If someone studies to become a nurse, allied health professional, dentist, etc. then their course fees are usually paid by the NHS. Naturally not everyone that starts a course finishes it, so something that's monitored carefully is the attrition rate for each course.
I used to work for one of the NHS organisations that commissioned education and monitored the activity on each of the courses we had paid for. Different regions used slightly different calculations for their attrition rates, which caused problems when you tried to look at attrition across the country as a whole (which I later did, when I moved onto a national NHS workforce organisation).
Of course everyone agreed that it would make sense to have one single attrition calculation across the country. Indeed the now defunct National Audit Office had commented on exactly this, and suggested a single definition to be used nationwide, which the Department of Health tried to get everyone to adopt. Some areas adopted it, but I'm pleased to say my area refused to (mainly on my own recommendation, if I may say so myself) - because yes indeed, this definition contained errors a 9-year-old would be ashamed of.
Let's get to the detail. Don't worry, none of this is at all hard to understand, but there are some definitions to get to grips with. Basically there are two ways you can join a course - you either start at the beginning (making you a starter), or you join it mid-way through, having already started a course that brings you up to the relevant level (making you a transfer in). Conversely there are two ways you can leave a cohort - by transferring out to another cohort or by discontinuing (due to academic failure, ill health or whatever).
If you start or transfer in to a course and don't transfer out or discontinue, then either you are still on the course or you have successfully completed it. In other words, the number of students on a course (if the course is still running) is the same as the number of successful completers (if the course has finished) and this is wholly dependent on the other variables:
N = s + t(in) - d - t(out)
With me so far? Great. So on to the NAO definition of attrition. Remember, these were proposed by the National Audit Office - the Government's chief maths-checkers - and were pushed hard by the Department of Health. There had been much discussion leading to this point, including recognising the importance of including transfers in the formula.
The NAO and DH published their attrition definition as two formulae, one for completed courses (with a reference to "numbers completing") and one for "cohorts not yet completed" with a reference to "numbers in training". But as we've already shown, these two things are the same, so really there was only one formula, and here it is:
Attrition = s + t(in) - t(out) - N
s
So far so good - it's a definition that looks straightforward, and, crucially, includes some mention of transfers in and out. Which is all very well until we remember that our numbers of completers / numbers on course (N) is in fact defined by some of these terms too. So the definition in fact is....
Attrition = s + t(in) - t(out) - (s + t(in) - d - t(out))
s
Oh. Can you see what's happening yet? Any decent nine-year-old mathematician would now collect like terms:
Attrition = s - s + t(in) - t(in) + t(out) - t(out) + d
s
Which of course means...
Attrition = d
s
Oops. So that definition is pretty rubbish after all. Thanks for nothing, National Audit Office.
The really annoying thing here is that we raised that issue with the Department of Health in 2003 and kept pushing it. We also explained it to the other NHS regions - some of whom agreed with us and used the definition we were using, and some of whom pressed on with the DoH definition. Eventually, once I was working for that national organisation several years later, we managed to persuade all the NHS education commissioners to adopt our recommended definition and drop the one above. It was still a year or two later that the DoH finally cottoned on, and even then it took a shouty email to a senior civil servant with the words "PLEASE READ THIS" splashed over the top for them to acknowledge that yes, actually, their proposed definition doesn't take account of transfers between courses and is therefore incorrect.
The BBC article begins with the words "A quarter of adults in some parts of England have maths skills below those of nine-year olds." Too right. I know where some of them work.
