# correlation does not always imply connection?



## NewAmerica

Well, I check out the definition of _correlation _in Oxford Dictionary, which seems to exactly mean connection.

What does "correlation does not always imply connection" refer to then? 

Thanks in advance

*************
But let me not rely solely on sociological statistics, where* correlation
does not always imply connection* given all the mitigating
factors. Even observers from the Christian side have
expressed dismay that the current dominance of evangelical
Christianity in America has not translated into a strengthening of
the nation's moral character or the characters of evangelical
Christians themselves.

--Victor Stenger


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## rhitagawr

It means correlation does not always imply causal connection. There's only a statistical connection.
For example, let's assume that in the United Kingdom you're statistically more likely to go to university if you have a Chinese background. Clearly you don't go to university just because you're Chinese. There's a second factor at work. Chinese parents may be more ambitious for their children, for example.
That's how I see it anyway. I suppose some sociologist or statistician is now going to shoot me down in flames.


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## Glasguensis

Correlation does not mean connection. In statistics, a correlation means that one variable changes with the same pattern as another. That does not mean necessarily that they are connected - sometimes it is purely chance that they seem to be following each other.


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## heypresto

I agree. I've often heard it expressed as 'correlation doesn't imply causation'.


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## rhitagawr

This isn't a linguistic point, but I think we should omit the word _always_.


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## Thomas Tompion

rhitagawr said:


> This isn't a linguistic point, but I think we should omit the word _always_.


I'm not sure I agree, Rhita.

You'd admit that correlation does sometimes imply connection, wouldn't you?

Maybe I've missed your point.


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## Thomas Tompion

If a rise in *a *is found to occur at the same time as a rise in *b*, then we are tempted to say that

_the rise in a causes the rise in b_, though we shouldn't overlook the possibility that

_the rise in b causes the rise in a_, or that

_the rises in a and b are both caused by a rise in some third factor or factors c_, or that

_the apparent relationship is the result of pure coincidence_.


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## rhitagawr

Interesting though this discussion is, I hope we're not going to be told off for straying from the point of the original question. I was going by what Glasguensis said. I agree that sometimes there's an implied connection. But an implied connection isn't part of the definition of correlation. 
Rich people tend to travel by train more than poor people. There's an implied connection in that travelling by train is expensive. 
It may be that if your name's Richard, you're more likely to have a blue front door. But that's just coincidence.
Sometimes it's psychologically difficult not to think in terms of a connection. An abstract thing like a recession, to use the Oxford dictionary's example, doesn't cause crime. Only people cause crime. But it's difficult not to think that people have less money in a recession and so are more likely to turn to crime to make both ends meet.


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## PaulQ

There's a website "Hilarious Graphs Prove That Correlation Isn’t Causation" (Hilarious Graphs Prove That Correlation Isn’t Causation)
There are several graphs as examples. The first graph compares the rate of divorce in the state of Maine, USA with the consumption of margarine: both are basically the same graph, but, of course there is no connection (correlation) between divorce and margarine.


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## Thomas Tompion

rhitagawr said:


> An abstract thing like a recession, to use the Oxford dictionary's example, doesn't cause crime. Only people cause crime


You say you are afraid of straying from the point, but this is precisely the point, in my view.

If every time there has been a recession, there has been found to be a rise in crime, we seem to have a correlation: whether there is necessarily a connection is exactly what we are being asked to discuss, surely?

I'm afraid, Rhita, that, for once, I can't agree with you when you talk about only people causing crime - if the effect of the recession on people is to make them commit more crimes, then I think we can say that the recession causes crime.


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## PaulQ

rhitagawr said:


> Only people cause crime.


I think that the point is that that statement is trivial as only people are able to cause crime.


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## Thomas Tompion

It's easy to be too sceptical about this.

If you wished to establish a *connection* (a causal relationship) between two factors, what could be more sensible than to try to find a *correlation* (a statistical relationship)?


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## ain'ttranslationfun?

PaulQ said:


> I think that the point is that that statement is trivial as only people are able to cause crime.



Only people can _commit_ crimes. The _reasons _why they do - the causes for their doing so - can be many: natural disasters; man-made disasters (war, the famine resulting therefrom, improper preparations for natural disasters; illogical legislation (regarding, for instance, drugs  or guns, inadequate control of the food chain, construction and infrastructures due to bribery, corruption, and greed); undiagnosed and untreated mental illnesses; and so on. As pointed out above, a correlation between certain things and others can be, and has been, established. These are'nt _post hoc ergo propter hoc_ fallacies, but cases where *b* is clearly the result of *a*.


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## Andygc

I wonder if this is wandering too far from the question. Things seem to have gone a bit astray from here:


rhitagawr said:


> For example, let's assume that in the United Kingdom you're statistically more likely to go to university if you have a Chinese background. Clearly you don't go to university just because you're Chinese. There's a second factor at work. Chinese parents may be more ambitious for their children, for example.


The point of the original sentence is merely that statistical correlation does not necessarily mean causal connection.

Chinese going to university, recession being related to crime, and margarine consumption leading to divorce are all beside the point. Wasn't the question answered accurately in posts #3 and #4, and expanded on in post #7? (Although the misuse of "mitigating" has slipped by)

By the way, if it wasn't completely off topic, I could give you a rational explanation for a causal relationship between margarine consumption and divorce ...


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## Thomas Tompion

Andygc said:


> Wasn't the question answered accurately in posts #3 and #4, and expanded on in post #7?


This is to suggest that Hume was wasting his time when he wrote section 4 of the _Enquiry_.  After all, Hume argues that there is no distinction between causation and statistical relationship.

We are being asked about the whole logical basis of the social sciences.


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## PaulQ

Thomas Tompion said:


> Hume argues that there is no distinction between causation and statistical relationship.


If that was indeed what he wrote, then he was wrong: See the graph of divorce and margarine above.


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## Andygc

Silly me, I thought we were being asked about the meaning of "where correlation does not always imply connection", which doesn't appear to be particularly profound.



Thomas Tompion said:


> After all, Hume argues that there is no distinction between causation and statistical relationship.


He doesn't, he argues that it is not reasoning but experimental evidence ("experience") which allows the prediction of similar outcomes from similar circumstances.


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## MattiasNYC

Andygc said:


> Silly me, I thought we were being asked about the meaning of "where correlation does not always imply connection", which doesn't appear to be particularly profound.



The phrase "correlation does not mean causation" (and other versions of it) is often used in discussions on faith vs. atheism. So while it doesn't appear particularly profound I think it's fair to point out that many people actually commit the logical error and actually assume that causation exists where only correlation does. In my opinion it might be better to describe the phrase as 'annoyingly seemingly overused', or something like that, since it's actually an appropriate point to make many times.


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## PaulQ

"Correlation does not mean causation" is an aphorism and as such it is a shortened form of a broader argument. It can be used as part of a statement (usually as a caveat) or simply as the aphorism to remind people of a general truth.


Andygc said:


> "...correlation does not always imply connection", which doesn't appear to be particularly profound.


No, it is not profound, but it is quite remarkable how many people do operate on a principle of "correlation implies connection" and these are to people who need correcting via the aphorism.


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## Thomas Tompion

Andygc said:


> He doesn't, he argues that it is not reasoning but experimental evidence ("experience") which allows the prediction of similar outcomes from similar circumstances.


I was too delicately brought up to be allowed this sort of contradiction of someone.

I was paraphrasing Hume's actual definition in the _Treatise_, where he describes a cause as:

_An object precedent and contiguous to another, and so united with it, that the idea of the one determined the mind to form the idea of the other, and the impression of the one to form a more lively idea of the other._


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## PaulQ

Hume is describing a cause. He is not saying that because the incidence of A and B seem to be related, that they must be related.


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## MattiasNYC

I agree with Paul.


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## Andygc

Thomas Tompion said:


> I was too delicately brought up to be allowed this sort of contradiction of someone.


How about this, then - Your summary misrepresents Hume's argument in Part 4 of his Enquiry, which contains no reference to statistics, but discusses the importance of experience rather than theory in making predictions of outcomes from circumstances. However I phrase it, you are still misrepresenting his argument. 

You gave a much better description of the inferences to be drawn from correlation earlier in the thread, and I still agree with that post, as I said before.


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## Egmont

PaulQ said:


> There's a website "Hilarious Graphs Prove That Correlation Isn’t Causation" (Hilarious Graphs Prove That Correlation Isn’t Causation)
> There are several graphs as examples. The first graph compares the rate of divorce in the state of Maine, USA with the consumption of margarine: both are basically the same graph, but, of course there is no connection (correlation) between divorce and margarine.


Ah, but there could be. Suppose husbands* don't like margarine. They want real butter. If their wives serve them margarine, they will tend to get upset. This may add to the factors that lead to divorce. Hence this correlation could be the result of a connection.

Or, consider that margarine is less expensive than butter. In times of economic stress people may economize by buying margarine instead of butter. Economic stress can also lead to a higher divorce rate. Hence, while neither eating margarine nor getting divorce causes the other, they are connected because both are statistically caused by a third factor (economic stress).

Or, suppose their is a long-term societal trend toward more self-indulgence. This might result in people splurging on butter and on getting divorced to follow their own path. Again, neither causes the other, but there is a connection via a third factor.

(These assume that margarine consumption in Maine follows the margarine consumption trend in the U.S. overall. I don't know if this is true, but it seems reasonable, and can be checked if anyone cares.)

The conclusion: while a correlation may seem absurd on the surface, there might be a real connection at work.

________________________
*This assumes traditional gender roles. Feel free to reverse them, to substitute either type of single-sex couple, or to modify this example in any other way.


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## PaulQ

Egmont said:


> Ah, but there could be.[...]


No, seriously, there isn't. 

This sort of graph (and there are hundreds of them) are chosen by shape alone within selected regions. If you look at the real graphs, you will see that prior to and after the times in question, the graphs look nothing like each other at all.


> The conclusion: while a correlation may seem absurd on the surface, there might be a real connection at work.


That is a possibility that the aphorism does not exclude; it merely cautions against jumping to conclusions/ making assumptions without evidence.

The human brain loves patterns and find them everywhere.


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## MattiasNYC

Egmont said:


> The conclusion: while a correlation may seem absurd on the surface, there might be a real connection at work.



But I think both Hume and the author referred to in the first post actually are talking about _causal_ connections. The way I read your interpretation the sentence in question (in the OP) could be rewritten as "correlation does not always imply correlation", or "connection does not always imply connection", because your interpretation seems to equate the two, which is also what confused the OP and thus makes _causal_ connection a more reasonable assumed interpretation (of "connection").


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## Thomas Tompion

MattiasNYC said:


> "correlation does not always imply correlation", or "connection does not always imply connection",


This looks terribly like an abuse of language.


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## JulianStuart

Thomas Tompion said:


> This looks terribly like an abuse of language.


The guilty party is Stenger, the author of the quoted sentence!


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## Thomas Tompion

JulianStuart said:


> The guilty party is Stenger, the author of the quoted sentence!


You may well be right, Julian.

I thought we were discussing *correlation does not always imply connection.*

Did he say the other things somewhere else?


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## MattiasNYC

Thomas Tompion said:


> You may well be right, Julian.
> 
> I thought we were discussing *correlation does not always imply connection.*
> 
> Did he say the other things somewhere else?



Re-read my post.


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## Thomas Tompion

Your post suggests that you are the guilty party, Mattias.

Stenger was a famous scientist.


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## MattiasNYC

Thomas Tompion said:


> Your post suggests that you are the guilty party, Mattias.
> 
> Stenger was a famous scientist.



The OP asked: "What does "correlation does not always imply connection" refer to then?" That was the question.

The answers here seem to say that Stenger's _intended meaning_ of "connection" was a _causal_ connection, not "just" a "connection". PaulQ pointed out the other way of phrasing it, "Correlation does not mean Causation". What I was saying was that that seems to make sense. The OP also told us what was confusing, namely "I check out the definition of _correlation _in Oxford Dictionary, which seems to exactly mean connection." Of course, if the dictionary definition is the correct interpretation then Stenger's statement is a self-contradiction.

So, Egmont then said that "while a correlation may seem absurd on the surface, there might be a real connection at work." My point then - responding to _that _post specifically - was that his interpretation and reasoning in the context of the original post actually seems to imply that "correlation" essentially _is_ "connection", because he was juxtaposing "connection" to "causality". He was essentially saying that A and B can be independently linked to C, and that A and B therefore do not cause each other. Therefore the relation of A and B is not causal, it is not a causal connection. What Stenger calls the relationship is "correlation", on that we all agree, but Egmont then added "a real connection". And since that "real connection" isn't a "causal connection", since he dismissed causality, it seems to really just say the same thing as the word "correlation" does.

See my point?

C causes A
C causes B
A and B are connected via C
A and B correlate with each other

With that logic and definition, is it still possible to say "correlation does not always imply connection"? I mean, it seems as if he reasoned himself back to defining "connection" as "correlation", because they 'do' the same thing... they 'function' the same way in his examples....

In my opinion, if one was to shorten the term "causal connection" and/or pick one of the two it seems better to choose "causation" rather than "connection", since the latter appears to be confusing. 

Or did I miss something in Egmont's post???


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## bennymix

The question was answered by rita, heypresto and Paul, in posts 2, 4, and 9 respectively.   One cannot infer cause (causal connection, A causes B) from correlation (A is correlated with B [i.e. there is a pattern, more than one occasion]).   Soon after a clock tower in New York City strikes 12 noon, I, in S. Ontario, leave for my afternoon shift, daily.   The striking is without causal effect on me (for one thing, I do not hear it).


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## Glasguensis

Much of this discussion seems to be based on the mistaken premise that correlation has a meaning similar to connection. In the context of statistics, *it does not*. To quote from our own dictionary, the relevant definition is "the degree to which two or more attributes or measurements on the same group of elements show a tendency to vary together." A correlation can be present when there is absolutely *no* connection, causal or otherwise. The original statement is perfectly coherent, and I agree with Andygc that Hume's work makes no comment on this and in any case he was writing well before modern statistical science had been formalised.


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## Thomas Tompion

Thank you very much Glasguensis.

Hume was concerned with the problem of induction, which seems to me to be the issue raised by Stenger.

It's central to the scientific method, and, of course, the sentence in the OP becomes a vapid pleonasm if one doesn't distinguish between connections and correlations.

This is why I have been trying from the start to indicate the difference in meaning between the two words.

I can't share your view that modern statistical methods have rendered the issue obsolete.  There are plenty of moderately intelligent people who believe that social sciences can never be  truly scientific, because, they think, society does not possess what Hume called _uniformity of nature_ - societies, they think, behave with less regularity than hydrogen atoms.


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## Glasguensis

I simply meant that Hume would not have been familiar with the terminology used in modern statistics. I didn't mean that his work was no longer valid. Indeed in my opinion he highlights precisely the same danger as the OP: we form our conclusions based on observed past behaviour, and inherent in this is the possibility that we induce a causal link which is not in fact present. 

The OP is pointing out that this is a particular danger in sociology because of the difficulty (or impossibility) in controlling the sample to isolate variables.


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## Thomas Tompion

Glasguensis said:


> I simply meant that Hume would not have been familiar with the terminology used in modern statistics. I didn't mean that his work was no longer valid. Indeed in my opinion he highlights precisely the same danger as the OP: we form our conclusions based on observed past behaviour, and inherent in this is the possibility that we induce a causal link which is not in fact present.
> 
> The OP is pointing out that this is a particular danger in sociology because of the difficulty (or impossibility) in controlling the sample to isolate variables.


That's fine.  Thank you.  I think we are very much in agreement.


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## Thomas Tompion

MattiasNYC said:


> C causes A
> C causes B
> A and B are connected via C
> A and B correlate with each other


I think this is where I disagree with your representation of events, Mattias.

The case is similar to the one I described in #7 - as an example where we mustn't infer a causal *connection*.


Thomas Tompion said:


> _the rises in a and b are both caused by a rise in some third factor or factors c_


A typical example would be the clocks striking nine in London (A) being regularly followed by the people turning up for work in Manchester (B).

Here the *correlation* of the two events is explained by the convention of time (C).

So, for me, your description should be:

C causes A
C causes B
A and B are each connected to C (but not to each other, as you suggest).
So, A and B correlate with each other.

To say that A and B are connected (the people turn up for work in Manchester *because* the clocks have just struck nine in London) is not a reasonable inference, in my view.

The fact that A and B are each connected to C, does not make them connected (causally) to each other.


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## MattiasNYC

Thomas Tompion said:


> I think this is where I disagree with your representation of events, Mattias.



Sorry, I guess I wasn't clear: What you're disagreeing with is my representation of what Egmont said, which I also disagree with. That was my whole point.


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## Thomas Tompion

Two minuses make a plus, Mattias. 

It sounds as though we agree.


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## ironman2012

Thomas Tompion said:


> C causes A
> C causes B
> A and B are each connected to C (but not to each other, as you suggest).
> So, *A and B correlate with each other*.


Since correlation means there's a statistical connection (i.e. when one gets bigger, so does the other), what is the statistical connection between A (i.e. the clocks striking nine) and B (i.e. the people turning up for work)? When what gets bigger, what is the other that also gets bigger?


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## PaulQ

ironman2012 said:


> Since correlation means there's a statistical connection (i.e. when one gets bigger, so does the other),


When A happens, B happens also -> this is also a correlation.
When A happens, 72% of the time B happens also -> this is also a correlation.


ironman2012 said:


> what is the statistical connection between A (i.e. the clocks striking nine) and B (i.e. the people turning up for work)


You will note that this may not happen on Sundays or public holidays.

These are interesting graphs that show spurious correlation:





Beware Spurious Correlations​


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## ain'ttranslationfun?

I think we could rephrase "correlation does not always imply connection" as "Because two things follow the same pattern over a period of time does not necessarily mean that one causes the other or vice-versa"...if by "connection" the author meant "relation" (as in cause and effect).


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## Thomas Tompion

You might also say 'Don't commit the_ post hoc ergo propter hoc_ fallacy'.


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## dojibear

ironman2012 said:


> Since correlation means there's a statistical connection (i.e. when one gets bigger, so does the other),



That is not a connection. That is not a statistical connection. That could be a statistical coincidence.

More accurately, "When one *got* bigger, the other also *got* bigger."

If you say "When one *gets *bigger, so does the other." you are implying a cause-effect connection between the two: you are predicting that, in the future, when one *gets* bigger the other *will *get bigger. You do not know that, just because the past graphs are the same shape.


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