Tuesday, January 26, 2010

A Beguiling Fallacy

Correlation implies causation: it is a subtle, beguiling fallacy, often persuading to foolish or dangerous conclusions.

Correlation is a statistical term. It means that changes in two sets of measurements appear to be linked: variation in one is copied by variation in another.
For example, in Britain, over the next three months the daily duration and intensity of sunshine will increase, and the mid-day temperature will increase too. Insolation data is correlated with temperature data. No surprise - we know sunshine warms us; if no correlation were observed then something would be seriously wrong.

But consider this second example. Over the past half century the human population of 'Oman has increased approximately four-fold, while the population of red deer in Scotland has increased by a comparable factor. These two population data-sets may show a good mathematical correlation, but few would conclude that they are causally related: it is hard to see why they should be.

Similarly I'm sure it would be possible to show good correlation between the length of womens' skirts and the prevalence of tuberculosis in Britain in the past century - both have reduced progressively. Most people would need a lot of convincing that one caused the other.

Correlation is no proof of causation.
It is perhaps the most important principle to remember when considering such statistics. It is especially important when they are used to support particular political, social and economic theories. 

We know that a child's chance of a university education increases with the family income. How you interpret this depends on your point of view. If you vote labour you may argue this proves it is right to tax the rich and give to the poor. If you favour the other team you might contradict this argument, and identify parental failings which inflict both family poverty and poor educational progress on their children.

It is especially difficult when the statistics match what we want to believe. So it is reasonable to predict that surgical bypass of small intestine will reduce food absorption and cause weight loss. Operations are done and patients lose weight. The theory is right!
Umm, no, more detailed studies suggest reduced appetite is a consequence of the operation, and accounts for the weight loss.

But causation and correlation can flirt and intrigue. 

At one time it was argued that the correlation between cigarette smoking and lung cancer did not prove a causative link. Maybe genes causing lung cancer also increase the desire to smoke tobacco. It was right to question the conclusion that smoking causes lung cancer, although most recognised special pleading, suspecting [rightly] the influence of tobacco money. Then we observed that doctors who stopped smoking reduced their cancer risk. Eventually the sheer mass of observations and laboratory work made it impossible to deny that in this case the correlation did indeed arise from causation. 

Correlation may suggest causation, but the link must be proved by other means.

Many argue that climate change is the most important problem we must manage. In particular Homo must reduce the amount of carbon dioxide waste dumped into the atmosphere, whatever the cost.
This prevailing opinion is based on a correlation perceived between two sets of data: mean global temperatures and atmospheric carbon dioxide concentration. Both sets show progressive increases during the past century, and carbon dioxide is a greenhouse gas - it has molecular vibration modes which capture radiant heat energy.
So there is a correlation, and a theory which explains possible causation. So the theory is supported, if not proved?

Umm, no again. Studies over much longer periods fail to confirm correlation between global temperatures and atmospheric carbon dioxide. And in the past decade global temperatures have tended downwards, while carbon dioxide has continued to increase.
Solar activity varies. Solar activity increased during the past century, especially in its second half. Since the turn of the century solar activity has reduced. Here is an alternative correlation, between solar activity and global temperature, and again there are reasons to associate the two, and maybe infer causation.

Umm, no again. Correlation still does not prove causation. If present trends in solar activity and global temperature continue then we may observe correlation during increase and decrease. That would be a stronger argument, but extended observations over several solar activity cycles would be needed before probability approaches proof.

But right now I would strongly advise our leaders to reconsider the need to borrow one hundred billion pounds to install thousands of wind turbines in our seas. In twenty years time that may prove to be a most foolish decision. By then we may be worrying about global cooling. [Even if warming picks up again, it is still a stupid decision.]

Correlation does not prove causation. It cannot be repeated too often or too loudly.

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