Undergrad Correlation vs. Causation: Knowing the Difference

[entropy1]

If we observe that: IF A happens THEN B happens, we speak of correlation and not of causation, right?

So when do we speak of causation?

 

[.Scott]

Commonly, causation is determined by taking some control of the presumed cause "A" and testing "B" to determine whether there is still a correlation. It can also be demonstrated by hypothesizing a mechanism for the effect and testing that mechanism.

So, there is certainly a correlation between moon phases and tides. Both the illumination of the moon as viewed from Earth and the gravitational tidal effects have been well-modeled and well-demonstrated. So it is the location of the moon that causes both effects.

 

[entropy1]

So, depending of the way the inertial frame of the observer moves with respect to the frame of A and the frame of B, either A can be observed to happen before B, or B before A, right? But then it seems to me there can be no causal mechanism between A and B, right?

 

[PeterDonis]

If we observe that: IF A happens THEN B happens, we speak of correlation and not of causation, right?

Generally language like "If A then B" implies causation, not just correlation.

depending of the way the inertial frame of the observer moves with respect to the frame of A and the frame of B, either A can be observed to happen before B, or B before A, right?

If events A and B are spacelike separated, yes.

But then it seems to me there can be no causal mechanism between A and B, right?

That is the general assumption for spacelike separated events in relativity, yes.

 

[entropy1]

If events A and B are spacelike separated, yes.

So just to get this clear, is that a prerequisite for :

either A can be observed to happen before B, or B before A

 

[entropy1]

Generally language like "If A then B" implies causation, not just correlation.

That was not my approach; I aimed at A and B satisfying the truth table of IF A THEN B. This is statistics, right?

 

[PeterDonis]

So just to get this clear, is that a prerequisite for

Yes.

I aimed at A and B satisfying the truth table of IF A THEN B.

Well, that truth table is satisfied if A is false, with B being either true or false; in other words, the only way "if A then B" is false is if A is true and B is false. Is that really what you intended?

 

[PeterDonis]

I aimed at A and B satisfying the truth table of IF A THEN B. This is statistics, right?

If you're doing statistics, truth tables are irrelevant. You should be looking at correlation coefficients. We say A and B are correlated if the correlation coefficient between them is positive (and the more positive, i.e., the closer to 1, the better).

 

[entropy1]

Is that really what you intended?

Is there a problem if I did?

Yes.

Ok, that is useful to me. Otherwise I might have had to conclude that a causal mechanism can be seen as retrocausal.

 

[PeterDonis]

Is there a problem if I did?

Aside from the issue about statistics that I raised, yes: if A is false it makes no sense to say that A caused B, or that A is correlated with B, even if B is true. So saying you are using the truth table for "if A then B" includes cases where it makes no sense to talk about the things you say you want to talk about.

 

[entropy1]

I have a obvious question left: if A and B are spacelike separated, can there be a causal mechanism between them? (Asking this just to make sure)

 

[entropy1]

Aside from the issue about statistics that I raised, yes: if A is false it makes no sense to say that A caused B, or that A is correlated with B, even if B is true. So saying you are using the truth table for "if A then B" includes cases where it makes no sense to talk about the things you say you want to talk about.

I can't follow you so I can't answer that one.

 

[Nugatory]

That was not my approach; I aimed at A and B satisfying the truth table of IF A THEN B. This is statistics, right?

This just goes to show that we have to be careful with natural language: context is everything, and there are nearly always additional unstated assumptions implied by that context. Without context, the statement "If A then B" could mean any of several different things:
1) A causes B, as in "If I hit this glass with a hammer then it will break"
2) A and B are correlated, as in "If my dog is barking then the neighbor's dog is also barking". Perhaps my dog is responding to the neighbor's dog, perhaps the neighbor's dog is responding to mine, perhaps thay are both responding to the deer wandering through the neighborhood. We discover the correlation through observation, and that may or may not lead us to a causal connection.
3) A implies B, as in "If this number is prime then this number has no integral square root". Not many native English speakers would naturally use the word "cause" for this relationship, especially if B also implies A (as in "If this number has no factors other than one and itself then thsi number is prime").

This list probably is not exhaustive, and in any case the categories are somewhat blurry... but this is enough to suggest that the question in the original post is incompletey specified.

 

[PeterDonis]

if A and B are spacelike separated, can there be a causal mechanism between them?

See the last sentence of my post #4.

 

[entropy1]

Aside from the issue about statistics that I raised, yes: if A is false it makes no sense to say that A caused B, or that A is correlated with B, even if B is true. So saying you are using the truth table for "if A then B" includes cases where it makes no sense to talk about the things you say you want to talk about.

If I take the equivalent version of IF NOT(B) THEN NOT(A), can I accommodate the objection?

You can correlate how often the truth table is satisfied statistically, right?

 

[.Scott]

Generally language like "If A then B" implies causation, not just correlation.

It "generally" can. It says that "A cannot be true when B is false" or equally that "B cannot be false when A is true". So the causation can go in either direction.
Or neither: If the tide is minimal, then we have a quarter moon.

 

[PeterDonis]

the causation can go in either direction.

No, it can't, since B can still be true when A is false, so "if B then A" might not be true.

The logical connective that expresses "the causation can go in either direction" is equivalence--the truth values of A and B must be the same--which is not the same as "if A then B".

 

[PeterDonis]

if I take the equivalent version of IF NOT(B) THEN NOT(A), can I then accommodate your objection?

No.

You can correlate how often the truth table is satisfied statistically, right?

You could, but that still wouldn't be the same as the correlation coefficient.

 

[entropy1]

You could, but that still wouldn't be the same as the correlation coefficient.

But to measure how often A and B satisfy the truth table is a different correlation, right?

I can image that in a physics experiment, if A would cause B, there still would be trials where measurment is not agreeing with this due to minimal margins of error.

 

[entropy1]

Perhaps this is right: if you can predictically manipulate the correlation between A an B, that counts as causation?

That would not hold for quantum entanglement thought, I think.

 

[PeterDonis]

to measure how often A and B satisfy the truth table is a different correlation, right?

It's not a correlation at all. The correlation coefficient tells how often A and B are the same (both true or both false, assuming you are dealing with binary measurements--with measurements that can have more than two results or where the results can be continuously distributed, it's more complicated). Measuring how often A and B satisfy the truth table tells you nothing useful about their relationship, since, as I've already noted, they will satisfy the truth table if A is false regardless of whether B is true or false.

 

[PeterDonis]

if you can predictically manipulate the correlation between A an B, that counts as causation?

Go back and read post #2.

 

[PeterDonis]

I can image that in a physics experiment, if A would cause B, there still would be trials where measurment is not agreeing with this due to minimal margins of error.

Yes, measurement error can cause a particular run of an experiment to not detect A causing B even if it actually does. However, note that in post #2, @.Scott described manipulating A in an experiment and then seeing what happens to B. That means varying A and seeing if there is a corresponding variation in B. So you're not just looking at one run; you're looking at a lot of runs over which A varies, and seeing if B varies in a corresponding way. The only way measurement error will cause you to fail to detect that is if your measurements are so poor that you can't measure variation in A or B at all. In which case you wouldn't even be doing the experiment in the first place because you would know it couldn't tell you anything useful.

 

[stevendaryl]

I am not in agreement that “if A then B” says anything about causality. To me. it means that A is sufficient reason to conclude B. No causality implied. You want to know if someone is dead or unconscious, and someone tells you: “If he has no pulse, then he’s dead.” His death wasn’t caused by his not having a pulse.

The mismatch between natural language and logic I think is due to pragmatics of language. You would never say “If A then B” in the case that you already know that B is true, or you already know that A is false, but that’s because in those cases, it’s not a helpful thing to say. It’s as if someone asks you where the umbrella is, abd you say it’s either in the closet or in the car. If you actually know which is the case, you wouldn’t use “or”, you would just say which one.

 

[PeterDonis]

I am not in agreement that “if A then B” says anything about causality.

It would depend on the context; @Nugatory in post #13 gave examples where it would and examples where it wouldn't. I agree that my original statement in post #4 that it generally does imply causality was too strong.

 

[.Scott]

No, it can't, since B can still be true when A is false, so "if B then A" might not be true.

The logical connective that expresses "the causation can go in either direction" is equivalence--the truth values of A and B must be the same--which is not the same as "if A then B".

If the roads are dry, then it is rain-free.

	Rain	Rain-free
Dry Roads	No	Possible
Wet Roads	Possible	Possible

"If A, then B" simply eliminates the combination "A and not B".

It does not say whether there is a direct causal relationship, or if there is, which is the cause and which is the effect.

My if/then statement (above) simply eliminates the Dry-roads/Rain combination. It leaves open four possible causal relationships:
1) There is a third factor that causes the the roads to be wet whenever it allows it to rain.
2) There is a third factor that causes rain-free conditions whenever it allows dry roads.
3) Dry roads cause rain-free conditions.
4) Rain causes wet roads.

There are actually two other possibilities: a combination of 1 and 2, a combination of 3 and 4.

from your Boolean-minded SW Engineer

 

[Demystifier]

If we observe that: IF A happens THEN B happens, we speak of correlation and not of causation, right?

So when do we speak of causation?

Correlation is something that we measure. Causation is a theoretical concept that we use to explain the causation. If we don't want to explain the correlation, then we can talk about correlation without talking about causation.

 

[atyy]

@Demystifier stated it correctly.

However, there is a different (?) agent-based conception. A causes or contributes to causing B if manipulating A affects B.

If C is the common cause of X and Y, and there is no causal link between X and Y, then manipulating X will not affect Y, and manipulating Y will not affect X, even though X and Y are correlated. One has to manipulate C to affect X and Y.

 

[stevendaryl]

However, there is a different (?) agent-based conception. A causes or contributes to causing B if manipulating A affects B.

If C is the common cause of X and Y, and there is no causal link between X and Y, then manipulating X will not affect Y, and manipulating Y will not affect X, even though X and Y are correlated. One has to manipulate C to affect X and Y.

I wrote a paper once (unpublished; it was a paper for a college class) suggesting this notion of causality. The moon causes the tides because, in the thought experiment in which we take the moon far from the Earth, there would be no tides. It's a little more difficult to use this to argue that the phases of the moon do not cause the tides, because you can't easily manipulate the phases of the moon without also changing all sorts of other things (particularly, the position of the moon relative to the Earth and Sun).