Pulling a fast one with statistics

Statistics are a dangerous weapon and require careful handling.

I've always felt that those who use them should be licensed. No, I'm serious.

You shouldn't be allowed to use statistics publicly without possessing proper certification.

Think of the chicanery that has just occurred over the prevalence data.

If your practice has exactly average prevalence for, say, mental health, you might imagine that your quality payment wouldn't be reduced. And you'd be wrong.

This is how the DoH does it (watch carefully): first it gathers the raw prevalences. Then any practice in the lowest 5 per cent band has their score brought up to the 5 per cent cut-off value. Why?

Are these prevalences accurate or not? If they are accurate, why change them?

Then the national average prevalence is recalculated, using these increased levels. This artificially increases the 'average' prevalence, thus depressing the relative prevalences of all other practices.

But the DoH has an even nastier trick up its sleeve. A few practices are very high-prevalence.

A single practice can apparently drag up the 'average' prevalence hugely, depressing the relative scores of ordinary practices. The only way this can happen is if the DoH is abusing the mathematics.

Statistically, you can't average percentages. For example, practice A has 10,000 patients, of whom 200 have CHD, giving a prevalence of 2 per cent. Practice B is much smaller with 1,000 patients of whom 40 have CHD - a prevalence of 4 per cent. The average prevalence of CHD across the two practices is not 3 per cent (the average of 2 per cent and 4 per cent), but 'the total number of affected patients (200 plus 40) expressed as a percentage of the total population (10,000 plus 1,000), which is 2.18 per cent. So if you use the incorrectly calculated 'average' of 3 per cent, then the big practice with a prevalence of 2 per cent loses quality payments.

You can't average percentages. If you do, then a small-sized practice with a non-average prevalence will skew the final 'average'.

But that is what the DoH seems to have done. They've used a statistically corrupt method on the remaining practices to obtain the apparent 'average' prevalence. And on that basis they've paid us a lot less than they should have. Can I cry foul?

- Dr Lancelot is a GP from Lancashire. Email him at GPcolumnists@haynet.com.

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