Lies, Damned Lies, and Statistics (33): The Omitted Variable Bias, Ctd.

I discussed the so-called Omitted Variable Bias before on this blog (here and here). So I suppose I can mention this other example: guess what is the correlation, on a country level, between per capita smoking rates and life expectancy rates? High smoking rates equal low life expectancy rates, right? And vice versa?

Actually, and surprisingly, the correlation goes the other way: the higher smoking rates – the more people smoke in a certain country – the longer the citizens of that country live, on average.

Why is that the case? Smoking is unhealthy and should therefore make life shorter, on average. However, people in rich countries smoke more; in poor countries they can’t afford it. And people in rich countries live longer. But they obviously don’t live longer because they smoke more but because of the simple fact they have the good luck to live in a rich country, which tends to be a country with better healthcare and the lot. If they would smoke less they would live even longer.

Why is this important? Not because I’m particularly interested in smoking rates. It’s important because it shows how easily we are fooled by simple correlations, how we imagine what correlations should be like, and how we can’t see beyond the two elements of a correlation when we’re confronted with one that goes against our intuitions. We usually assume that, in a correlation, one element should cause the other. And apart from the common mistake of switching the direction of the causation, we often forget that there can be a third element causing the two elements in the correlation (in this example, the prosperity of a country causing both high smoking rates and high life expectancy), rather than one element in the correlation causing the other.

More posts in this series are here.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s