Correlation vs Causation [closed]

Elsewhere on Stack Exchange I came across the following comment.

The sorting is based on values, not family. If you value knowledge, you will be set to Ravenclaw, for example. Needless to say, if your parents value the acquisition of knowledge most and foremost, their children are likely to share those values, but it is not a guarantee. Correlation, not causation.

I stated that this was causation rather then correlation because the commenter is arguing for a cause-and-effect relationship. The fact the cause-and-effect isn't guaranteed doesn't change that. Other comments have not agreed with me, and I thought rather than an off-topic discussion there, I'd ask over here to see if my understanding of causation vs correlation was correct.

• The "correlation, not causation" thing is idiomatic. It just means "that's bad statistics," even if they recognize the minor, indirect causative avenue.
– Chel
Commented Jan 23, 2012 at 1:00
• @Daniel δ: Are you suggesting rdhs needs to back up the meaning of "correlation, not causation" (his assertion that it can be summarised as "bad statistics") or his assertion that it's a common "idiomatic" expression/collocation? Both seem blindingly obvious to me. Commented Jan 23, 2012 at 1:20
• @rdhs, ok, but "it's bad statistics" doesn't make any sense (to me at least) in context. Commented Jan 23, 2012 at 1:39
• @FumbleFingers, yes, causation (of some sort) usually goes with correlation. They are distinct concepts, but in reality often come together. When the commenter said, "correlation. not causation" I understood him to say no causation (of any sort) but just correlation. That's why I thought he was incorrect. What he was actually saying was, only a weak form of causation, not a strong causation. Commented Jan 23, 2012 at 3:50
• This question really ought to be migrated to Philosophy.SE. Commented Jan 28, 2012 at 2:42

You are using cause in a different sense to the quoted comment: the quotation seems to be talking about proximate cause while you are going deeper. The sorting is based on the individual without regard to the effect or not of the parents.

Taller than average parents more often than not have taller than average children: you would regard that as caused by genetics. Similarly, taller than average children more often than not have taller than average parents. Is that causal? Not to mention the Sam Levenson line “Insanity is hereditary — you get it from your kids.”

There is evidence that cities with more storks' nests have more human births. Is that causal or correlation? Is it indirectly causal if both seem to be related to the number of buildings in the city, which gives both storks and people potential places to live?

Ultimately this boils down to how cause is used. It is used differently by different people in different circumstances, which leads to a lot of confusion.

And then there is the xkcd 552 comment

• Are you getting upvoted because you've got a good answer or because you have an XKCD strip? :P If the comment had said ultimate not proximate causation, then I'd agree with your answer. But he said correlation not causation, and I have trouble seeing how that implies what you argue here. Commented Jan 23, 2012 at 1:32
• I think you're right it boils down to how cause is used. The particular case in point is a very borderline one. Do you vote the way you do because your parents vote/voted that way? Most people like to think they make up their own mind - but then again, most people like to think they think, and even that ain't necessarily so... Commented Jan 23, 2012 at 1:32
• @Winston Ewert: Should we describe the fact of my comment appearing directly after yours as correlation or causation? In this restricted context, you were the "ultimate cause" with your original question. Henry's answer was the "proximate cause", but what if I'd pressed return a few seconds earlier instead of fiddling about changing the exact wording? There is considerable overlap between correlation and causation, so it's not a good area to get too hung up on right/wrong interpretations. Commented Jan 23, 2012 at 1:40
• btw - I didn't follow the link (and still haven't), so the answer to your question is because it's a good answer. IMHO, obviously - YMMD. Commented Jan 23, 2012 at 1:42
• @FumbleFingers, I'm not sure how not-clicking on the link establishes that upvotes haven't occurred because of the image. :P Commented Jan 23, 2012 at 2:00

The author of the comment you cite does not seem to be remarking on genetics but rather on indoctrination. Consider one possibility. A child could be raised by parents who fit the author's description and yet, despite the parents' best efforts, turn out to be the sort who despises knowledge. This is obviously unlikely. But it's possible and, no doubt, has occurred. Under such conditions we wouldn't reasonably say that his hatred of knowledge is a result of his parents' love of it (though certainly that happens too). Likewise, even though there are bound to be cases where the parents' love of knowledge literally engenders it in the child ( which, yes, would be cause and effect), the fact that this isn't always the result is enough to prevent us from playing an if-a-then-b tune. The concept of correlation allows for an increased or decreased likelihood without making any such sweeping ascription. There is that which causes, and there is that which increases the odds of a certain outcome. It seems the author is correct in his conclusion.

• How does the fact that the causation doesn't alway happen mean its not causation? Smoking causes cancer, but that doesn't mean everyone who smokes dies of cancer. Commented Jan 23, 2012 at 1:29

There are several different relationships in play in the comment quoted, and like much internet discourse, it's written pretty informally, so it's unclear which of the relationships the commenter argues are causative and which are correlated.

Assuming for the purposes of this answer that your values cause you to be sorted into a particular house (whether with certainty or, since an individual can hold multiple values, with a greater or lesser likelihood), it seems reasonable to say that there is a correlation between the values of your parents and the house that you're sorted into.

It seems less reasonable, mathematically, to say that the values of your parents cause you to be sorted into a particular house. It may be so, but it doesn't follow from the values->house relationship, and we would need more information to ascertain whether there was a causative relationship.

However, English is not mathematics, and it is reasonable, in English, to say that your parents' values have a cause-and-effect relationship with which house you end up in, because parents often pass on their values to their children.

• The question isn't whether we have data to infer the relationship. The question if we infer that the same parents tend to cause the same values which tends to cause the same house, is that correctly labeled causation or correlation? Commented Jan 23, 2012 at 1:29
• In mathematics, that's correctly labeled correlation, because the parents don't directly cause the house. In English, it can reasonably be labeled causation. Commented Jan 23, 2012 at 1:34
• that surprises me. Do you have a reference to back it up? Commented Jan 23, 2012 at 1:35

The short answer: yes, the relation suggested in that comment by Borror is causal.

There can be several kinds of causal relations between phenomena A and B (though C may or may not be causally related):

1. Direct causal relations:

• I ) A causes B (blowing up the earth causes the death of many people).
• II) A is caused by B (the falling of a rock to the ground is caused by gravity).
2. Indirect causal relations:

• I ) A and B are both caused by C (the tsunami and the fires were caused by the earthquake).
• II) A is caused by B through C (the earthquake caused the reactor meltdown, because the tsunami disabled the cooling systems).
3. Other relations:

• I ) A and B together cause C (combination of high tide and west wind cases dikes to break, but there is no causal relation between tide and wind).
• II) A seems to cause B but in fact does not (I pray to God for the sun to come up every morning).

Many other variations and combinations are possible.

Another important distinction is that between a necessary cause, and a sufficient cause. Any cause can be one or the other, or both, or neither.

• A. Sufficient and necessary: a sizeable quantity of alcohol entering my bloodstream causes me to to get drunk (nothing else is needed to get me drunk, and nothing else could).

• B. Sufficient (but not necessary): spreading a lethal virus causes the death of many people (you don't need anything more, but you could use something else instead).

• C. Necessary (but not sufficient): light causes an oak tree to grow (it needs light, but it also needs water).

• D. Neither: Smoking causes lung cancer (you don't always get it even if you smoke, and you could get it even if you don't smoke).

The last example is of the type 1.II: A causes B. So is your example from the Harry Potter question: there is a direct causal relation between your parents' valuing knowledge and your ending up in a house that values knowledge, though it is neither necessary nor sufficient.

However, between your parents' having been in that house (A) and your ending up there (B), there is no direct causal link. But there is an indirect causal link: the fact that your parents value knowledge (C) causes both their ending up in the house (A) and your ending up there (B), of type 2.I (A and B are both caused by C). But it is still a causal link.

In the example of my praying for the sun to come up and its coming up, there is certainly no direct causal link; but one could argue that the earth's rotation on the one hand causes the sun to come up in the morning, while, on the other hand, it causes darkness of night, which in turn causes me to be afraid and pray every night.

Similarly, I could say my pressing the "fire" button causes my enemy to die (direct causal link) or, conversely, I could say my pressing the button causes an electric charge to build up in my phaser gun, which in turn causes the lethal beam to strike my enemy to die, so that the relation is only indirect. That is a matter of definition; it shows the limits of the usefulness of the concept of "causation".

If we define correlation as a "statistically significant relation between phenomena A and B", we are dealing with two things that are probably causally linked, but it might be a coincidence after all. If it turns out to be so, it is of the type 3.II (appears to be causal but is not). In any case, where there is causation, there must be correlation, so that Borror's suggestion about the children of smart parents' having a higher chance of ending up in a certain house is about both correlation and causation.

To complicate things further, most competent philosophers since Hume and Kant have held that causality is a human category that we apply to our perceptions, not something that exists independently (i.e. not a Ding an sich). All we really know is a statistical relation based on previous instances (people fall down when they jump off a cliff); we know nothing else that adds anything of interest over and above this correlation—nothing that could help us make a more accurate prediction than the correlation already can. So causal relations are just a simplification of a reality of correlations. "A causes B" just means "there is a correlation between A's taking place at a certain time and B's happening a certain amount of time afterwards.

This statement seems to me to be clearly incorrect. The context tells me that what the writer means is "The parents actions may cause this, but it is not guaranteed to do so." Correlation is used entirely wrongly. If some kids don't get these traits from their parents, then there isn't any correlation either, regardless of the cause.

Like another answerer, I must also offer a cartoon to illustrate.