Chocolate: Correlation, Causation and Misinformation

The headlines today (and my Twitter and Facebook feeds) tell me that if I eat chocolate, I’ll stay slim… but only if I eat chocolate regularly. Good news? No, not really. It’s just the old mistake of confusing correlation with causation. Drop that chocolate bar, and read on.

Several news outlets are reporting that a study involving over 1,000 participants in the US revealed that people who eat chocolate several times a week are slimmer than those who only eat it occasionally. Apparently, the relationship holds even after factors like levels of exercise are taken into account, and is independent of the amount of chocolate eaten.

This finding has led to headlines like ‘Chocolate may help people slim’ in the BBC news website, Chocolate lovers tend to weigh less’ over at Reuters, or ‘A Chocolate a Day to Get Slimmer?’ in the Wall Street Journal. Moreover, judging by the posts on Facebook and Twitter, the news travelled the world. A typical case of misinformation travelling wide and fast over the Internet – like Chinese Whispers.

So, should you reach for the chocolate bar to loose that love handle?

Of course not.

The fact that slim people may (or not) eat chocolate more frequently than their overweight counterparts does not prove that chocolate helps you loose weight. There is a correlation, but not a causal relationship.

A correlation is the extent to which two variables are related to each other. That is, the extent to which they occur together. Like flowers and Spring – they occur together. They are correlated. But it can not be said that flowers bring the Spring.

A causal relationship is when the change in one variable leads to a change in another. Like the temperature of water and the speed at which ice melts – change the former and the latter will change, as well.

I did NOT read the paper reporting on the study – if you are interested, it is available here (though you may need to pay in order to access it). But it strikes me as reasonable that slim people will eat chocolate more regularly than overweight people simply because they are not trying to loose weight. In other words, if you are overweight, already, and trying to loose weight, you may be eating less chocolate than your slimmer counterparts, all else equal. That’s because the slimmer ones are not trying to reduce their calorie intake, whereas the heavier ones are.

So, there is correlation between being slim and eating chocolate frequently; but the causal relationship is not:
Eating chocolate frequently => loosing weight
Rather, it should be:
Trying to loose weight => eating chocolate less frequently

The news about the chocolate / weight study reminded me of another one widely reported when I was in University, back in the early 1990s.

Back then, a study showed that, whenever the fire brigade was called to put out a fire, the value of damages (and, thus, insurance claims) was higher than when they stayed away.

Did this finding mean that the brigade was a fire hazard and that you should avoid calling them? Certainly not.

The reason damages were higher when the fire brigade was involved is that firefighters were called to tackle large fires, to start with. So, we have:
Large fires => call the fire brigade
Large fires => large damages

But it is NOT true that fire brigade => large damages.

Another case of correlation mistaken for causation is the old storks and babies tale.

In this part of the world, storks are around in the Spring. Spring is also the time of the year when more babies are born. Are births related to the influx of storks? Correlation is not causation.

What other misleading correlation / causation stories have you come across?