You Ask, I Answer: Causation Without Correlation?

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You Ask, I Answer: Causation Without Correlation?

Vito asks, “Let’s assume we have the joint probability distributions of A and B. In that scenario, is it possible that A causes B, but A and B are not correlated?”

This is possible and even probable when you have missing data, especially if the missing data is also partially causal.

Some examples:
– Distributions that are not normal, are causal, and have a Pearson R score of zero (like stress before a test)
– Hidden data – A / B / C vs A / D / C – and B has no correlation to D
– Unobservable data – like gravity, which is not something that can be measured at all because we have no quantum particle for it
– Many causes of A > B and A is not the primary cause
– Causes that collide – A > B and C < B, net R of 0, like treatment and illness

You Ask, I Answer: Causation Without Correlation?

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In today’s episode Vito asks, let’s assume that we have the joint probability distributions of a and b.

In that scenario, is it possible that A causes B but a and b are not correlated? So this is a comment that was left on my website about a post I did a number of years ago on correlation and causation.

It is generally accepted that correlation is not causation.

Just because two variables are correlated, does not mean that one causes the other.

The textbook example of this is ice cream and drowning deaths.

Ice cream death, consumption of ice cream, and number of deaths from drowning are strongly correlated in a lot of datasets.

Why? Well, logically, we know that there’s this thing called summertime and as people, the weather gets warmer, people eat more ice cream, people go swimming more Second years of pandemics, and you have an increase in drowning deaths.

So what about the reverse which is what Vito is asking, Can the reverse be true? Can you have causation? Without correlation? The answer is yes, it is possible.

In fact, it is probable in some cases where you have, you know, hidden data or missing data, things like that.

So, let’s talk about a few of these situations, five of them.

The first is, anytime you have a distribution of data, that is not a normal distribution, there may be something causal in it, but it may end up having a statistical correlation of zero.

So, if you think about your typical plots, right, those dots scattered all over the places, or there may be a line of dots So, you can draw a line with the dots.

That’s your typical Pearson correlation.

If you have a shape, for example of dots that looks like a big square, guess what, you have a statistical Pearson score of zero, even though there may be something very causal in that data, you could have something it looks like a smiley face, right? Again, that would have a score of zero.

But you could, that could very well be something causal happening there.

So that’s an example where you have non normal distributions.

And you still have a correlation, a mathematical correlation of zero.

Even if those things are causal in nature.

You can have hidden data hidden did that it is observe the unobserved you didn’t see it.

There may be a pathway to because, but it’s not.

But if you’re used to measuring in stages, it may not make sense.

So for example, let’s say you have a, b and c column look at past conversion, your Google Analytics, a leads to b b leads to C and you may have Carlin’s Along those, there may be a D in there somewhere, right and maybe a D, C, and then B has no correlation to D, you may end up having a break in correlation, even though that fourth interfering factor there that you didn’t measure, or you didn’t know about, was playing a role.

That’s where things like, especially with analytics, like propensity score modeling come really handy to be able to tease out Oh, there’s something else at play here.

Even if the regression score is zero, net across your chain of conversion, they may be interfering factors along the way.

A third way this can happen is when you have some bits on observable that cannot be measured.

Again, textbook example here.

We know there that gravity exists, right? Who’s the debate about this? by anybody who has even grade school education I’m sure there’s some people out there believe that because the earth is flat, there’s no gravity, but they’re idiots.

Gravity has no particle that we’ve been able to find yet in quantum physics.

So even though we know it exists is causal, we cannot measure it.

And therefore, there is no correlation because there’s you can’t correlate something that you don’t have data for.

So that’s an example that’s very obvious.

Oh, there’s there’s a cause gravity, but there’s no data to back it up.

A fourth situation, what happens a lot in marketing is when you have say A and B, and you’re looking for a relationship.

And B has many, many, many, many causes.

A, maybe causal but very weakly causal, it may not show a relationship, especially there’s a lot of noise.

Again, in marketing.

This is you see this a lot with attribution analysis was the impact of Facebook of Twitter of email of referrals of direct traffic of SEO of SEM All these different channels and any one channel may have a very strong or weak relationship to the the outcome that you’re looking for that conversions, you may not be able to show a, a correlation between A and B, because there’s like D that’s just making all the noise.

But that doesn’t mean that a is not causal to B, it just means you can’t measure it because it’s you’ve got too much interference.

And then the last situation where this is likely to happen is when you have causes that collide.

Again, the textbook example is here is things like illness, right illness and mortality are two variables and there may be a negative correlation there and then a positive correlation and you may have treatment and mortality, you may have a negative karma And the more treatment, the less mortality.

And if you put those together, if you were grouping them together, you would get a net of zero, right? Because the effect would cancel each other out.

And so in that instance, you are zero.

But that doesn’t mean that there’s no causal relationship.

In fact, you would have to break up the data to figure out that, Oh, actually, the illness and mortality is positively correlated, the treatment and the mortality is negatively correlated, and you separate those two out, a and b and b and c should not be grouped together.

Because if you’re trying to measure illness, and treatment and mortality together, yet, they cancel each other out.

Correlation perspective.

So those are five examples.

And then they were just weird things.

I guess the weird things would be like, stuff that fall in the first category, like if you if you’re trying to measure for example, performance on a test and academic test and you have like stress or fatigue or something like that is again not gonna be a normal a normal linear distribution, it could be all over the place and you might not find a a mathematical relationship even though there is a causal relationship like a little bit of stress for a test is good motivates you to study a lot of stress before tests that keeps you up all night.

Not so good, right, because you go into the test a zombie.

So, there are there are instances where causation and correlation mathematical correlation do not line up.

They are much less rare and obviously the the case where correlation is not causation is much more common.

But it does exist in cases where you’ve got pieces of data either missing or on observable or lots of interference, so be aware of them.

A couple of examples talked about like an attribution analysis are real problems that marketers may have to face, especially if you’re doing more and more complex attribution.

models, you may need to use different techniques than just regression analysis if you’ve got a lot of either contributing causes or cancelling causes, so being aware of how you’re doing your computations is really important.

So that’s a set of answers.

Interesting question a tough one to dig through hopefully made sense.

You got follow up questions, leave them in the comments box below.

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