Correlation Is Not Causation But What *Really* Drives Your Data Decisions

When I entered the tech world, there was one phrase everyone seemed to know, regardless of age or background:

“Correlation does not equal causation.”

It’s a catchy line you’ve probably quoted before, and you’ve likely given it an approving nod when someone else brought it up. It tends to come up most often with datasets that have nothing to do with each other, yet people love implying a cause-and-effect link as a joke or curiosity!

Here are two strikingly fun facts:

• Countries where people consume more pizza tend to have higher math test scores.
• As the number of sunglasses sold goes up, the number of shark attacks also tends to rise.

Now, if those were the only pieces of data you had… what would you jump to conclude?

Does eating pizza improve your math skills? Will purchasing sunglasses somehow trigger a shark attack?

As amusing as it is to imagine, the honest answer is “almost certainly not.”

Still, these are genuine examples of something real: Correlation.

The real question we should ask is: if correlation doesn’t equal causation, then what actually is it?

That’s where confusion often sets in.

Because correlation often gets treated as a vague notion, many people think of it as a loose idea like “These two things are somehow related” or “They sort of follow each other.” But correlation is not just a hunch; it’s a precise, numeric measure showing how two variables vary together.

Instead of just repeating the classic warning, we’re going to actually explore the meaning behind it. Once you grasp it, those oddball examples stop feeling surprising and start making logical sense.

So let’s dive in!

What Does Correlation Mean?

When people say two variables are “correlated,” they usually mean one of three things:

• “Those two things appear connected.”
• “Those two things tend to change together.”
• “There seems to be some sort of relationship.”

At a basic level, all three of these impressions are understandable, but they’re missing important detail.

Correlation is not a feeling. It’s a measurement. And like any measurement, it answers a specific question clearly.

To see this clearly, consider gathering data on the number of hours students studied and the scores they received on a test.

After plotting it, you might see something like this:

Each dot represents a student. The horizontal axis shows hours studied, the vertical axis shows their score.

Looking at the chart, you can see that the dots generally rise from left to right. You might then say: “As study time increases, scores tend to go up as well”—which we refer to as a positive correlation.

But is that just a visual impression, or is the data revealing something more solid?

In this case, the pattern you’re seeing means: whenever one variable is above its average, the other tends to be above its average as well.

That’s the key idea most people overlook: correlation isn’t about raw numbers—it’s about how each variable moves in relation to its own average.

So, the core question correlation answers is:

Do two variables consistently move together in a predictable way?

That question leads to one of three possible outcomes:

• Both rise together → positive correlation
• One rises while the other falls → negative correlation
• No consistent movement → no correlation

Understanding the Math Behind It

To make the idea of correlation easier to grasp, let’s look at the Pearson correlation coefficient, defined as:

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

I realize that formula doesn’t scream “intuitive” at first glance… But stay with me—we’ll break it down without making it feel like a textbook.

Step 1: Covariance — Do They Move Together?

Covariance checks how two variables deviate from their respective averages. If both are above average at the same time, covariance is positive; if one is high while the other is low, it’s negative.

In simple terms, covariance tells us: “Are these variables aligned in how they differ from their own averages?”

Step 2: Normalize It

On its own, covariance is hard to compare because it depends on the units of measurement. To fix that, we divide by the standard deviations: $sigma_{X}$ and $sigma_{Y}$. This rescales everything into a clean, universal range: from –1 to 1. That gives us a standardized basis for comparison.

With these two steps in place, we can compute the Pearson coefficient! The result tells us:

1. +1 → a perfect positive relationship.
2. 0 → no linear relationship.
3. –1 → a perfect negative relationship.

This number simply captures how consistently two variables move together—not how large they are, but how aligned their patterns are.

What Different Correlations Look Like