Forgive me for writing 2 posts in a row about regression to the mean. But it’s an important statistical concept, which also happens to be widely misunderstood. Sometimes with important consequences.

Last week, I blogged about a claim that student tuition fees had not put off disadvantaged applicants. The research was flawed, because it defined disadvantage on the basis of postcode areas, and not on the individual characteristics of applicants. This means that an increase in university applications from disadvantaged areas could have simply been due to regression to the mean (ie the most disadvantaged areas becoming less disadvantaged) rather than more disadvantaged individual students applying to university.

Today, we have a story in the news where exactly the same statistical phenomenon is occurring. The story is that putting hospitals into “special measures” has been effective in reducing their death rates, according to new research by Dr Foster.

The research shows no such thing, of course.

The full report, “Is [sic] special measures working?” is available here. I’m afraid the authors’ statistical expertise is no better than their grammar.

The research looked at 11 hospital trusts that had been put into special measures, and found that their mortality rates fell faster than hospitals on average. They thus concluded that special measures were effective in reducing mortality.

Wrong, wrong, wrong. The 11 hospital trusts had been put into special measures not at random, but precisely because they had higher than expected mortality. If you take 11 hospital trusts on the basis of a high mortality rate and then look at them again a couple of years later, you would expect the mortality rate to have fallen more than in other hospitals simply because of regression to the mean.

Maybe those 11 hospitals were particularly bad, but maybe they were just unlucky. Perhaps it’s a combination of both. But if they were unusually unlucky one year, you wouldn’t expect them to be as unlucky the next year. If you take the hospitals with the worst mortality, or indeed the most extreme examples of anything, you would expect it to improve just by chance.

This is a classic example of regression to the mean. The research provides no evidence whatsoever that special measures are doing anything. To do that, you would need to take poorly performing hospitals and allocate them at random either to have special measures or to be in a control group. Simply observing that the worst trusts got better after going into special measures tells you nothing about whether special measures were responsible for the improvement.