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.

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Scottish Labour's defeat to the Tories confirms a political transformation

The defining divide is no longer between left and right but between unionist and nationalist.

It was Scotland where Labour's recovery was supposed to begin. Jeremy Corbyn's allies predicted that his brand of left-wing, anti-austerity politics would dent the SNP's hegemony. After becoming leader, Corbyn pledged that winning north of the border would be one of his greatest priorities. 

But in the first major elections of his leadership, it has proved to be Labour's greatest failure. A result that was long thought unthinkable has come to pass: the Conservatives have finished second (winning 31 seats). For the first time since the 1910 election, Labour has finished third (winning 24). Scottish Labour leader Kezia Dugdale stood on a left-wing platform, outflanking the SNP on tax (pledging to raise the top rate to 50p and increase the basic rate by 1p), promising to spend more on public services and opposing the renewal of Trident. But rather than advancing, the party merely retreated.

Its fate confirms how Scottish politics has been realigned. The defining divide is no longer between left and right but between unionist and nationalist. With the SNP as the only major pro-independence party, the Tories, led by the pugnacious Ruth Davidson, framed themselves as the pro-UK alternative - and prospered. In contrast, Dugdale refused to rule out supporting a second referendum and suggested that MPs and MSPs would be free to campaign for secession. The result was that Scottish Labour was left looking dangerously irrelevant. "Identity politics. Labour doesn't get it," a shadow minister told me. Its socialist pitch counted for little in a country that remains ideologically closer to England than thought. The SNP has lost its majority (denying it a mandate for a second referendum) - an outcome that the electoral system was always designed to make impossible. But its rule remains unthreatened. 

Corbyn's critics will seek to pin the baleful result on him. "We turned left and followed Jeremy's politics in Scotland, which far from solving our problems, pushed us into third," a senior opponent told me. But others will contend that a still more left-wing leader, such as Neil Findlay, is needed. Dugdale is personally supportive of Trident and was critical of Corbyn before his election. Should she be displaced, the party will be forced to elect its sixth leader in less than five years. But no one is so short-sighted as to believe that one person can revive the party's fortunes. Some Corbyn critics believe that a UK-wide recovery is a precondition of recovery north of the border. At this juncture, they say, SNP defectors would look anew at the party as they contemplate the role that Scottish MPs could play in a Westminster government. But under Corbyn, having become the first opposition to lose local election seats since 1985, it is yet further from power. 

In Scotland, the question now haunting Labour is not merely how it recovers - but whether it ever can. 

George Eaton is political editor of the New Statesman.