There are not 120,000 "troubled families"

This zombie statistic refuses to die.

The Department for Communities and Local Government has released a report focusing on so-called "troubled families", which presents a compelling case that the worst of these families have problems which need urgent intervention. But it also takes the opportunity to revive one of the department's favourite zombie statistics. A report which is based on formal interviews with 16 families ("although she met and talked with many more") is generalised out to cover 120,000.

This six-figure number is one of the DCLG's favourites. It has been pushing it since at least February, when NIESR's Jonathan Portes first drew attention to the problems with the definition of "troubled". When the Prime Minister quoted the figure, he called these families:

The source of a large proportion of the problems in society. Drug addiction. Alcohol abuse. Crime. A culture of disruption and irresponsibility that cascades through generations.

As Portes pointed out, the actual definition of troubled families focuses far more on them being families with troubles, rather than families causing trouble. The DCLG has an explanatory note on the topic, which defines the families as any holding five or more of the following characteristics:

a) no parent in work
b) poor quality housing,
c) no parent with qualifications,
d) mother with mental health problems
e) one parent with longstanding disability/illness
f) family has low income,
g) Family cannot afford some food/clothing items                                                        

So back in February, the overarching problem with the statistic was how it was used, rather than the number itself. Whether or not there were 120,000 of them, these troubled families are in no way "irresponsible".

But last month, the dishonesty became clearer. Perhaps realising that the rhetoric didn't match up with the definition, the department published a new explanatory note, which claimed that troubled families were:

Characterised by there being no adult in the family working, children not being in school and family members being involved in crime and anti-social behaviour.

That definition does sound much more like one of a family suffering "a culture of disruption and irresponsibility", certainly. But normally, when one changes a definition of something, the number of cases falling under that definition also changes. Not so with the troubled families. The department continued – and continues – to refer to "120,000" of them.

Even worse, when the Prime Minister first referred to the families (using the kinder definition), he did so with an extraordinary level of granularity, saying:

There are an estimated 4,500 of these families in Birmingham, 2,500 in Manchester, and 1,115 here in Sandwell.

Once the definition changed, had the location? Like hell.

As Jonathan Portes concluded his post:

It is difficult to conclude anything except that the Department, and the governnment, have become hung up on the 120,000 number despite the fact that they are well aware that it is now completely discredited, either as a national estimate of the number of "troubled families" or as a sensible guide to local policy.

The release of today's report just confirms that feeling. The figure of 120,000 is mentioned exactly twice in the 30,000 word report (pdf), once in author Louise Casey's foreword and once in the introduction. It is also mentioned twice in the 600 word press release, and twice in each of the Guardian and Mail's reports on the topic. It seems like something which has little to do with the content of the report (an admirable qualititative study of what it's like to live in an incredibly disfunctional household, but one which offers little guidance as to how widespread the problems are) and everything to do with a need to push a continuing narrative.

People like to put numbers on things, so here's one: with the actual information the DCLG has put out, we know of just 16 troubled families, the ones interviewed by Casey. Pick a number any higher than that and you're getting into the same voodoo mathematics the government has been performing for the last six months.

Syringes lie on the floor. But are they from a "troubled family"? Photograph: Getty Images

Alex Hern is a technology reporter for the Guardian. He was formerly staff writer at the New Statesman. You should follow Alex on Twitter.

David Cameron addresses pupils at an assembly during a visit to Corby Technical School on September 2, 2015. Photograph: Getty Images.
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Can Cameron maintain his refugee stance as he comes under attack from all sides?

Tory MPs, the Sun, Labour and a growing section of the public are calling on the PM to end his refusal to take "more and more". 

The disparity between the traumatic images of drowned Syrian children and David Cameron's compassionless response ("I don't think there is an answer that can be achieved simply by taking more and more refugees") has triggered a political backlash. A petition calling for greater action (the UK has to date accepted just 216 refugees) has passed the 100,000 threshold required for the government to consider a debate after tens of thousands signed this morning. Scottish Conservative leader Ruth Davidson has tweeted: "This is not an immigration issue, it's a humanitarian one, and the human response must be to help. If we don't, what does that make us?" Tory MPs such as Nicola Blackwood, David Burrowes, Jeremy Lefroy and Johnny Mercer have similarly appealed to Cameron to reverse his stance.

Today's Sun declares that the UK has "a proud record of taking in desperate people and we should not flinch from it now if it is beyond doubt that they have fled for their lives." Meanwhile, the Washington Post has published a derisive piece headlined "Britain takes in so few refugees from Syria they would fit on a subway train". Labour has called on Cameron to convene a meeting of Cobra to discuss the crisis and to request an emergency EU summit. Yvette Cooper, who led the way with a speech on Monday outlining how the UK could accept 10,000 refugees, is organising a meeting of councils, charities and faith groups to discuss Britain's response. Public opinion, which can turn remarkably quickly in response to harrowing images, is likely to have grown more sympathetic to the Syrians' plight. Indeed, a survey in March found that those who supported accepting refugees fleeing persecution outnumbered opponents by 47-24 per cent. 

The political question is whether this cumulative pressure will force Cameron to change his stance. He may not agree to match Cooper's demand of 10,000 (though Germany is poised to accept 800,000) but an increasing number at Westminster believe that he cannot remain impassive. Surely Cameron, who will not stand for election again, will not want this stain on his premiership? The UK's obstinacy is further antagonising Angela Merkel on whom his hopes of a successful EU renegotiation rest. If nothing else, Cameron should remember one of the laws of politics: the earlier a climbdown, the less painful it is. 

George Eaton is political editor of the New Statesman.