# Ritchie and maths now

I am afraid the question makes little sense. Regression to the mean suggests at some time all services will be average. Indeed, at some time all services will be unresponsive just as at others they may be fantastic. Daniel Kahneman pretty much got a Nobel prize for pointing this out. And it’s not a fact for government alone: it’s what happens in human behaviour whether in the public or private sector. The only myth has been that it does not happen in the latter and only the former. That’s as wrong as the question was misplaced.

The question has to be how is the average improved. That’s a different issue.

Regression to the mean means that all services will at some time be average?

Eh?

Erm, no, the fact that we are surveying all services to decide upon what is the most common status of them (mean, mode or median) means that the most common status will be, umm, the average.

As to how to increase that average that’s simple. We need to use the experimental method that markets allow. Try things out, see how they work better or worse than other methods and then adopt those that work better more generally.

For example, if we wanted to improve total factor productivity (ie, gaining more output for any given set of inputs) then we would very definitely want to have a market based economic system. The experiment of the 20th century proved that to us. The Soviet Union (according to a Paul Krugman essay at least) managed not to increase tfp by one iota in all its long and bloody life. 80% of western world economic growth in the same time period came from improving tfp.

Thus, in order to get more output from any given set of inputs we want to have a market based economic system.

And would we like to have more people cured of their ailments for whatever amount of money it is that we’re willing to put into health care? Why, yes, we would. Therefore we want a market based system in health care. QED.

## 16 thoughts on “Ritchie and maths now”

1. “Regression to the mean” is a statement of statistical expectation, not a law. And, frankly, it has nothing to do with the work for which Daniel Kahneman received his Nobel (yes, before the pedantry kicks in, I know, Sveriges Riksbank Prize).

So, Ritchie has managed to miss the point (as Tim said – it is to increase the average – I would add, you might want to reduce the variation as well), introduce a completely irrelevant authority, and get his maths wrong.

Can somebody please explain to me just how this weasel has ended up in a position of quite so much influence? There’s clearly “money for old rope” in there and I could do with a bit extra in the wine & whisky fund.

2. Well, even if you get the average up to an acceptable level you can still end up there (or below) because of regression to the mean. The important thing is is that “average” level (and indeed the lowest quality level) actually acceptable?

Reminds me of a medic friend who said it was very important the public never got to understand that half of doctors are below average. “Sack them all!!!”. Then next week, with half the number of doctors, half the remaining doctors are below average, and so on.

Or my take – being that there is nothing wrong with mediocrity as it is the best half of all humans can aspire to.

3. I typed “pendantry” in, saw the spell dis-checker kick in, went back, changed it, and it’s turned up as bloody “pedantry” anyway. Sighs …

Oh, and, for a given measuring stick, slightly fewer than half of all doctors are below average. Some are average. Although there is probably regression to the mean as they begin to sober up about lunch time.

4. Doctor’s definition of an alcoholic: someone who drinks more than she does.

5. The very word “regression”, which statisticians use for lines of best fit and all that, derives from Galton’s study of ” Regression towards mediocrity in hereditary stature”.

He noticed that tall fathers tended to have tall sons too, but not quite as tall since they regressed towards the mean. Similarly short fathers had, on average, shortish sons.

Ritchie hasn’t grasped that regression to the mean need not change the total variation. Generations of application of regression to the mean on human height has not left all people of identical stature…

6. SE,

Can somebody please explain to me just how this weasel has ended up in a position of quite so much influence? There’s clearly “money for old rope” in there and I could do with a bit extra in the wine & whisky fund.

“being a prejudiced hypocritical ignorant polemicist…”

Media: “is this person saying stuff that will sell papers / get us traffic / get us social media shares?”

media, organisations (e.g unions), politicians: “is this person saying stuff that we agree with and urging change that we desire?”

answer: give him a platform / money

moderation and nuance isn’t so popular.

7. 250,000 years for regression to the average to work its magic on humans,
So since we’re now all average we are all equal. So socialism is redundant. Glad Richie has cleared that up.

Most doctors are probably above average, because the number who are catastrophically bad are more, and at an extreme of incompetence, than the number who are brilliantly good. Can’t prove it, though.

8. It was a whimsical observation on the level of public understanding of stuff, not intended for pendantic dissection.

9. He really hasn’t got a fucking clue about anything, has he?

10. Yes JamesV, never took it as anything else. My observations are also whimsical. Some say they are nuts, so you’re ahead there.

11. This is unfair to Richard Murphy. The Observer made a stupid remark “…while few public services will ever sink to the nadir of Mid-Staffs, many will be average…”: Murphy is pointing out that that’s inevitable. (I think the Observer was using “average” to mean “inferior”, but it should know better.)

Murphy is not saying that all services will become average simultaneously, just that if each one’s quality under some measure follows a random walk, it will at some time be average.

MyBurningEars is right of course about the origin of “Regression to the Mean”, but nowadays it’s usually used to mean that if a statistic contains a random element which can change over time, outliers will tend to regress, because they will tend to have extreme values for the random element. And that is relevant in the context of Mid-Staffs, where the meaning of “excess deaths” has been widely misrepresented. (However, it seems that some of the excess deaths at Mid-Staffs may be attributable to diagnosis coding practices there: if that’s true, regression to the mean is certain once the explanation is discovered.)

Having defended Murphy, I should add that like SE I don’t recognize his description of Kahneman’s Nobel Prize.

12. PaulB – I think that Murphy is likely referring, inaccurately, to Kahneman and Tversky’s research into cognitive biases which included the classic example of regression to the mean as it affected the Israeli Air Force.

Pilots who did well in training, got praised for it, then tended to show poorer performance next time. Pilots who did poorly, and got the hairdryer treatment for it, tended to improve next time. The IAF concluded that more stick and less carrot was in order. The psychologists realised both outlying groups were just regressing towards the mean, as probability theory suggested they would.

But like with Galton’s regression of stature, this regression of performance did NOT mean the pilots’ performances tended to converge towards some average value, which is one of the biggest misconceptions about regression to the mean (probably second only to the IAF mistake of not noticing its application at all) and sounds like the trap Murphy fell into.

Failing to notice regression to the mean is a real bane in low quality education research. Bunch of students take an assessment, some fare sub-par, they get targeted for intervention (new teaching method or extra help), reassessed, regress up towards the mean … and bingo, what a successful intervention strategy we have! Am sure this problem applies in medical research too, sure Ben Goldacre has lamented it before.

13. MyBurningEars

Yep, as Regression to the Mean is NOT a causal Phenomenon it does NOT mean that all scores/services etc will converge to a mean. A further point I don’t think I’ve read yet. If we invent – innovate, if we change the sample the theory is then irrelevant.

14. @ MyBurningEars
Yes, the problem you mention “Failing to notice regression to the mean is a real bane in low quality education research. Bunch of students take an assessment, some fare sub-par, they get targeted for intervention (new teaching method or extra help), reassessed, regress up towards the mean … and bingo, what a successful intervention strategy we have! Am sure this problem applies in medical research too, sure Ben Goldacre has lamented it before.” is very important but it is NOT regression towards the mean.
A good statistician (i.e. not me) gave an example of how to explain it to police chiefs pleased with the drop in death rates that they thought was due to speed cameras (which could only be erected where there had been three deaths) “each of you toss a pair of dice” and only if they turn up fives or sixes, throw again. Amazingly the average of the second throw is lower than the first for those who threw twice.
Regression towards the mean occurs when there is a causal effect (the 50:50 chance of inheriting genes that influence height) that should cause some divergence from the mean. What you are describing is merely selection bias in randomly distributed populations.
Murphy is (a) wrong (b) cannot even get the name right. Regression towards the mean does *not* ipso facto reduce variability of the population – there is an interesting proof which I don’t think I can reproduce that you get the same degree of regression towards the norm if you start with the sons’ heights and analyse the fathers’ heights. So regression towards the norm does NOT mean that at some time all (anything) will be average.

15. @john77

The speed cameras are another nice example. The dice are a lovely way to explain it

Whether regression to the mean requires a “causal effect” seems to be a matter of definition. In the sense that Galton originally meant “regression to mediocrity”, yes. But latterly the term seems to be used much more widely, even including the dice model you mentioned. I suppose if one wanted, the dice can be considered as a linear model with zero slope and hence pure random error. I have just had a look at the wikipedia entry and found – somewhat to my disappointment! – that it covered all the areas I mentioned, including the test score results and the IAF example. Incidentally, Kahneman’s very readable classic article where he talks about the IAF pilots, is widely available online:

Kahneman, D. & Tversky, A. (1973). On the psychology of prediction, Psychological Review, 80, 237-251

It doesn’t cover much mathematical ground though, just an observation that regression to the mean is at play. For something meatier, with actual data of US pilots, this is fun: http://economics-files.pomona.edu/GarySmith/flightTests.pdf

I wonder if Ritchie is confusing Kahneman and Tversky’s work on regression to the mean (specifically, as it affects heuristics, rather than any modelling of long-term trends), which formed a small part of their wider work on cognitive biases, and the work on prospect theory they got the Nobel for.

16. @ MBE
Thanks, but aaaargh! I doubt that I am competent to completely rewrite Wikipedia.