The danger of specious correlation

Human foibles

Humans biased towards causal explanations

Most readers will know that correlation does not, in itself, indicate cause.

I concluded in recent post that phoney statistics are a common cause of the erroneous conclusions we and others we rely on to explain the world, the economy or the markets and also to make forecasts or predictions. We rely on them to our peril. I mentioned in passing that our mistaken conclusions can also stem from our tendency to use correlation as a stand in for cause. Today’s post is all about correlation and cause.

Take a look at the following chart. It overlays two charts with the red y scale on the left and the black y scale on the right. It accompanied a discussion suggesting certain conclusions about the relative performance of the Toronto composite index (TSX) and the S&P 500 to inflation.

This type of chart is designed to create a visual impression of correlation and to suggest a causation interpretation. Overlaying two charts to suggest correlation in this fashion is very common in finance and economics. You see them every day. They are mostly useless.

Don’t bother trying to figure out an interpretation of the chart. Just accept that they are offered to us all the time. We are suckers for these kinds of charts. And, we rely on them to our peril. Let me explain.

Daniel Kahneman, a psychologist who has won a Nobel Prize in economics, tells us that as humans we are strongly biased towards causal explanations. This explains why we have a problem with charts like this. Kahneman, D. (2011). Thinking, Fast and Slow. P183.

A stupid example

Take a look at the following chart. It is constructed in the same way as the TSX/S&P 500 chart above. It makes just about as much sense:

A test for our readers

Do you think you are too smart to make this mistake?

Let’s try a simple test given to us by Daniel Kahneman. You will probably agree that the correlation between the intelligence scores of spouses is less than perfect. Even if you reflect on it for a moment you will probably find it perfectly true and obvious. Men and women are not always likely to marry a spouse of exactly the same intelligence.

Now let’s see whether you agree with the following: Highly intelligent women tend to marry men who are less intelligent than they are. If you reflect for a while you may still wonder if it’s true and, if so, why it’s true. Are you thinking that highly intelligent women will likely choose partners who less likely to compete with them. 

Interestingly the two statements are saying the same thing and are algebraically identical. It is mathematically inevitable that highly intelligent women will marry husbands who on average will be less intelligent than they are. Of course the reverse is true also. (Kahneman, 2011)p.183.

What we draw from this intelligent woman example is that we humans tend to look for causal explanations even when there is a simple mathematical explanation.

Another example

Kahneman gives another imaginary example. He suggests a made-up headline in a newspaper: “Depressed children treated with an energy drink improve significantly over a three–month period.” He tells us that the headline is true even though the improvement will have nothing to do with the drink. The children will improve because the mood of depressed children will regress toward the mean i.e. normal mood, in time anyway.

Legalization of marijuana

There is a billboard near where we live that says that states that have legalized marijuana experienced an up to 12% reduction in thefts. The sign is obviously there to support a legalization campaign. With a moment’s thought a narrative comes to mind: Illegal marijuana causes crime and legalization will help to stem this. And what about the qualification ‘up to’? What do you think?

The billboard makes no claim of causation but certainly invites us to jump to that conclusion. There may be data mining at work. As well, thefts may have gone down for entirely different reasons. We don’t need to get to the bottom of it here. We just need to be conditioned to be alert to these kinds of correlation/causation claims.


Now go back to look at the TSX/S&P 500 correlation to inflation chart. Do we still think we can draw any sensible conclusions just by looking at the chart? And, if the commentary accompanying the chart offers a persuasive narrative as to what the chart is telling us, we should now be protected against accepting any of this bunk at face value. And remember, this is all because we have a behavioral bias toward causal explanations.


Other posts on investment psychology

This post, which is really about faulty inductive reasoning, is part of a series on investment psychology. Readers are invited to read Investment psychology explainer for Mr. Market – introduction .This will give you a better understanding of some of the terms and ideas and give you links to other posts in the series.

Beyond the series of posts on investment psychology, there is also the Motherlode, Part 2: Human Foibles and Investment Decision Making

And specifically to look further into faulty inductive reasoning check out Chapter 16. We Overgeneralize and Find Causes


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