Critical Thinking Toolkit: The Correlation-Causation Fallacy

Here, I’d like to discuss two interconnected tendencies we human beings have. We like looking for patterns, and we like explaining things. These are both incredibly important features of the way we think as humans. But they are not identical. It is easy to get them confused, and we often do get them confused. This is a problem, because any error in critical thinking allows opportunities for our personal biases to creep in. For example, suppose I find a patter, and I want that pattern to not be a coincidence, but it actually the pattern just is a coincidence. Then if I come to believe that the pattern I found is not a coincidence, I now believe something false that might give me a lot of problems later on.

What I am referring to is the so-called correlation-causation fallacy. The idea here is that just because you find a correlation between two things (a pattern) that does not mean there is causation between them (a cause-and-effect relationship). I find it a little difficult to explain correlation and causation in any simpler terms than that, because these are both hard to define without using even weirder language. What I’ve decided will be more helpful is a list of examples with some discussion. Perhaps not all of them will make sense – but I hope some of them will. And if I’ve missed any good examples, it isn’t too hard to find lots of examples with a quick google search.

With all that said, let’s begin with some examples.

Example 1: A Silly Example

I dug around the internet for a bit to find a silly example of the correlation-causation fallacy, and found this one. There is a significant mathematical correlation between the number of movies Nicolas Cage stars in correlates with the number of people who drown by falling into a swimming pool. This means that you could write down an equation that does a really good job of predicting one based on the other. Should we then infer that those people fell into those pools because of the movies, or that Cage stars in movies in honor of victims of pools? Surely not. It is mere coincidence that the data line up well between those two counts.

Example 2: A Mathematical Example

Perhaps you’ve seen a “trick question” like this before:

Which number comes next in the pattern 1, 2, 3, …?

Surely, you think, it must be 4. But actually, it might be 5, if the pattern is really that 1+2=3, so 2+3 must be the next number. It could, in fact, be literally any number at all. Mathematically, I can write down an equation that would spit out 1, 2, 3, 123, or 1, 2, 3, -7, or anything at all you’d like it to spit out. It actually isn’t terribly difficult either – you just have to use polynomials in a clever way (if you’re a mathematically inclined reader, find a way to produce such sequences on your own as a mental exercise).

The point that is generally taken from this mathematical fact is that any finite collection of data can be explained an infinite number of different ways. This makes the same basic point that the correlation-causation fallacy wants to make. Just because you think you see a pattern, doesn’t mean that pattern is actually there. There could be no pattern at all, or it could be a quite different pattern than you thought.

Example 3: The President

This one is a rather famous example, and in fact has its own Wikipedia article, which I will link to a bit later. Your goal is to guess which American President I am talking about.

  • Elected to congress in ’46 and to the presidency in ’60
  • Played a significant role in a key step towards civil rights for African American people.
  • Lost a son while living in the White House.
  • Assassinated by a gunshot to the head sitting next to his wife.
  • His successor was President Johnson.

Which President do you think I’m talking about? The truth is, surprisingly, I didn’t give you enough information, because all of those facts are true of both Abraham Lincoln and John F. Kennedy. In fact, there are a great many more similarities between them. You can check them out yourself. Should we then assume that because there are a shocking number of commonalities between the two, that one of them is a myth/legend based on the other? That is, did someone use the story of Abraham Lincoln to invent a story about JFK, or vice versa? Although I’ve never met either of these people, and never could, I’m about as sure as I can be that both of them really did exist and really did have these features.

This is a sort of historicized version of the correlation-causation fallacy, or perhaps you could call it a post hoc ergo propter hoc fallacy, which is a sort of after-therefore-caused-by fallacy. Regardless of how you want to classify this fallacy, I think it illustrates the main points about correlation-causation fallacies.

  • Correlation: The number of common features shared by Abraham Lincoln and John F. Kennedy is extremely surprising.
  • Causation: None of these common features have any cause-and-effect connections between them. The features they have in common are coincidental, not real.

An Example with Real Causation: Based On a True Story

I’ve given a couple examples that illustrate the distinction between correlation and causation. But, of course, often there really is causation behind a correlation. To use an example, consider fictional movies that are ‘based on a true story’. Like the example of Abraham Lincoln and John F. Kennedy, the real story and the movie version will have a long list of very detailed parallels. But this time, there will be a clear reason why – because we know the movie is based upon a real person. We know which one came first, and we know how the movie came about (we could talk to the director). By comparing and contrasting based-on-a-true-story narratives with the Lincoln-Kennedy coincidence should begin to give a feel for when a correlation should make us think there is causation going on versus when we should treat the correlation as a coincidence.

Example 5: “Pagan Origins of Christianity”

I’ve seen a fair number of secular people try to claim that the way Christians view Jesus today is just an amalgamation of various stories of pagan gods and/or goddesses. Mithras is a key example that is often used, but many others are mentioned as well. The claim is that, since the supposed lives of these pagan figures share many key similarities with what the four gospels say about Jesus, that the people who wrote the four gospels must have just “copy-pasted” that information over onto Jesus’ life.

Now, I won’t go here into whether or not the lives of these figures actually are similar. From everything I’ve seen, they aren’t at all similar, or are only trivially similar, just as there are trivial similarities between you and any random stranger you don’t know. There ought to be an obvious correlation-causation fallacy going on here, just like with Abraham Lincoln and John F. Kennedy. Just because there are similarities does not mean there is a connection! To show some kind of historical copy-paste like that, you not only have to find key similarities, you also need to find hard evidence that there is a cause-and-effect connection between those. For instance, do the gospel writers have a compelling motive to steal those stories? No, they were Jewish monotheists and would have found paganism repulsive to its very core. Why then would they use it in their Jesus story? That doesn’t make sense – if they were making up a story, they would have copy-pasted from other religious stories they actually liked – say Moses, Elijah, or King David. Other potential motives don’t seem to check out. So, it seems rather unlikely that the gospels were made up out of thin air by stealing bits and pieces from pagan mythology. This is correlation without causation.

There is a similar problem with some people who think Christmas or Easter have pagan origins. I’ll stick with Christmas. Whenever someone tries to argue for this position, often they will list a bunch of similarities between some pagan holiday (perhaps Saturnalia) and Christmas as proof. But that is a textbook definition of a correlation-causation fallacy! That’s not good enough. In order to show an actual causal connection, you’d have to show some kind of cause-effect connection that shows how one became the other. For instance, are there early Christian documents that state a link between pagan holidays with Christian ones?

For instance, what about the day of Christmas, December 25th? You can find a lot of people saying that the reason this date was chosen for Jesus’ birth is because of ancient pagan holidays celebrated on that day. But this just isn’t why Christians came to believe this dating for Jesus’ birth – it is a correlation, but not a causation. The real reason is, to be fair, equally strange, but it isn’t pagan. Jewish believers in this time frame tended to believe that important religious figures would be conceived on the same day as they died, that this sort of ‘perfect symmetry’ ought to exist for key figures in human history. So, if they could just figure out what day Jesus died, then they’d (according to this view) also know the day he was conceived, and so just add 9 months to that and you get Jesus’ birthday. Some Christians from a couple hundred years after Jesus’ death estimated that Jesus was crucified on March 25th, hence he would have been conceived on that day, and then born 9 months later on December 25th. This is strange, and we of course no longer believe in this reason, but this origin definitely is not from a pagan holiday. The idea of symmetry between conception and death was a Jewish idea, not a pagan one, so there seems to be no pagan connection.

Conclusion

The big takeaway here is that sometimes, patterns and similarities can be deceiving. It is not enough to find patterns if you want to show that two things are connected – you must show why or how they are connected in order to convincingly show that they are connected. But this does not discount the value of pattern-hunting. On the contrary, we should always be keeping our eyes out for patterns, for very often there is a truth behind the pattern. The point is that we must be humble when we find patterns and not jump to conclusions too quickly. If these examples weren’t helpful enough, it wouldn’t be hard to find different ones that might be more helpful.

2 thoughts on “Critical Thinking Toolkit: The Correlation-Causation Fallacy

    1. If the argument is “because these graphs look similar, therefore man-made climate change” then yes that’s a good example. However, proponents of that position do not argue in that form, and so this appears to be a straw man fallacy. Regardless of whether or not a person agrees with the position, the argument for man-made climate change is usually presented as an inference to the best explanation, and in this form no fallacy is committed. To rebut an inference to the best explanation, one must present an explanation which better fits the available evidence or present new evidence that shifts the balance of likelihood in favor of a different explanation

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