Cause And Effect: The Revolutionary New Statistical Test That Can Tease Them Apart

Statisticians have always thought it impossible to tell cause and effect apart using observational data. Not any more.

One of the most commonly repeated maxims in science is that correlation is not causation. And there is no shortage of examples demonstrating why. One of the most famous is the case of hormone replacement therapy, which was studied by numerous epidemiologists at the end of the last century.

These studies showed that women who took hormone replacement therapy had less chance of developing heart disease. Naturally, doctors suggested that hormone replacement therapy somehow protected against heart disease.

That turned out to be an erroneous conclusion. Later studies showed that women who took hormone replacement therapy were likely to be from higher socio-economic groups with higher incomes, better diets and generally healthier outcomes. It was this that caused the correlation the earlier studies had found. By contrast, proper randomised controlled trials showed that hormone replacement therapy actually increased the risk of heart disease.

In the absence of controlled trials, statisticians have widely assumed that it is impossible to determine cause and effect from an observed correlation alone. Does Y cause X or X cause Y? The apparent symmetry of this scenario seems to exclude the possibility that any statistical test could tease them apart.

But in the last few years, statisticians have begun to explore a number of ways to solve this problem. They say that in certain circumstances it is indeed possible to determine cause and effect based only on the observational data.

At first sight, that sounds like a dangerous statement. But today Joris Mooij at the University of Amsterdam in the Netherlands and a few pals, show just how effective this new approach can be by applying it to a wide range of real and synthetic datasets. Their remarkable conclusion is that it is indeed possible to separate cause and effect in this way.

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The results make for interesting reading. They say the additive noise model is up to 80 per cent accurate in correctly determining cause-and-effect. And they say that the method is robust against small perturbations of the data that can arise from the way it is handled statistically. “Our empirical results provide evidence that additive-noise methods are indeed able to distinguish cause from effect using only purely observational data,” they conclude.

That’s a fascinating outcome. It means that statisticians have good reason to question the received wisdom that it is impossible to determine cause and effect from observational data alone.

It’s worth pointing out that this applies only in the very simple situation in which one variable causes the other. But of course there are plenty of much more complex scenarios where this method will not be so fruitful.

Nevertheless, this is likely to be a powerful new addition to a statistician’s armoury. There are many situations in science where controlled experiments are simply not possible because they are too expensive, unethical or technically impossible. In those situations, the additive noise model could be a game-changer.