A Truth Moment at the CRB

According to the BBC, the Home Office really, really doesn't get the basic truth that 0.01% of a really big number is quite a big number. The Torygraph reported that the Criminal Records Bureau had mistakenly told its customers between February 2007 and February 2008 that some 680 people had criminal records when in fact they had none. The Home Office's response:

The Home Office said CRB has a 99.98% accuracy rate in vetting people working with children and vulnerable adults.

Indeed. I keep saying this; 99.98% accuracy, which is the politician's way of saying a 0.02% failure rate, is only good enough if 0.02% of the total isn't a large number. It must seem silly to people outside the telecoms business that we go on about 99.999% reliability. But that is a percentage of up to hundreds of millions of calls and signalling events.

Fortunately, there are some numbers in the story. The Home Office claims that 80,000 (a round number, but we've got nothing else to go on) people were prevented from taking up posts involving "vulnerable people"; there's no way of telling whether this means only ones involving "vulnerable people", only ones where a job offer was withdrawn, or just the total CRB checks that came up positive, and there's no telling what period of time it refers to. If it was the total for 2007-2008, that means the chance of a positive CRB check being a false positive is 0.85 per cent (99.15 per cent in contractorspeak). And we *haven't* even considered the false negatives....

So where's your 0.02 per cent now? Naturally, it's possible that the 80,000 covers more than one year...but hold on. If there were many more, some such figure recurring every year, then this suggests the actual numbers are even worse. The CRB has been going since, what, 2002? 13,333 refusals a year on average. We know the 680 false positives are for just one year; which would make it a 5.1% false positive rate for 2007-08. (That's 94.9% in contractorspeak.) So, the Home Office's figures cannot possibly be right; it's impossible to have a negative number of false negatives, so we *know* that the CRB does not provide 99.98% accuracy. Surely this means the Government should be suing Capita or whoever?