Anyone who wants to understand the statistics on Incapacity Benefit and its successor, Employment and Support Allowance, had better set aside a couple of days. Straightforward it isn’t.

Now the UK Statistics Authority has told the Department of Work and Pensions it needs to do better. Sir Michael Scholar, UKSA’s chair, has written to the Commons Work and Pensions Committee to support its view that the presentation of the data needs improvement, and to Iain Duncan Smith, the Pensions Secretary, suggesting that the statistics should be formally assessed against the same rules that would apply if they were classified as National Statistics.

Users of the statistics want to know whether the new tests being applied to applicants for ESA are having any effect. Are they reducing the numbers who qualify for the benefit? Or are they finding that most of the recipients of the benefits are genuinely unfit for work?

Newspapers have not been shy of saying that many of those on IB and ESA are workshy scroungers. Politicians naturally don’t go that far, though they manage to convey at dog-whistle frequencies that is what they believe. Even Ed Miliband has said that some IB claimants are “just not taking responsibility” and are “shirking their duties”.

Suspicions got back a long way. In the second volume of his diaries, Decline and Fall,  Chris Mullin records an exchange on 24 January 2006 with John Hutton, then Work and Pensions Secretary. Hutton had just introduced plans to reduce the numbers on IB, and in a division in the House of Commons whispered to Mullin that he knew of an amateur football team, currently topping a local league, in which eight of the eleven players recently fielded had been on IB.

The political background is important because it helps explain why the statistics are so hard to understand. Pensions ministers want to stress how tough they are being, feeding the media mob with headlines, while the statistics actually show the changes in numbers who qualify are relatively small. Squaring this particular circle is the task of the DWP statisticians, who deserve sympathy.

The headlines that greeted the most recent release of statistics at the end of July make the point. Some papers claimed that the figures showed only 7 per cent of applicants had been judged unfit for work - “Only one in 14 qualify” said The Press and Journal - others that 75 per cent of claimants were faking, yet others that 39 per cent of those on the benefit had been found to be fit for work. Not one of these is fully correct.

As Sir Michael’s letter points out, to find how many qualify for the benefit you have to add those in the “Support Group” (7 per cent) to those in the “Work-Related Activity Group" (17 per cent). That means that near-enough a quarter are found to qualify for the benefit, not 7 per cent.

As for the 39 per cent found fit for work - those that have “failed” the assessment, as the DWP rather quaintly puts it - they can appeal against the decision, and around 40 per cent of appeals are successful. So in the end it is probable that about 23 per cent will be found fit for work. And finally, the suggestion that 75 per cent are faking comes (I guess) from adding the 39 per cent (which is itself wrong) to the 36 per cent who withdraw their claims before the assessment is complete. They may be faking, but it’s equally possible they suffered a short-term disability which has now resolved. It is simply impossible to say how many of this 36 per cent are fakers; some may simply tire of the whole process and abandon it in disgust.

A set of statistics that produces so much misunderstanding is certainly lacking something, and Sir Michael suggests some improvements. He adds that the UKSA would also like to see more distinction between the assessment of new claims and the re-assessment of existing claims; and some information on trends in the statistics over time.

That last point is the key. Both the last Government and the present one, going back to John Hutton and his football team of IB recipients, wanted to put a cap on the benefit. Are all the tests and appeals achieving this, or not?

I commend in this respect a blog by an expert, Professor Paul Gregg, who concludes that on present evidence the new regime is leading to about 10 per cent fewer people, after the appeals process is completed, being passed eligible for ESA – “a story far removed from just 7 per cent being fit for work” he comments.The total number of new claims is actually rising, he points out, from 130,000 per quarter in 2008 to 160,000 now, probably a consequence of the recession.

So while ministers would like us to believe they have a firm handle on the issue and are busily sorting out the genuinely disabled from the chancers, the evidence isn’t very strong that this is actually reducing numbers much. Any ordinary member of the public who, unaided, could deduce that from the DWP’s statistics would deserve an award. It’s hard to escape the conclusion that they are meant to be incomprehensible. Better statistical commentary is urgently needed and the DWP statisticians should be given an unfettered opportunity to provide it.