost of its pupils' education is paid out of a charitable trust, so it funds more places for socially deprived children than any other independent boarding school. Only 2.7 per cent of pupils pay full fees. More than half are from single-parent families or are orphans.
John Franklin, Christ's Hospital's headmaster, said: "There are two comprehensives in Hemel Hempstead where more of the pupils are affluent and middle-class than ours - but we are an exception. We know which of our pupils would be eligible for free meals because we check when they apply. Sometimes we'll even send someone round to look at what cars are in the driveway and how many flatscreen TVs they have. It's only a small minority of private school pupils in this country who are being dropped off by Jeeves in the roller."
Christ's Hospital is unusual, but its approach is catching on. Eton hopes to rase a large enough endowment fund to make its admissions completely "needs-blind" by 2018, while St Paul's School in London aims to do so by 2030.
So while independent schools cannot yet boast of being more socially deprived than the top state schools, it may only be a matter of time before they can do so with confidence.