Correlation Does Not Mean Causation! But What Does It Mean?

entered data science, there was a phrase we had all heard; everyone knows, young and old:

“Correlation does not imply causation.”

It's a catchy phrase, and say it once or twice, and you might have nodded confidently when someone else said it. Especially for unrelated datasets, but when it's funny and interesting to suggest a cause!

Here are two very interesting facts:

• Consuming countries More pizza they often have more math scores.
• When selling sunglasses, i More shark attacks occur.

Now, if that was all the information you had… what would you have concluded?

Does eating pizza make you better at math? Will buying new sunglasses cause a shark attack?

As funny as it is to think about it, the answer to those questions is yes “probably not”.

However, these are examples of the real thing: Relation.

The question you must ask now is: if correlation does not equal causation, what does it mean?

That's when things get sour.

Because we tend to treat relativity as a vague concept, we think of it as if it means “They are related”, or “They go together somehow.” But correlation isn't just a feeling, it's an accurate measure of how well two variables relate to each other.

Instead of repeating the warning, let's actually understand the concept. Once you do, those strange examples stop surprising you and start making sense.

So, let's get into it!

What is correlation?

When people say two things “it is related,” usually means one of three things:

• “Those two things seem to be related.”
• “Those two things go together.”
• “There is some connection between those two things.”

At a superficial level, all three are wrong, but they lack certain nuances.

Communication is not a vibe. It's average! And like any scale, it answers a very specific question.

Stepping back, imagine you are collecting data on how many hours students have studied and their test scores.

You edit it, and you see something like this:

Each point represents one student. The x-axis is how long they studied, and the y-axis is their score.

If you look at this plot, you notice that the scores tend to go higher. So he concludes that, “As the study period increases, the scores tend to increase”, which is what we call a positive correlation.

But, is that just a trend or does the data tell you something more?

In this example, the relationship you have just established is: if one variable is above your average, the other is usually above your average as well.

That's an important idea that many people miss: correlation isn't about raw values, it's about how variables move relative to their measurements.

So, the answer to the question is:

Do the two variables go together in a constant way?

This question has one of three answers:

• Up + up → positive correlation
• Up + down → negative correlation
• No consistent pattern → no correlation

The Math Behind Correlation

Let's try to simplify the thinking about correlation. We will do that by using the Pearson correlation coefficientwhich we can define as:

$r = frac{cov(X, Y)}{ sigma_{X}.sigma_{Y}}$

Okay, I know the equation isn't what anyone thinks of when I say “accurate”… But stay with me and let's break it down without turning it into a lesson.

Step 1: Covariance (AKA Do They Go Together?)

Covariance looks at how two variables move relative to their measurements. For example, if both variables are above their averages, we get positive covariance; if one is above and the other is below, we get negative covariance.

Basically, the covariance answers: “Are these variables consistent with how they deviate from their measurements?”

Step 2: Get used to it

Covariance alone is difficult to interpret because it depends on the scale. To overcome that, we divide by standard deviation: $sigma_{X}$ again $sigma_{Y}$. This scales everything into a clean range: -1 to 1. That gives us a common place to compare variable values.

After these two steps, we can now calculate the Pearson coefficient! If we receive:

1. +1 → perfect relationship.
2. 0 → no linear relationship.
3. -1 → perfect negative relationship.

This code simply measures how well these two variables go together—not how big they are, but how well they fit together.

What Different Links Look Like

• Left: strong positive correlation → specify an upward pattern
• Middle: no correlation → random dispersion
• Right: strong negative correlation → decreasing pattern

Correlation measures the constant of motion, not just that two variables are related.

That's What Correlation Really Tells You

Correlation tells you: these variables go together in an orderly way. It tells us that there is a pattern here that we should pay attention to.

But, it does NOT tell you why or how, or that one causes the other.

A classic example of correlation is that ice cream sales and drowning incidents are related.

In fact, we can plot the number of ice cream sales and drowning incidents to find:

We can see a very clear relationship between these two conditions… more ice cream sales lead to more drowning?…

But that is misleading. Because the real driver is temperature: warmer weather means more ice cream sales, more people going to the beach, and more swimming.

Therefore, although we can clearly see that the correlation is real, the meaning is hidden.

Communication and Nonlinearity

Now consider this relationship:

y = x²

This is clearly a strong relationship, as x increases or decreases, y increases! But if you calculate correlation:

np.corrcoef(x, y)[0,1]

You will get something close to 0.

That's because correlation only measures: How well a straight line fits the relationship. This is an important limitation. If the relationship is crooked, the relationship may fail, even when a strong relationship exists.

So, instead of thinking: “Correlation = relationship”, it is better to think: “Correlation = how well a straight line defines a relationship.”

Misunderstanding

The vagueness of the concept of relativity, and the way it is taught to us, leads to some misunderstandings. The three most common are:

1. Considering the cause: Just because two variables go together doesn't mean one causes the other.
2. Ignoring hidden variables: There may be a third factor driving both.
3. Indirect relationships that do not exist: Correlation only sees straight line patterns.

Are you wondering now, if correlation is such a simple term that doesn't tell us much, why is it still important?

Because it is incredibly useful as an early signal. It tells you:

“There might be something interesting going on here.”

From there, you investigate further. Alignment of integration steps; further investigation provides an explanation.

The final takeaway

“Correlation does not imply causation.” That is true. But here's the problem: people hear this and think: “Relationship doesn't make sense.” That is not true!

Correlation measures how variables move together; ranges from -1 to 1, capturing a linear relationship, but NOT causation.

Relation is not misleading. We just expect too much from it if it doesn't try to explain the world. It's just a signal that shows:

“Hey…this looks interesting.”

Now, the real work begins, as we investigate why this is really interesting.