# Correlation vs causality implied by a graph

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• phinds
phinds
Gold Member
TL;DR Summary
can a graph that shows strong correlation imply causality?
The graph below shows a very clear, but not perfect, correlation between the red line and the blue line. That fact says nothing whatsoever about causality. BUT ... if you add in the additional fact that there is absolutely zero chance that the blue events cause the red events and a quite reasonable possibility that the red events cause the blue events, how strongly does that imply that the red causes the blue?

The contention that went with the graph is that causality is clearly and absolutely implied, but I contend that because the correlation is not exact, nor does the red clearly lead the blue, that causality is certainly possible but that it is not at all absolutely implied as definite. That is, it is my contention that the graph, taken together with the stated relationship between the red and blue, suggests causality but does not imply it.

On the other hand, if the correlation were exact in every point, plus the relationship, I would agree that causality is implied.

I just want to make sure I'm not overlooking something, so what say you?

DeBangis21 and hutchphd
What about the case where both are caused by the same source? Red and blue will be strongly correlated to the source in the same way but red will not be the cause of the blue.

DeBangis21, Vanadium 50, phinds and 1 other person
phinds said:
TL;DR Summary: can a graph that shows strong correlation imply causality?

I just want to make sure I'm not overlooking something, so what say you?
Do you have the raw data? There a many ways to slice it onto a graph, and I suggest that you try them all. In particular you should plot Red vs Blue in some form. If it is a straight line then your answer is pretty strong and simple . If it looks like a picture of Mickey Mouse the answer is also strong, but more complicated. If it looks like random spray then the correlation is weak and you make a different graph. This technique is extraordinarilly powerful because your eyeballs (et al) are very very good at this type of analysis and one can chew through data very quickly without a lot of predigestion. Interesting results are self evident. Perseveration is neither required nor encouraged.

pines-demon said:
What about the case where both are caused by the same source? Red and blue will be strongly correlated to the source in the same way but red will not be the cause of the blue.
That's the kind of logical inconsistency that I am looking for (that I have not thought of) but no, in this case that would be impossible.

pines-demon
hutchphd said:
Do you have the raw data? There a many ways to slice it onto a graph, and I suggest that you try them all ...
That would be ideal, but not possible in this case. I have what I have and no more. I'm looking for the kind of things you and @pines-demon have pointed out but I am limited to the graph, as is, and the statement regarding causality (blue cannot cause red, red COULD cause blue).

I should add, for clarification, there is no possibility of any causal relationship other than the fact that the red could cause the blue. The red is utterly independent of the blue. There is no possibility that both could be caused by something else. That's the constraints under which I want to figure it out, if possible.

I still think my original conclusions are correct but I'm not 100% positive which is why I posed the question here.

I think it depends a bit on what question exactly you are asking. Hutchphd's technique will give you a good idea of the correlation and, in particular, if the blue line lags the red line. But that doesn't tell you that there's causation there - for example a red and a blue bottle cap floating on a swimming pool will move pretty much together, one lagging the other, if there's a wave source nearer one than the other.

To look at causation you need some kind of physical model that predicts how blue moves if red is driving it, some model of noise, some assurance that it can't be some other unknown source driving both, and Bayes' theorem. For example, tides follow the moon and the tide height follows the phase of the moon. We have a physical model (gravity) that suggests a causal relationship between tides and the moon, but why should the phase matter? In fact, phase is a consequence of the position of the Sun, and tide height depends on whether the solar and lunar tides align or not, so both phase and tide height are consequences of solar position vis a vis the moon.

Ultimately, this is why we do experiments. If we can control red in some way and blue reacts to arbitrary changes we make at arbitrary times to red, then we can be reasonably sure of a causal link. As long as we've taken reasonable precautions not to directly affect blue ourselves, of course.

pines-demon and hutchphd
Ibix said:
Ultimately, this is why we do experiments. If we can control red in some way and blue reacts to arbitrary changes we make at arbitrary times to red, then we can be reasonably sure of a causal link. As long as we've taken reasonable precautions not to directly affect blue ourselves, of course.
The condition is that red is a totally independent variable that has no external cause. I do NOT see red leading blue, however and the correlation is not exact so my belief is that the red could be causing the blue only indirectly. There is no way to test for indirect causality, but I think that the fact alone that indirect is possible means that direct causality is not shown as definite.

Consider the case of length of left arms and right arms. They are clearly correlated, but one does not cause the other. Even if one factor precedes the other, you can not draw any conclusion simply from that fact. You can use subject matter knowledge to support causation theory, but not simply the correlation.
If you can control one factor in an experiment, you can use the correlation of a designed experiment to imply causation.
It's my understanding that there are some recent statistical methods to determine if causation is implied, but I have no experience with them. I think it is called causality. The book Causal Inference in Statistics - A Primer might explain more.

Last edited:
Justina and phinds
FactChecker said:
Consider the case of length of left arms and right arms. They are clearly correlated, bu one does not cause the other.
Clearly true but they have correlation in their underlying causes and that is not the case in my question.

phinds said:
Clearly true but they have correlation in their underlying causes and that is not the case in my question.
How do you know that just from the graph? I don't see anything in your question to say that there are no underlying causes.

phinds said:
That would be ideal, but not possible in this case. I have what I have and no more. I'm looking for the kind of things you and @pines-demon have pointed out but I am limited to the graph, as is, and the statement regarding causality (blue cannot cause red, red COULD cause blue).
But you have the data right? If you only have the plot, then you can extract the date and try all sorts of manipulations. Maybe propose a model and check somehow what is the probability for the blue curve to be correlated with the red curve by pure luck.

pines-demon said:
But you have the data right? If you only have the plot, then you can extract the date and try all sorts of manipulations. Maybe propose a model and check somehow what is the probability for the blue curve to be correlated with the red curve by pure luck.
No. I say again, I have NOTHING but the graph and the statement about causality. I am just trying to look at the graph and the statement logically, since it is divorced from anything else.

phinds said:
No. I say again, I have NOTHING but the graph and the statement about causality. I am just trying to look at the graph and the statement logically, since it is divorced from anything else.
You can use online (or offline) tools to extract the data from the image...

phinds said:
. if you add in the additional fact that ... a quite reasonable possibility that the red events cause the blue events, how strongly does that imply that the red causes the blue?
Question: "how strongly does that imply that the red causes the blue?"
Answer: "a quite reasonable possibility", where ever that fact came from and how ever it is logically supported.
The graph does very little to support that conclusion other than it does not contradict it. There are vast quantities of correlated graphs of variables that have no conceivable causal relation.

phinds
phinds said:
The graph below shows a very clear, but not perfect, correlation between the red line and the blue line. That fact says nothing whatsoever about causality.
No, and it never will.

phinds said:
BUT ... if you add in the additional fact that there is absolutely zero chance that the blue events cause the red events and a quite reasonable possibility that the red events cause the blue events, how strongly does that imply that the red causes the blue?
It doesn't change anything.

phinds said:
On the other hand, if the correlation were exact in every point, plus the relationship, I would agree that causality is implied.
No it isn't.

phinds said:
I just want to make sure I'm not overlooking something, so what say you?
Yes, you are overlooking the fact (which I think you know but are trying to avoid) that correlation never implies causality.

There is a very strong correlation between the height an apple has fallen from and the speed with which it hits the ground, but that does not imply that Newtonian gravity is correct.

phinds
pbuk said:
Thre is a very strong correlation between the height an apple has fallen from and the speed with which it hits the ground, but that does not imply that Newtonian gravity is correct.

Um, what?

The only way you can prove something is casual is a very carefully controlled experiment in general. But people are allowed to take their understanding of the world and try to infer things - you might be right and you might be wrong, but if you're wrong in a way that matters hopefully you have the ability to notice

This reminded me of

phinds
So much for "shiver me timbers".......

FactChecker and phinds
I think this is unlikely to converge.

First, correlations sometimes don't have any causal relationship. They just don't.

Second, I don't biy the argument "these can't possibly be caused by a common 3rd factor". Did you know that Covid deaths were correlated with stock market volatility? You'd think "they can't possibly be coming from a common 3rd factor." But they are.

FactChecker said:
Question: "how strongly does that imply that the red causes the blue?"
Answer: "a quite reasonable possibility", where ever that fact came from and how ever it is logically supported.
The graph does very little to support that conclusion other than it does not contradict it. There are vast quantities of correlated graphs of variables that have no conceivable causal relation.
My thoughts exactly. Thanks.
Second, I don't biy the argument "these can't possibly be caused by a common 3rd factor".
I agree w/ you that one should be VERY leery of making such a statement, BUT ... it's a given in the scenario I am trying to understand.

I think the discussion in this thread has confirmed my point of view that in the scenario I presented, causality is a possibility but absolutely is not guaranteed or even implied, just suggest as a possibility.

FactChecker
Do correlation causes casualties? I thought that even though they seem similar they are independent, am I wrong ?

phinds said:
"these can't possibly be caused by a common 3rd factor"

I agree w/ you that one should be VERY leery of making such a statement, BUT ... it's a given in the scenario I am trying to understand.
Perhaps I'm picking nits here but if it is a "given" that there can't be a common third factor, that suggests to me this is a thought experiment, not a real-world scenario.

Is it possible in a real world scenario to declare there is not a common third factor? (I guess if the red data is from inside a closed box and the blue data is from outside the box ... but that still sounds pretty contrived...)

I'm not used to just taking it as a given in real world scenarios that things are definitely not connected; so it makes it hard to use conventional real world logic (such as, say, engineering or communication principles).

DaveC426913 said:
Is it possible in a real world scenario to declare there is not a common third factor?
Possible, maybe, but unlikely.

Justina said:
Do correlation causes casualties?

phinds said:
I think it's a joke. A pun. (Or maybe a bona fide typo...)

phinds said:
Sorry for any misunderstanding, I just wanted to know that if correlation between variable always leads to casualties, like, do always correlated particles end up in casualties?

Justina said:
Sorry for any misunderstanding, I just wanted to know that if correlation between variable always leads to casualties, like, do always correlated particles end up in casualties?
correlation mean a relationship but says nothing about causality. Look up the words with Google.

Justina said:
Sorry for any misunderstanding, I just wanted to know that if correlation between variable always leads to casualties, like, do always correlated particles end up in casualties?
Do you perhaps mean causalities? Or do you really mean casualties?

DaveC426913 said:
Do you perhaps mean causalities? Or do you really mean casualties?
I think he just isn't a native speaker.

phinds said:
I think he just isn't a native speaker.
Yes you're right
Just wanted to mention about that phenomenon in which an event is connected by cause and effect. Sorry for the inconvenience

Justina said:
that phenomenon in which an event is connected by cause and effect.
Yes, that is causality, or you can say it is a causal relationship.

phinds said:
Yes, that is causality, or you can say it is a causal relationship.
Thank you,
That correlation always don't end up on causality . Is it wrong?

Justina said:
Thank you,
That correlation always don't end up on causality . Is it wrong?
It is RIGHT, not wrong, to say that correlation does not imply causality.

Justina
phinds said:
It is RIGHT, not wrong, to say that correlation does not imply causality.
Well than what results in causality?

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