Correlation implies causation (logical fallacy)

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Correlation implies causation, also known as cum hoc ergo propter hoc (Latin for "with this, therefore because of this") and false cause, is a logical fallacy by which two events that occur together are claimed to be cause and effect.

For example:

Teenage girls eat lots of chocolate.
Teenage girls are most likely to have acne.
Therefore, chocolate causes acne.

This argument, and any of this pattern, is an example of a false categorical syllogism. One observation about it is that the fallacy ignores the possibility that the correlation is coincidence. We can pick an example where the correlation is as statistically "robust" as we please, but we still cannot assume one factor causes the other. If chocolate-eating and acne were strongly correlated across cultures, and remained strongly correlated for decades or centuries, it may not be a mere coincidence. However, in this particular example, the last statement is a logical fallacy because it ignores the possibility that a third factor may be the cause of eating chocolate and having acne (e.g. being young). See joint effect.

Another important consideration is the presence or absence of a known mechanism which may explain how one event causes the other. Using the above example, if chocolate contains large quantities of hydrogenated fats, or trans-fatty acids, and if those have been shown to clog pores and thus cause acne, then the link between chocolate and acne is more believable. A counter-example would be astrology, where there is no convincing known mechanism to describe why personality would be affected by the position of the stars. Of course, the absence of a known mechanism doesn't preclude the possibility of an unknown mechanism.

For one event to be the cause of another it must happen first. In some cases the precipitating event may happen so quickly before the result, or may overlap the result in time, so they are said to occur simultaneously. However, the precipitating event can't happen after the result, for example, by concluding that a current increase in population caused a baby boom many years ago.

Another example:

Ice-cream sales are strongly (and robustly) correlated with crime rates.
Therefore, ice-cream causes crime.

The above argument commits the cum hoc ergo propter hoc fallacy, because it prematurely concludes ice cream sales cause crime when a more plausable explanation is that high temperatures increase crime rates (presumably by making people irritable) as well as ice-cream sales.

Another possibility in correlated factors is that the direction of the causation may be wrong as stated. For example:

Gun ownership is correlated with crime.
Therefore, gun ownership leads to crime.

In the above example, because it may be the case that an increase in crime leads to more gun ownership by concerned citizens who do not commit crimes, we cannot conclude from the first statement alone that gun ownership causes crime. See wrong direction.

The statement "correlation does not imply causation" notes that it is dangerous to deduce causation from a statistical correlation. If you only have A and B, a correlation between them does not let you infer A causes B, or vice versa, much less 'deduce' the connection. But if there was a common cause, and you had that data as well, then often you can establish what the correct structure is. Likewise (and perhaps more usefully) if you have a common effect of two independent causes.

But while often ignored, the advice is also overstated, as if to say there is no way to infer causal structure from statistical data. Clearly, we should not prematurely conclude something like ice-cream causes criminal tendencies. We expect the correlation to point us towards the real causal structure. Again, the tendency is to conclude robust correlations imply some sort of causation, whether common cause or something more complicated involving multiple factors. Hans Reichenbach suggested the Principle of the Common Cause, which asserts basically that robust correlations have causal explanations, and if there is no causal path from A to B (or vice versa), then there must be a common cause, though possibly a remote one.

Reichenbach's principle is closely tied to the Causal Markov condition used in Bayesian networks. The theory underlying Bayesian networks sets out conditions under which you can infer causal structure, when you have not only correlations, but also partial correlations. In that case, certain nice things happen. For example, once you consider the temperature, the correlation between ice-cream sales and crime rates vanishes, which is consistent with a common-cause (but not diagnostic of that alone).

In statistics literature this issue is often discussed under the headings of spurious correlation and Simpson's paradox.

David Hume argued that any form of causality cannot be perceived (and therefore cannot be known or proven), and instead we can only perceive correlation. However, we can use the scientific method to rule out false causes.

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Humorous examples

An entertaining demonstration of this fallacy once appeared in an episode of The Simpsons (Season 7, "Much Apu About Nothing"). The city had just spent millions of dollars creating a highly sophisticated "Bear Patrol" in response to the sighting of a single bear the week before.

Homer: Not a bear in sight. The "Bear Patrol" is working like a charm!
Lisa: That's specious reasoning, Dad.
Homer: [uncomprehendingly] Thanks, honey.
Lisa: By your logic, I could claim that this rock keeps tigers away.
Homer: Hmm. How does it work?
Lisa: It doesn't work; it's just a stupid rock!
Homer: Uh-huh.
Lisa: But I don't see any tigers around, do you?
Homer: (pause) Lisa, I want to buy your rock.

Another example is the Witch hunting scene from Monty Python and the Holy Grail:

Sir Bedevere: Tell me, what do you do with witches?
Mr. Newt: Burn them!
Sir Bedevere: And what do you burn apart from witches?
Peasant #1: More witches! [Peasant gets slapped]
Peasant #2: Wood!
Sir Bedevere: So, why do witches burn?
Peasant #3: .......... 'Cause they're made of... wood?
Sir Bedevere: Good! So how do we tell whether she is made of wood?
Peasant #1: Build a bridge out of her!
Sir Bedevere: Ahh, but can you not also make bridges out of stone?
Peasant #1: Oh ya.
Sir Bedevere: Tell me, Does wood sink in water?
Peasant #1: No, no, it floats. Throw her into the pond!
Sir Bedevere: No, no. What also floats in water?
Peasants yell various answers: (Bread!) (Apples!) (Very small rocks!) (Cider!) (Gravy!) (Cherries!) (Mud!) (Churches!) (Lead! Lead!)
King Arthur: A duck!
Sir Bedevere: Exactly! So, logically.....
Peasant: If she weighs the same as a duck, she's made of wood.
Sir Bedevere: And therefore?
Peasant: A Witch!

A further often-quoted example is the (unverified) claim of a strong causative correlation between teachers' pay and the volume of whiskey sales.

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See also

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External links

he:קום הוק ארגו פרופטר הוק nl:Cum hoc ergo propter hoc fi:Cum hoc ergo propter hoc

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