an autodidact meets a dilettante…

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some thoughts on regression to the mean and what causes what

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Regression effects are ubiquitous, and so are misguided causal stories to explain them. Daniel Kahneman

Canto: So here’s an interesting thought, which in some ways is linked to the placebo effect and our attributing recovery from an illness to something we ate, drank or did, rather than to the silent and diligent work of our immune system. You know about the regression to the mean concept?

Jacinta: Of course. It’s a statistical phenomenon that we tend not to account for, because we’re always looking for or imagining causal effects when they don’t exist.

Canto: Well, they do exist but we attribute the wrong causal effects – we don’t account for ‘bad luck’, for example, which of course is caused, usually by factors we can’t easily uncover, so for convenience we give it that name. For example, a golfer might be said to have had an unlucky day with the putter because we observe that she she went incredibly close to dropping a number of difficult long putts, but none of them went in, so she made five over par instead of even. Of course every one of those failed putts was caused – one because her aim wasn’t quite true, another due to a tuft of grass, another because of a last moment gust of wind and so on… 

Jacinta: And some of those causes might be deemed unlucky, because on a less windy day, or with a better maintained green, those putts might’ve gone in.

Canto: Okay okay, there is such a thing as luck. But luck, I mean real luck, like the effect of a sudden gust of wind that nobody could’ve factored in, tends to even itself out, which is part of regression to the mean. But let me get back to illness. Take an everyday illness, like a cold, a mouth ulcer (which I suffered from recently)…

Jacinta: Or a bout of food poisoning, which I suffered from recently…

Canto: Yes, something from which we tend to recover after a few days. So the pattern of the illness goes something like this – Day 1, we’re fine. Day 2, we feel a bit off-colour. Day 3 we definitely feel much worse. Day 4, much the same. Day 5, starting to feel better. Day 6, definitely a lot better. Day 7, we’re fine. So it follows a nice little bit of a sine wave – two peaks and a trough – as shown above. 

Jacinta: So you’re saying that getting back up to the peak again is regression to the mean?

Canto: Well, sort of, but you’re getting ahead of me. Maybe it isn’t precisely, because a mean is the midpoint in a fluctuation between two extremes. Sort of. Anyway, let me explain. When you’re ill, you can choose to ride it out, or you can go to a doctor, or take some sort of medication, or some concoction recommended by a friend, or a reflexologist, whatever. But here’s the thing. You’re not likely to go to the doctor/acupuncturist/magus on day 2, when you’re just starting to feel queasy, you’re much more likely to go when you’re at the bottom of the trough, and then you’ll attribute your recovery to whatever treatment you’ve received, when it’s really more about regression to the mean. Sort of.

Jacinta: Hmmm. I agree that we’re unlikely to rush to the doctor or even the medicine cabinet when we’re just feeling a bit queasy, but that’s probably because experience tells us we’ll feel better soon – that maybe we’re already at the bottom of a little trough. But when we start going into a deeper trough, naturally we start getting worried – maybe it’s pneumonia, or tuberculosis…

Canto: Or diphtheria, malaria, typhoid, cholera, bubonic plague, acute myeloid leukaemia….

Jacinta: Don’t mock, I’ve had all of those. But it’s interesting to think of illness and wellness in this wave form. I’m not sure if it works as regression to the mean. Because wellness is just, well, feeling well. Feeling ‘normal’ or okay. We don’t tend to feel super-well – do we?

Canto: You mean you don’t believe in biorhythms? So you think the line pattern would be like, a straight horizontal one with a few little and big troughs here and there, and then finally off the cliff and straight down to death?

Jacinta: Well, no, isn’t it a slow decline into second childhood and mere oblivion – sans teeth, sans eyes, sans taste, sans everything?

Canto: Haha well not so much with modern medicine – though my hearing’s starting to go. But one of them-there invisible implants should fix that, at a price. But you’re probably right – what we call wellness at sixty is a lot different from the wellness we felt at twenty, but we’re probably lucky we can’t feel our way back to that twenty-something feeling. But getting back to the case of the person who applies a treatment and then gets better, there are, I suppose, three scenarios. The treatment caused the improvement, the treatment had no effect (the person improved for other reasons – such as our super-amazing immune system), or the treatment actually had a detrimental effect, but the person got better anyway, probably due to our wondrous immune system.

Jacinta: So that’s where the placebo idea comes in. And our tendency to over-determine for causality. You mention something like a cold, which is generally a viral infection, and mostly rhinoviral. The symptoms, like a runny nose and a sore throat, are actually caused by a mixture of the virus itself and the immune system fighting it, but mostly the latter….

Canto: Yeah, is that about antigens, or antibodies, I always get confused…

Jacinta: Well, it’s very very complicated, with T cells, immunoglobulin and whatnot, but essentially antigens are the baddies which trigger an antibody response, so antibodies are the goodies. So, if someone has a cold then unless they know their immune system is compromised in some way, the best thing is to let their immune system do its job, which might cause a few days’ discomfort, like extra phlegm production as the system, the antibodies or whatever, attempts to expel the invaders.

Canto: Yes, but the immune system is invisible to us, and is vastly under-estimated by many people, who tend to like to see something, like a big bright red pill, or a reflexology foot massage, or a bunch of needles needling their chi energy points, or unblocking their chakras…

Jacinta: Can they see their chakras?

Canto: No, but the magus can, with his various chakra-probing methods, and aural and oratorical senses developed over a lifetime – that’s why he’s a magus, dummy.

Jacinta: Yeah, and I’m sure we can all feel when our chakras are unblocked. It’s sort of like body plumbing.

Canto: So, getting back to reality, there is definitely something like this regression to the mean, to our own individual ‘normal’, but maybe ever-declining physical and mental state, that our wonderful immune system helps us to maintain, a system we rely on more than we realise….

Jacinta: Yes, but you know, it’s good that we don’t realise it so much, because think of all the acupuncturists, Alexander technicians, anthroposophicalists, antipharmaceuticalists, aromatherapists, auriculotherapists and ayurvedicists whose jobs might be on the line – and that’s just the A’s! Then we have the baineotherapist, the bead therapists and the bowen therapists, not to mention the chakra scalpel weaponmasters… can you imagine all those folk not being able to make a living?

Canto: Okay, that’s enough. It truly is a sad thing to think upon, but never fear, your horror scenario will never eventuate, my faith in human nature tells me….