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# Correlation almost always equals causation

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Those who know, know

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Do you understand why correlation and causation are separate concepts? If something is causal, it will obviously be correlated. The problem is the sufficient condition part of the necessary and sufficient condition.

>If something is causal, it will obviously be correlated.

Obviously not. A heater with a thermostat is set to keep the temperature in a room constant while the outside temperature changes. The temperature in the room is uncorrelated with the power consumption of the heater even though it is caused by it.

moron.

>The temperature in the room is uncorrelated with the power consumption of the heater even though it is caused by it.

No that is ignorant, more power equals more heat, if the heater is electric, all the power at the input is being converted to heat in the room.

Do you know what a dictionary is, and how to look up what "thermostat" and "constant" mean? The building cools down due to cold air outside drawing the heat out through the walls. The heater supplies heat as a replacement. The temperature inside stays virtually constant, give or take some noise. A constant ± noise isn't correlated with the power output.

I said "moron" for style, but evidently you really a moron.

Yet the temperature is correlated with the outside temperature and the temperature supplied to the heater and it will be apparent since as soon as you cut off the power to the heater you will see a corollary in the temperature change in the room..

>Yet the temperature is correlated with

nothing. It's correlated with nothing. The correlation of the random variable "inside temperature" is zero with any variable at all. The temperature inside is a constant ± noise thanks to the heater and thermostat that keep it so, causally. If you record your measurements of the inside temperature and the power consumption of the heater, they will be uncorrelated. There will be no statistical relationship between them. Because there is no statistical relationship between noise and anything. The correlation of noise is zero with anything, no matter how hard you try. You shouldn't use words you don't understand, like "correlation."

>The correlation of the random variable "inside temperature" is zero with any variable at all.

Its is correlated to the outside temperature/humidity/pressure, the temperature absorbing and emitting properties of the material the room is made of, and the power supplied to the heater because if you know all those, you can figure out the temperature of the room.

>The temperature inside is a constant ± noise thanks to the heater and thermostat that keep it so, causally

Would you acknowledge that the power needed for the heater to achieve a certain temperature is correlated to the outside temperature and the current room temperature along with the material that compose the room?

>if you know all those, you can figure out the temperature of the room.

That is not what correlation means. "Correlation" is a term. You're throwing around terms you don't understand and isn't a good look. The covariance of [math] t_textrm{inside} [/math] and [math] P_textrm{heater} [/math] is zero, and so is their correlation because zero divided by anything is zero. For an even more stark example, suppose the random variable [math] X [/math] is distributed as [math] mathcal{N}(0, 1) [/math], and define the random variable [math] Y [/math] as [math] Y = X^2 [/math]. The covariance between these is also zero — this is a basic exercise to show it using the definition of expectation — and so is their correlation. Read a book.

They aren't random variables though, the room temperature is a function of the outside temperature, the room's materials, and the heater output and if some value is a function of other values they are always correlated by the functional relationship.

A random variable is any measurement which is an input to a statistical procedure. Also a term. The physical nature of the underlying generative mechanism is entirely ignored when we compute the covariance of one variable with another.

In other words, your answers are not correlated to any actual truth and your process can't even identify inherently connected variables like functional relationships that are entirely dependent one way or the other.

In other words, I am correcting this false statement:

>If something is causal, it will obviously be correlated.

"Correlation" in the phrase "correlation doesn't imply causation" (and so the entire context of this thread) is a mathematically defined term — the covariance divided by the product of the deviations. This is the same as if someone barged into a discussion of addition on the reals and insisted that "addition" meant something else than it did because one water plus one water is one water. It's important not to misuse mathematical terms, not least because the "identification functional relationships" relies on the mathematics being correct far, far down in the foundation — "double machine learning" (and other causal inference methods) and "automated model discovery" build on years of coursework where the definition of covariance and correlation occurs in the first year.

>I can identify your ignorance in physics mixed with your smugness about the physics you don't understand.

You are painfully moronic for missing that the argument is not at all about physics and I do not talk about the physics even though I was very clear about it in

and

. The correlation of temperature [math] T [/math] with any variable [math] Y [/math] is [math] frac{ mathbb E left [(T- mu_T)(Y- mu_Y) right]}{ sigma_T sigma_Y} [/math]. That's it. There's no physics in that formula, moron. The only relevant fact about the temperature [math] T [/math] is that it is a constant plus random noise: [math] T = C + varepsilon [/math]. Because it is kept that way by the heater. The thermostat is set to keep the inside temperature at a constant [math] C [/math]. No physics comes into it after this point. This is entirely an example of causation not always implying correlation. The heater causes the temperature but nothing is correlated with that temperature, because the covariance of [math] C + varepsilon [/math] with anything is zero.

>mathematically

Ok ,but physically, the temperature of a room is entirely a function of the outside temperature, the room's materials, and any additional heat supplied, so if your language and models can't account for the correlation between something that specifically physically depends on something else, then your language and models are obviously flawed and don't account for the full scope of reality.

>account for the RELATIONSHIP between something that specifically physically depends on something else

Another part of mathematics accounts for the relationship. I'm sure physicists can write down a model of the room and heater mathematically, it just won't use the device of statistical covariance. The device of statistical covariance is useful as part of other tools to approach reality. Such as the "double machine learning" and "automated model discovery" I have mentioned. Or just classical econometrics with its quasi-experimental designs, since that too is reality and we can't run physical experiments on world economies. It's as if you insisted on redefining the mathematical device of "addition" because what you really wanted to do was division. The argument isn't about physics, the argument is about not misusing terms.

No, its like the idea of correlation isn't just mathematical concept and there are also physical correlations that matter, but can't be identified with your faulty inherently incomplete modelling techniques.

Physical relationships can be identified with other tools that build on top of mathematical statistics (e.g. https://sciml.ai/) they just aren't correlations, they're relationships.

I'm telling you that your ignorance of physics is what's destroying your argument. As I explained, the power of the heater is correlated with the temperature increase of the room. The energy of the radiator is correlated with the raw temperature of the room. This isn't complicated and if you don't understand the difference between energy and power, then don't bother responding to me again.

>As I explained, the power of the heater is correlated with the temperature increase of the room.

As I explained, this is irrelevant because it does not in any way contradict me. You write this as though it contradicts me or as though I don't understand this, but you fail to understand that this is irrelevant because it does not refute my example of variables being in a causal relationship yet uncorrelated. You are giving me OTHER VARIABLES. This doesn't mean that MY VARIABLES are correlated. Yours are. Mine aren't. Both are causally linked.

AAAaAAAaaAAAAAAAaaAa your lack of reading comprehension, it hurts

>it does not in any way contradict me.

Sure it does. Because you don't understand the difference between power and energy. It's just hilarious to me to see you, the climate shill, in other threads having a meltdown over how you get exposed for not understanding basic physics.

>you, the climate shill, in other threads

>not realizing there's more than one anon

Aight, schizo.

Your meltdowns are unmistakable

>The temperature in the room is uncorrelated with the power consumption of the heater even though it is caused by it.

Cute. Power is a rate. Temperature is a number. You need to compare either rate of temperature increase to power (which is indeed correlated) or temperature to energy (which is obviously correlated). If I may quote another anon: moron. I can tell you're a global warming shill on this board because I can identify your ignorance in physics mixed with your smugness about the physics you don't understand.

>The temperature in the room is uncorrelated with the power consumption of the heater even though it is caused by it.

No, temperature is not "caused" by the power consumption. In your logic the same power consumption could "cause" any arbitrary temperature, that is, a given power consumption would, absurdly, be the sufficient condition for any temp the room might have.

The truth of course is that the causative relationship is between the power consumption and the temperature gradient, the "consumption" of energy from the in- to the outside. There indeed you can have a functional relationship.

You're using "correlation" quantitatively but "causation" colloquially. You're dumb.

>You're using "correlation" quantitatively but "causation" colloquially.

No, you're just ignorant of the definition of causality too, in the context of "causation doesn't always imply correlation". Causality also has specific definitions in each school of causal inference. In Pearl's structural causal models framework ("do-calculus") — [math] Pr(T mid mathrm{do}(P)) [/math] — the relationship of [math] T [/math] and [math] P [/math] is by definition causal: if we intervene to change the power consumption of the heater, the temperature will necessarily change, even though without an intervention into the system the temperature is uncorrelated with anything. In Rubin's potential outcomes framework we can also write down this causal relationship with some technical fiddling.

You're using correlation in the ultra-narrow social science of linear correlation i.e. two things are correlated if they go up together, or one goes up and the other down, etc

The temperature in the room and the power consumption of the heater are absolutely correlated, it's just in a nonlinear way with other significant variables (the outdoor temperature)

>correlation in the ultra-narrow social science of linear correlation

I've never before heard probability theory and mathematical statistics be described as social science.

>The temperature in the room and the power consumption of the heater are absolutely correlated

Not with each other they are not.

>correlated, it's just in a nonlinear way with other significant variables (the outdoor temperature)

In the "social science" of probability theory and mathematical statistics, the term for this is statistical dependence, and calling general statistical dependence "correlation" is a colloquial use by engineers and physicists who aren't careful with mathematical terms. But yes, modulo the misuse of the term, you're right, the temperature and the power consumption are dependent when you add other variables. I'll still point out that causation doesn't even need to imply non-linear dependence in the case of two variables — we do have to add the outdoor temperature to get the relationship.

Granted the term is used your way in applied statistics. But in the general sense of probability theory, variables are correlated unless they are independent. i.e. unless the joint distribution factorizes.

We both know what we are talking about - and Wikipedia addresses the overloaded definition in the article on "correlation"

>In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistics it usually refers to the degree to which a pair of variables are linearly related.

I disagree with their framing that "in statistics it usually means linear correlation", as I'd say that in many parts of statistics that kind of linear correlation is useless and not discussed

This can be done another way, and it's better. The pain and time is far too much, I'd use your imagination. Or wait until I'm able to contact.

Causation is everywhere.

Causation necessarily implies correlation.

Spurious correlations necessarily must be rare.

Therefore of all the possible correlations that can ever be found, nearly all of them are indicative of causation.

Idiots saying correlation doesn't imply causation, via spurious and odd examples oversell the frequency with which these occur

Why must spurious correlations be rare? This is an odd assumption that should be justified. In fact, I'd expect spurious correlations to be more common than causal correlations, they would just contribute a lower effect size.

Do you know about Fourier analysis for periodic signals? Almost all of the signal power is captured in the lower order harmonics, and yet the higher order harmonics which contribute high frequency information will be strongly correlated in a signal processing sense with the overall trend.

What you're claiming (that spurious causations are by definition rare and negligible) would imply that these low power contributing factors wouldn't be correlated. You don't know when you are observing a trend which contributing factors you are capturing and which you are not.

It's simple. Take all the possible correlations that can be observed with high confidence. Only a small fraction of those are spurious. Next, take a sample of all possible events, correlated or not. Only a small fraction of those are spurious. Therefore, by combining both it must be the case that spurious correlations are definitionally rare. That's why they're spurious.

This is a very odd way of looking at probability and statistics. What is your definition of spurious? Just probabilistically rare?

You might want to read https://gwern.net/causality

Read that dudes about section. Sounds like a total and colossal homosexuals whose opinion is less than worthless. I doubt I want to read that pseuds article

>gwern

yikes

All jokes aside, one of his posts helped me cope with schizophrenic psychosis and basically cured me

No, but causation is a specific type of correlation.

Correlation isn’t causation but it’s often an excellent idea of where to look for a cause.

How does ice cream consumption cause drowning deaths?

Ice cream makes you fat. When you're fat you don't swim as much, because that requires activity. When you go to the water park and fall off your floaty, you lack the muscular strength to save yourself. You're too fat to save. You drown. See? Easy.

Ice cream only makes you fat after long-term consumption but the correlation is immediate, that is ice cream consumption and drowning rise at the same time.

This is *a* causal chain. You've established that there is *a* causal chain that could possibly produce the transition from starting state to ending state. Correlation = causation would imply that it is *the* causal chain. You have no way of knowing that this causal chain was followed. You're getting got by Bayes Theorem and the Burgler Alarm problem.

>copium for frustrated undergrads

>Correlation almost always equals causation

everything is correlation and causation is just a particular case of near 100% correlation, but most things are not like that. Almost everything is just influenced by hundreds of things with no clear single "cause"

Saying that correlation equals causation is highly correlated with being wrong and butthurt about something.

https://en.wikipedia.org/wiki/Simpson's_paradox

paradox can be resolved when confounding variables and causal relations are appropriately addressed in the statistical modeling

I reject causation as a notion in exact sciences. It's pointless to try and prove something that depends on time and is therefore not in the realm of pure logic. Your human opponent will just pilpul you if you try.

You win against sophomoric pseuds who tell you correlation is not causation by refusing to play their game.

When your point is refuted by an xkcd comic you may want to go sit in a corner and think about your life

Here's another one:

>Absence of evidence IS the evidence of absence

And

>Ad homenin is the highest form of debate

Correlation usually implies some causal relationship and nothing more.

Fine I will chim inn.

A hypothetical random clinical trial;"is schizophrenia a degenerate brain disease"

>we are going to take MRI image of the brain

healthy control group (HC)

schizofrenia(SZI)

results

HC= no change

SZI= rapid degradation

Now since being diagnosed with schizophrenia shows that the brain degenerate, schizophrenia is therefor a degenerate disease? right correlation equals causation, schizophrenia is leads to degradation of the brain yes?

Now since I ain't moronic like people in psychiatry is; I know one can not have a diagnosis, without being forcefully injected with a neurotoxin, currently labeled anti-psychotic(AP).

I decide to use this information to create a new study;"Does anti-psycotic cause brain degradation"

healthy control(HC) group, schizofrenia(SIZ), schizofrenia(SIZ)+neurotoxin(Anti-psycotic)(AP))

we now have 3 groups lets see what happens.

results

HC= no change

SZI= increase in brain volume

SZI+AP= rapid degradation of brain volume

first study we had

schizofrenia= decrease in brain volume,

second study we have

schizofrenia=increase in brain volume

schizofrenia+ neurotoxin(AP) = rapid decline in brain volume

Meaning, brain degeneration

>Schizophrenia brain degradation correlation=/= causation

>AP brain degradation correlation= causation

Strong correlation does not necessarily mean its the cause of something, its just as likely that something else might be hiding, or co-occurring. On further investigation one can now see that the neurotoxin(AP) in the root cause.

This post is highly correlated with schizophrenia

Thank you =).

But the argument is sound yes?

Basically, correlation=causation

If there is low correlation there is low causation and etc.

>Oh but look this graph of unrelated things correlates

If it is unrelated then there is a bigger graph showing low correlation

Heh kind of funny, every midwit is put in their place eventually, amen

>almost