Correlation is usually not causation. But why not?
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Re: Correlation is usually not causation. But why not?
#2Disagree with the title. Correlation does imply casuation a lot of the times (especially for simple systems). But not always. Therefore, the caution is not to assume it apriori, but pursue further investigation to confirm or reject it. Even when it is rejected, a lot of those cases result in a third variable being the cause behind the correlated "effect" variables.
Re: Correlation is usually not causation. But why not?
#3Statistics serves as a tool to overcome our cognitive biases. But what if these biases are at the center of learning?
Take for example the Gambler's Fallacy where a player believes she can predict the outcome of a coin toss with greater certainty than is possible. Obviously she cannot. But if I had to design a Machine Learning algorithm, I would certainly want it to always assume that a pattern existed. That way, if the data were predictable, the algorithm would be able to take advantage of it.
Re: Correlation is usually not causation. But why not?
#4Statistics serves as a tool to overcome our cognitive biases. But what if these biases are at the center of learning? Take for example the Gambler's Fallacy where a player believes she can predict the outcome of a coin toss with greater certainty than is possible. Obviously she cannot. But if I had to design a Machine Learning algorithm, I would certainly want it to always assume that a pattern existed. That way, if…
A smarter algorithm would refrain from betting on the coin.
Re: Correlation is usually not causation. But why not?
#5Correlation vs causation is not actually a complex mathematical problem. The issue is more philosophical.
Bayesian networks are a highly sophisticated and flexible framework for thinking about causation. And yet the essence of Bayesian networks can be captured in much simpler methods like Instrumental Variables or simply regressions with controls.
In all cases, the true distribution of observables (which we can estimate from samples) combined with some assumptions about the possible nature of causality (either very sophisticated in the case of Bayesian networks, or very simple in the case of instrumental variables) lead to the actual causal relationships.
Where do these assumptions come from? Consider a randomized trial. Even though physically, it is possible that some hidden cause influenced both the random number generator which selected patients into a trial, and also whether patients will get better. And yet people universally believe that there is no such mechanism, and so they believe that randomized trials prove the causal relationship between taking a drug and getting better.
No physicist ever wrote down an equation proving this. It is simply something we deduced from our human understanding of how nature works.
Put simply, causality is not a physical notion, neither is it a statistical notion. It is a part of our intuitive understanding of the physical world, in which a higher level notion of causality exists, beyond that described by special relativity.
Re: Correlation is usually not causation. But why not?
#6Statistics serves as a tool to overcome our cognitive biases. But what if these biases are at the center of learning? Take for example the Gambler's Fallacy where a player believes she can predict the outcome of a coin toss with greater certainty than is possible. Obviously she cannot. But if I had to design a Machine Learning algorithm, I would certainly want it to always assume that a pattern existed. That way, if…
A smarter algorithm would refrain from betting on the coin.
That's great if you know a priori that you cannot predict the outcome of what you are betting with.
Re: Correlation is usually not causation. But why not?
#7This question is bound to be a can of worms. There has been a great deal written about the matter, particularly in regard to observational studies.
Drawing causal inference is overwhelmingly likely to be wrong when there is a good chance that unknown variables are influencing the correlates observed. In health-related sciences that more often than not is the case.
A few years ago there was a study correlating hours of TV watched and ADHD symptoms in children. The news media picked up on these "findings" and of course the causal influence of TV on ADHD was reported.
It was obvious that saying watching TV caused ADHD was absurd, that other variables weren't taken into account, e.g., some other characteristic of ADHD kids prompted watching TV more than other kids.
There was a great article published in PLOS several years ago (ATM I don't have the link) showing mathematically that the odds were about 1 in a million that an observational study like the above would turn out to be a "true" causal relationship, and the author concluded most published studies were junk.
In experimental studies, variables are limited and controlled as well as possible. With fewer and known variables, correlations would have a greater chance of revealing a reproducible causal relationship among events.
The discussion gets tripped up when it comes to defining "cause" or "causal relationship". The theory is controlled as an experiment may be, there's a possibility that unknown variables were present and affected the phenomena occurring in the experiment. Conclusions can't be absolute, but only true to some probability.
I think the history of science over the last 100 years or so has something to say about the nature of "causal relationships".
Re: Correlation is usually not causation. But why not?
#8[deleted]
Re: Correlation is usually not causation. But why not?
#9This article starts off with a common mistake.
It is ok to create the 3 categories:
> If I suspect that A→B, and I collect data and establish beyond doubt that A&B correlates r=0.7, how much evidence do I have that A→B?
> you can divvy up the possibilities as: 1. A causes B 2. B causes A 3. both A and B are caused by a C
So far so good, but here is the problem:
> Even if we were guessing at random, you’d expect us to be right (at at least 33% of the time...
No. It is not valid to assume each possibility is equally likely. If you do so, you are bringing your own assumptions to the problem.
If you ever find yourself assuming a distribution, pause and consider testing your assumption.
Re: Correlation is usually not causation. But why not?
#10Bad winter weather can cause auto accidents, and we expect a positive correlation between bad winter storms and winter auto accidents. Okay, but in the northern hemisphere, living in more northern latitudes also correlates with winter auto accidents but does not cause them.
For heart disease, we know that the main causes have to do with aging. Well, then, since now the audience for TV news is comparatively old, we can expect that watching TV news has positive correlation with heart disease. Still watching TV news does not cause heart disease.
In the US NE, hurricanes are positively correlated with pretty leaves on the trees, but the leaves do not cause the hurricanes, and the hurricanes do not cause the colors in the leaves. Instead, hurricanes are caused by the surface waters of the Atlantic Ocean hot from summer sun with cooler air on top, and that situation is caused by the fall weather with also causes the colored leaves. So, colored leaves have a spurious correlation with hurricanes but do not cause them.
Correlation is much more common and much easier to establish than causality. Usually the convincing evidence of causality if some basic physical connection.