The article missed the chance to include the quote from that standard compendium of information and wisdom, The Hitchhiker's Guide to the Galaxy:
> Since every piece of matter in the Universe is in some way affected by every other piece of matter in the Universe, it is in theory possible to extrapolate the whole of creation — every sun, every planet, their orbits, their composition and their economic and social history from, say, one small piece of fairy cake.
This is such a massive article. I wish I had the ability to grind out treatises like that. Looking at other content on the guy's website, he must be like a machine.
People didn't always use statistics to discover truths about the world.
This, once developed, just happened to be a useful method. But given the abuse using those methods, and the proliferation of stupidity disguised as intelligence, it's always fitting to question it, and this time with this correlation noise observation.
Logic, fundamental knowledge about domains, you need that first. Just counting things without understanding them in at least one or two other ways, is a tempting invitation for misleading conclusions.
„This renders the meaning of significance-testing unclear; it is calculating precisely the odds of the data under scenarios known a priori to be false.“
I cannot see the problem in that. To get to meaningful results we often calculate with simplyfied models - which are known to be false in a strict sense. We use Newtons laws - we analyze electric networks based on simplifications - a bank-year used to be 360 days!
Works well.
I don't disagree with the title, but I'm left wondering what they want us to do about it beyond hinting at causal inference. I'd also be curious what the author thinks of minimum effect sizes (re: Implication 1) and noninferiority testing (re: Implication 2).
Also, I'm convinced that the reason humans intuitively struggle to figure out causality is because the vast majority of causes and effects are self-reinforcing cycles and go both ways. There was little evolutionary pressure for us to understand the concept of causality because it doesn't play a strong role in natural selection.
For example, eat a lot and you will gain weight, gain weight and you will feel more hungry and will likely eat more.
Or exercise more and it becomes easier to exercise.
Earning money becomes easier as you have more money.
Public speaking becomes easier as you do it more and the more you do it, the easier it becomes.
> For example, while looking at biometric samples with up to thousands of observations, Karl Pearson declared that a result departing by more than 3 standard deviations is “definitely significant.”
Wait. Sir Arthur Conan Doyle lived at basically the exact same time as this Karl Pearson.
Is that why the Sherlock Holmes stories had handwriting analysis so frequently? Was there just pop science going around at the time that like, let's find correlations between anything and anything, and we can see that a criminal mastermind like Moriarty would certainly cross their T's this way and not that way?
I wonder if this tendency to correlate truly holds for everything? Intuitively it more or less demonstrates that nature tends to favor zero-sum games. Maybe analyzing correlations within the domain of theoretical physics would highlight true non-correlations in some particular approaches? (pun only slightly intended)
People interpret "statistically significant" to mean "notable"/"meaningful". I detected a difference, and statistics say that it matters. That's the wrong way to think about things.
Significance testing only tells you the probability that the measured difference is a "good measurement". With a certain degree of confidence, you can say "the difference exists as measured".
Whether the measured difference is significant in the sense of "meaningful" is a value judgement that we / stakeholders should impose on top of that, usually based on the magnitude of the measured difference, not the statistical significance.
It sounds obvious, but this is one of the most common fallacies I observe in industry and a lot of science.
For example: "This intervention causes an uplift in [metric] with p<0.001. High statistical significance! The uplift: 0.000001%." Meaningful? Probably not.
Really classic "rationalist" style writing: a soup of correct observations about statistical phenomena with chunks of weird political bullshit thrown in here and there. For example: "On a more contemporary note, these theoretical & empirical considerations also throw doubt on concerns about ‘algorithmic bias’ or inferences drawing on ‘protected classes’: not drawing on them may not be desirable, possible, or even meaningful."
This is such a bizarre sentence. The way its tossed in, not explained in any way, not supported by references, etc. Like I guess the implication being made is something like "because there is a hidden latent variable that determines criminality and we can never escape from correlations with it, its ok to use "is_black" in our black box model which decides if someone is going to get parole? Ridiculous. Does this really "throw doubt" on whether we should care about this?
The concerns about how models work are deeper than the statistical challenges of creating or interpreting them. For one thing, all the degrees of freedom we include in our model selection process allow us to construct models which do anything that we want. If we see a parole model which includes "likes_hiphop" as an explanatory variable we ought to ask ourselves who decided that should be there and whether there was an agenda at play beyond "producing the best model possible."
These concerns about everything being correlated actually warrant much more careful understanding about the political ramifications of how and what we choose to model and based on which variables, because they tell us that in almost any non-trivial case a model is at least partly necessarily a political object almost certainly consciously or subconsciously decorated with some conception of how the world is or ought to be explained.
This is why experimental science is different from observational studies.
Statistical analyses provide a reason to believe one hypothesis over another, but any scientist will extend that with an experimental approach.
Most of the examples given in this blog post refer to medical, sociological or behavioral studies, where properly controlled experiments are hard to perform, and as such are frequently under-powered to reveal true cause-effect associations.
This was my take as well. At least microeconomics has moved away from large-scale observational studies and has moved into experimental and quasi-experimental studies.
While the methods alone cannot fix it all ("You can’t fix by analysis what you bungled by design" [1] after all), it gets somewhat closer to unbiased results.
Looks like an impressive thorough piece of investigation. Well done.
That said, holistic supposition can certainly be traced back as far as writting dawns. Here the focus on more modern/contemporary era is legitimate to keep the focus delimited on a more specific concern, but is a bit obfuscating this fact. Maybe it's already acknowledged in the document, I read it all yet.
Statistical correlations anre important to establish but there are the easiest and least useful part of the research. Creating theories as to “why” and “how” these correlations exist are what advances our knowledge.
I read lot of papers that painstakingly show a correlation in the data, but then their theory about the correlation is a complete non sequitur.
the rest of the page has amazing design, but there's just something about the graphs switching from dark to light that flashbangs my eyes really badly - i think it's the sudden light!
For dark-mode, we rely on https://invertornot.com/ to dynamically decide whether to fade or negate/invert. (Background: https://gwern.net/invertornot ) The service uses a small NN and is not always correct, as in these cases. Sorry.
I have filed them as errors with InvertOrNot, and will manually set them to invert.
Arguments like this have been around for decades. I think it's important to keep in mind — critical even.
At the same time, as I've been forced to wrestle with it more in my work, I've increasingly felt that it's sort of empty and unhelpful. "Crud" does happen in patterns, like a kind of statistical cosmic background radiation — it's not meaningless. Sometimes it's important to understand it, and treating it as such gets no one anywhere. Sometimes the associations are difficult to explain easily when you try to pick it apart, and other times I think they're key to understanding uncontrolled confounds that should be controlled for.
As much as this background association is present too, it's not always there. Sometimes things do have zero association.
Also, trying to come up with a "meaningful" effect size that's not zero is pretty arbitrary and subjective.
There's probably more productive ways of framing the phenomenon.
Not commenting on the topic at hand, but my goodness, what a beautiful blog. That drop cap, the inline comments on the right hand side that appear on larger screens, the progress bar, chef's kiss. This is how a love project looks like.
I was recently looking at a large timeseries dataset.
I noticed when doing a scatter plot of two variables and noticed that there were several "lines" of dots.
This generally implies that subsets of the two variables may have correlations or there is a third variable to be added.
I did some additional research and it is possible for two variables with large N to show correlation for short bursts even if both variables are random.
I mention for two reasons:
1. I was just doing the above and saw the OP article today
2. Despite taking multiple college level stats classes, I don't remember this ever being mentioned.
33 comments
[ 1.5 ms ] story [ 59.0 ms ] threadEverything Is Correlated - https://news.ycombinator.com/item?id=19797844 - May 2019 (53 comments)
> Since every piece of matter in the Universe is in some way affected by every other piece of matter in the Universe, it is in theory possible to extrapolate the whole of creation — every sun, every planet, their orbits, their composition and their economic and social history from, say, one small piece of fairy cake.
This, once developed, just happened to be a useful method. But given the abuse using those methods, and the proliferation of stupidity disguised as intelligence, it's always fitting to question it, and this time with this correlation noise observation.
Logic, fundamental knowledge about domains, you need that first. Just counting things without understanding them in at least one or two other ways, is a tempting invitation for misleading conclusions.
I cannot see the problem in that. To get to meaningful results we often calculate with simplyfied models - which are known to be false in a strict sense. We use Newtons laws - we analyze electric networks based on simplifications - a bank-year used to be 360 days! Works well.
What did i miss?
For example, eat a lot and you will gain weight, gain weight and you will feel more hungry and will likely eat more.
Or exercise more and it becomes easier to exercise.
Earning money becomes easier as you have more money.
Public speaking becomes easier as you do it more and the more you do it, the easier it becomes.
Etc...
Wait. Sir Arthur Conan Doyle lived at basically the exact same time as this Karl Pearson.
Is that why the Sherlock Holmes stories had handwriting analysis so frequently? Was there just pop science going around at the time that like, let's find correlations between anything and anything, and we can see that a criminal mastermind like Moriarty would certainly cross their T's this way and not that way?
People interpret "statistically significant" to mean "notable"/"meaningful". I detected a difference, and statistics say that it matters. That's the wrong way to think about things.
Significance testing only tells you the probability that the measured difference is a "good measurement". With a certain degree of confidence, you can say "the difference exists as measured".
Whether the measured difference is significant in the sense of "meaningful" is a value judgement that we / stakeholders should impose on top of that, usually based on the magnitude of the measured difference, not the statistical significance.
It sounds obvious, but this is one of the most common fallacies I observe in industry and a lot of science.
For example: "This intervention causes an uplift in [metric] with p<0.001. High statistical significance! The uplift: 0.000001%." Meaningful? Probably not.
This is such a bizarre sentence. The way its tossed in, not explained in any way, not supported by references, etc. Like I guess the implication being made is something like "because there is a hidden latent variable that determines criminality and we can never escape from correlations with it, its ok to use "is_black" in our black box model which decides if someone is going to get parole? Ridiculous. Does this really "throw doubt" on whether we should care about this?
The concerns about how models work are deeper than the statistical challenges of creating or interpreting them. For one thing, all the degrees of freedom we include in our model selection process allow us to construct models which do anything that we want. If we see a parole model which includes "likes_hiphop" as an explanatory variable we ought to ask ourselves who decided that should be there and whether there was an agenda at play beyond "producing the best model possible."
These concerns about everything being correlated actually warrant much more careful understanding about the political ramifications of how and what we choose to model and based on which variables, because they tell us that in almost any non-trivial case a model is at least partly necessarily a political object almost certainly consciously or subconsciously decorated with some conception of how the world is or ought to be explained.
Statistical analyses provide a reason to believe one hypothesis over another, but any scientist will extend that with an experimental approach.
Most of the examples given in this blog post refer to medical, sociological or behavioral studies, where properly controlled experiments are hard to perform, and as such are frequently under-powered to reveal true cause-effect associations.
While the methods alone cannot fix it all ("You can’t fix by analysis what you bungled by design" [1] after all), it gets somewhat closer to unbiased results.
[1]: https://www.degruyterbrill.com/document/doi/10.4159/97806740...
That said, holistic supposition can certainly be traced back as far as writting dawns. Here the focus on more modern/contemporary era is legitimate to keep the focus delimited on a more specific concern, but is a bit obfuscating this fact. Maybe it's already acknowledged in the document, I read it all yet.
I read lot of papers that painstakingly show a correlation in the data, but then their theory about the correlation is a complete non sequitur.
For dark-mode, we rely on https://invertornot.com/ to dynamically decide whether to fade or negate/invert. (Background: https://gwern.net/invertornot ) The service uses a small NN and is not always correct, as in these cases. Sorry.
I have filed them as errors with InvertOrNot, and will manually set them to invert.
At the same time, as I've been forced to wrestle with it more in my work, I've increasingly felt that it's sort of empty and unhelpful. "Crud" does happen in patterns, like a kind of statistical cosmic background radiation — it's not meaningless. Sometimes it's important to understand it, and treating it as such gets no one anywhere. Sometimes the associations are difficult to explain easily when you try to pick it apart, and other times I think they're key to understanding uncontrolled confounds that should be controlled for.
As much as this background association is present too, it's not always there. Sometimes things do have zero association.
Also, trying to come up with a "meaningful" effect size that's not zero is pretty arbitrary and subjective.
There's probably more productive ways of framing the phenomenon.
I noticed when doing a scatter plot of two variables and noticed that there were several "lines" of dots.
This generally implies that subsets of the two variables may have correlations or there is a third variable to be added.
I did some additional research and it is possible for two variables with large N to show correlation for short bursts even if both variables are random.
I mention for two reasons:
1. I was just doing the above and saw the OP article today
2. Despite taking multiple college level stats classes, I don't remember this ever being mentioned.