But if it allows for transitive causal chains leading back to some X, then the principle risks triviality, since it is plausible that all events share at least some cause in common, if you go back far enough.
However, wouldn’t that be extremely unlikely? And wouldn’t the likelihood be related to the amount of correlation?
A second problem: How can we rigorously unpack the meaning of “by-chance” correlations?
I’m not sure because I lack the skill in mathematics to answer this question the proper way.
And third: How do you know that statistically significant correlations are usually not “by chance” in your sense?
I’m not sure if there is a mathematical formalism for this, pretty much for the same reasons as for problem two: I don’t have the mathematical abilities required. However, I do know what they’re about, and I’m rather confident that you and I both can tell apart results that could be explained by mere chance and those that could not—it would be rather surprising if it was not achievable by means of math if you can achieve that by mere fallible intuition?
Well I apologize if I’m mistaken here, but I’m still trying to be reasonable.. Hmm.
Let’s create an examples to illustrate a point:
Students at some school take a special test each schoolyear and their tests results are compared with something fairly trivial. Let’s say the number of pencils the students bring to the tests.
Then by means of correlation it is found that the number of pencils brought by the students to the school has been increasing in a way that is correlated to prowess in the tests by the students.
In this case it’s not sufficient to say that the correlation implies that the number of pencils is causing the increasing prowess in the tests, nor that the prowess in the tests is causing the increased number of pencils. Which is what the phrase traditionally stands for.
But there still can be a causal relationship, for an example the school’s funding has been increasing and they’ve been giving more free material to students, and if increased material is correlated with increased prowess and increased number of pencils, or increasing economy.. and so forth, that’s causality, but not of the same kind.
However we can also say that this is just a coincidence, particularly if there has been only a couple of events. Or by some trivial causal chain like then you mentioned, but....
… you can also see how these results could be of a nature where casuality is actually required. If we look at a single testing event and notice that for the 500 students of the school there’s a strong correlation between number of pencils and test prowess, we’re starting to talk about extremely small probabilities that the results are by coincidence, are we not? Even if the pencils are not the cause , we can still deduce that there is a cause at high likelihood?
Well anyway maybe I’m just making excuses, at least it’s important to consider that at this point, and I see your point anyway, and I think I was wrong. Oops, sorry.
But not exactly. Because I think there’s something to this. And I think you should know what I mean. Maybe it’s important to start asking what this coincidence actually means? Isn’t this actually something about Markov Blanket ? (or something similar, sorry if I misused the term)
You can measure the likelihood that the profile the datasets are similar by chance. For an example simple increasing tendency—correlation that is—that can be explained by coincidentially similar increasing tendency, but if there’s an complex profile to correlation, you can measure what the likelihood for a coincidence is? Even further, the more complex the profiles are, the less likely a coincidence becomes? ( if they match )
However, wouldn’t that be extremely unlikely? And wouldn’t the likelihood be related to the amount of correlation?
I’m not sure because I lack the skill in mathematics to answer this question the proper way.
I’m not sure if there is a mathematical formalism for this, pretty much for the same reasons as for problem two: I don’t have the mathematical abilities required. However, I do know what they’re about, and I’m rather confident that you and I both can tell apart results that could be explained by mere chance and those that could not—it would be rather surprising if it was not achievable by means of math if you can achieve that by mere fallible intuition?
Well I apologize if I’m mistaken here, but I’m still trying to be reasonable.. Hmm.
Let’s create an examples to illustrate a point:
Students at some school take a special test each schoolyear and their tests results are compared with something fairly trivial. Let’s say the number of pencils the students bring to the tests.
Then by means of correlation it is found that the number of pencils brought by the students to the school has been increasing in a way that is correlated to prowess in the tests by the students.
In this case it’s not sufficient to say that the correlation implies that the number of pencils is causing the increasing prowess in the tests, nor that the prowess in the tests is causing the increased number of pencils. Which is what the phrase traditionally stands for.
But there still can be a causal relationship, for an example the school’s funding has been increasing and they’ve been giving more free material to students, and if increased material is correlated with increased prowess and increased number of pencils, or increasing economy.. and so forth, that’s causality, but not of the same kind.
However we can also say that this is just a coincidence, particularly if there has been only a couple of events. Or by some trivial causal chain like then you mentioned, but....
… you can also see how these results could be of a nature where casuality is actually required. If we look at a single testing event and notice that for the 500 students of the school there’s a strong correlation between number of pencils and test prowess, we’re starting to talk about extremely small probabilities that the results are by coincidence, are we not? Even if the pencils are not the cause , we can still deduce that there is a cause at high likelihood?
Well anyway maybe I’m just making excuses, at least it’s important to consider that at this point, and I see your point anyway, and I think I was wrong. Oops, sorry.
But not exactly. Because I think there’s something to this. And I think you should know what I mean. Maybe it’s important to start asking what this coincidence actually means? Isn’t this actually something about Markov Blanket ? (or something similar, sorry if I misused the term)
Oh well I think I can answer the question:
You can measure the likelihood that the profile the datasets are similar by chance. For an example simple increasing tendency—correlation that is—that can be explained by coincidentially similar increasing tendency, but if there’s an complex profile to correlation, you can measure what the likelihood for a coincidence is? Even further, the more complex the profiles are, the less likely a coincidence becomes? ( if they match )