What is the difference between correlation and causation?

Question

What is the difference between correlation and causation? Pirates and Global Temperature Example

For example, how do we know when we're dealing with correlation only and not also causation here?

^{more examples: SpuriousCorrelations.com}

What Certain Philosophers Seem to Hold Regarding This

It would seem that

• Hume would say
  correlation ≡ causation.
• Aristotle would say that in general
  correlation ≢ causation
  and that
  causation ⇔ correlation
  only if we are not dealing with chance events.

^{("≡" means "is identical to," and "⇔" means "implies each other.")}

Answer 1

What is the difference between correlation and causation?

• Correlation is a descriptive relationship, all it says is: here are a bunch of measurements of two (or more variables) and there is a specific numerical relationship - that the correlation coefficient is above a certain threshold. Formally speaking correlation doesn't indicate anything more than that.
• Causation on the other hand is an explanatory relationship: It provides a logical relationship between the variables, which one should be able to generalize to cases beyond the set of measurements from which we drew the initial hypothesis. In your Pirates/Temperature graph case, one would have to provide a detailed explanation/mechanism of what is it exactly about pirates that kept global temperatures down? Was it their clothes? Was it their funny accents? Was it their obnoxious parrots? Then would should be able to generalize this mechanism to other cases. Let's suppose that on deeper analysis, I decide that it was their accents that were keeping global temperatures low. I could then generalize this by having normal non pirate people speak with a pirate accent, and measure the effect it has on global warming.

Causation is hard to define concisely, but here is a recent definition from Nancy Cartwright (See also this post):

C causes E if and only if C increases the probability of E in every situation which is otherwise causally homogeneous with respect to E. (Causal Laws and Effective Strategies, 423)

The key word here is "in every situation". Correlation doesn't involve every situation, only the data we have right now. Causation on the other hand involves every situation, including many not included in our current data. Notice the probabilistic definition, to allow for statements like "Smoking causes cancer" to be true even though we have met one or two heavy smokers who don't have cancer.

For example, how do we know when we're dealing with correlation only and not also causation here?

This is still an open question. Resolving it would have serious implications for philosophy of science (with regards to the demarcation problem and to the problem of induction).

To some extent, Karl Popper's falsificationism was an attempt to solve this problem. Before that, Logical positivists verificationism was problematic exactly because correlation doesn't imply causation, and one could verify all sorts of pseudo-scientific theories, provided they dug up enough suitably correlated data-points. However, falsification doesn't solve the problem completely.

Now given that two data sets A & B are correlated, lets look at the possibilities of why they are correlated:

1. Their correlated is purely coincidental.
2. A causes B.
3. B causes A.
4. A and B are both caused by a third variable C.

Falsification allows us to rule out cases like (1): In your pirate example, if one had a way of suddenly increasing the number of pirates, or managed to get everybody to starting speaking like a pirate for a few years, they would notice that after 10 or 20 years, the global average temperatures still didn't go down, so we can safely throw away the hypothesis that pirates have some causal relationship on global temperatures.

But that leaves us with (2), (3) and (4). For these, there are some heuristics for discerning between the possibilities, but no sure fire method.

• Time is a factor: In any real world physical case, cause always precedes effects, so if your data is timestamped with enough precision, you could use that as an indicator. This would allows to decide between (2) and (3), but still leaves us undecided between which ever one of those we select and (4).
• Generalization: If your explanatory theory explains only the two variables you have and nothing else, than you might want to dig deeper. A good theory should be able to explain other related questions, not just those posed by the data at hand. For example, although a causal relationship between pirates and climate might explain the data you have in your graph, it won't ever explain anything else. Explaining climate change using the concept of greenhouse gases also explains other phenomena, for example why greenhouses work, and why Venus is so much warmer than Earth.
• Does your explanation fit with other already existing theories? Is there a more general pattern that these theories follow? If pirates are linked to climate change, can we also link the decline in gladiators to water pollution?

Answer 2

Correlation and causality are not the same:

Correlation is a fact which stems simply from observation - like in your nice example.

On the opposite, causation answers in addition the question: Why?

To answer the Why-question means to give an explanation for the observation. An explanation should be more general than one specific observation. It should cover several cases, also cases not yet observed (predictive power). The best explanations are scientific theories. They allow to derive a lot of phenomena from few general assumptions.

Unfortunately I do not know a simple and striking definition of causality.

Aside, in your figure 35.000 should be replaced by a different value. Do you use a logarithmic scale?

Answer 3

Take this example: People wearing rain coats, people carrying umbrellas, and rain fall. These three will tend to happen together, or to not happen together. This is correlation.

There are three main cases for causality: The relation between rain and umbrellas is causal. When it rains people get their umbrellas out. There is no causal relationship in the other direction: Carrying an umbrella doesn't cause rain to happen. If you put away your umbrella during the rain, that won't make the rain stop. And the relationship between rain coats and umbrellas is different again: They both have a common cause.

Note that correlation works in both directions: Rain is correlated with umbrellas, and umbrellas are equally correlated with rain. Causality usually is a one-way relationship.

Answer 4

The difference between correlation and causation is best captured by the statement: "Correlation does not imply causation." Causation implies correlation, however the converse is not the case: correlation does not imply causation. That is, there is no way to legitimately deduce (or derive) a cause-and-effect relationship between A and B solely on the basis of an observed association or correlation between them.

The assertion that "correlation implies causation" is a case of the logical fallacy called "questionable cause".

When A and B are correlated, the following options exist:

1. There is no connection between A and B (null hypothesis: H0), i.e. coincidental correlation.
2. A causes B
3. B causes A
4. A and B are caused by a third variable C
5. (A causes B) AND (B causes A): "bidirectional" (A and B cause each other simultaneously) or "cyclic" (non-simultaneous, [A causes B] THEN [B causes A], etc.)

The idea that correlation implies causation is a case of the fallacy "questionable cause", in which two events occurring together are taken to have established a cause and effect relationship.

Questionable Cause Fallacy: "cum hoc ergo propter hoc" = "with this therefore because of this." Note that this differs from the "post hoc ergo propter hoc" (after this therefore because of this), in which an event following another is seen as a necessary consequence of the former event. An example of the "post hoc" fallacy is: "Every morning my rooster crows, then the sun rises. Therefore, my rooster crowing causes the sun to rise."

Correlation (P) cannot possibly imply causation (Q) because "implication" is necessarily something deductive. In logical sense of the term "implies" means "is a sufficient condition for". Therefore the (material) implication in the conditional "if P, then Q" sets up a sufficient condition between P and Q, such that 'P is sufficient for Q', which is equivalent to saying 'Q is a necessary condition for P.' The technical meaning of the material conditional "P implies Q" denoted as P -> Q means "If circumstance P is the case, then Q follows." In this sense of the word "imply," it is always correct to say "correlation does not imply causation." Correlation is a necessary condition for causation, not a sufficient condition!

Moreover, a mere correlation between A and B does not even establish the direction of causality: from the mere fact that A and B are correlated one cannot deduce that A is the cause or the effect and likewise for B.

Answer 5

Correlation is simply a spatiotemporal conjunction of two classes of events. Your pirate vs. global temperature graph is a good example.

Causation is consistent spatiotemporal conjunction of two classes of events. Hypothetically speaking, the number of pirates bears an inverse relationship to global temperature in other worlds as well.

Answer 6

What is the difference between correlation and causation?

The difference is having a model (a.k.a theory).

We can say that A causes B if we can explain why is that the case through logic and reason.

And while causation often creates correlation, it is no means implicit. "Too much of a good thing" is an example of such a paradox, one that everyone knows all too well.

For example, how do we know when we're dealing with correlation only and not also causation here?

We don't. But, since we can't identify the causation, we certainly should not assume one.