Causal relationships: how to prove cause versus correlation

Ever heard someone say, "Correlation doesn't imply causation"? It's a phrase that's tossed around a lot, but what does it actually mean? Understanding the difference between when two things happen together and when one thing actually causes the other is super important. Especially when you're making decisions based on data in product development or marketing.

We'll explore how misunderstanding correlation and causation can lead to some big mistakes. Plus, we'll look at how selection bias can trip you up and what you can do to figure out what's causing what. By the end, you'll have a better handle on how to make sense of the numbers and make smarter decisions. So, let's get started!

Understanding correlation vs. causation

Correlation is when two things seem to be related, but causation is when one thing actually causes the other. It's crucial to know the difference. Just because two things happen together doesn't mean one caused the other. Correlation does not equal causation, and this is often misunderstood when looking at data.

Take this classic example: ice cream sales and shark attacks both go up in the summer. Weird, right? But eating more ice cream doesn't make sharks attack more people. The real cause? It's warmer, so more people are at the beach. That's the causal relationship.

Mixing up correlation with causation can lead to bad assumptions and strategies that just don't work. Especially in product analytics, where user behaviors might seem linked to certain outcomes. But without running controlled experiments, you can't be sure what's really causing what.

Tools like linear regression and correlation analysis are great for spotting potential relationships in your data. But if you want to nail down causation, you need to get serious with testing and causal inference. Understanding this difference helps you make smarter, data-driven decisions and use your resources where they'll have real impact.

The role of selection bias in misinterpreting correlations

Selection bias is another thing that can really mess with how we interpret correlations. It can make us think there's a causal relationship when there isn't one. Think of the formula: Correlation ≈ Causation + Selection Bias. It's a way to remind us that bias can sneak in.

Here's an example: a study finds that people who take vitamin supplements live longer. Sounds like vitamins are the key to a long life, right? But maybe it's just that folks who take vitamins are already more health-conscious—they exercise, eat well, and so on. That's selection bias at work.

Selection bias happens when the group you're studying isn't a good snapshot of the whole population. Maybe certain people are more likely to be in your study because of something about them. That's a problem because it can skew your results.

To really figure out if something causes something else, we have to control for selection bias. That's where randomized controlled trials (RCTs) come in. By randomly assigning people to different groups, we make sure that any differences we see are because of the thing we're testing, not because of who the people are.

In product analytics, selection bias can trip you up. Say you notice that users who use a certain feature are more likely to convert. You might think the feature is causing conversions. But maybe those users are already more engaged overall. To find out if the feature really makes a difference, you'd need to run an experiment where you randomly give some users access to it and see what happens.

At Statsig, we know how important it is to account for selection bias. That's why we focus on helping teams run robust experiments to uncover true causal relationships.

Methods to establish causation from correlation

So, how do we figure out if one thing really causes another? The go-to method is running controlled experiments like randomized controlled trials (RCTs). By randomly splitting people into groups and testing something new with one group, we can see if changes are due to our intervention and not something else. This method is big in medical research and now it's catching on in business too.

But what if we can't do an experiment? That's where statistical techniques come in—things like regression analysis and propensity score matching. These methods try to account for selection bias by adjusting for other factors that could be influencing results. They're not perfect, but when experiments aren't possible, they can still give us useful insights.

In the world of digital products, A/B testing is super popular. We show different versions of a feature to different users at random and see which one performs better. It's a straightforward way to find out what's really making a difference in engagement or conversions. Plus, we use hypothesis testing to make sure our results are statistically significant—not just due to random chance.

There are also more advanced methods like instrumental variables (IV) and difference-in-differences (DID). These are fancy econometric techniques that help estimate causal effects when we can't randomize. They require some pretty careful assumptions, though, so they're best used in specific situations.

At the end of the day, figuring out causal relationships is key to making smart decisions. By combining experiments with statistical methods, we can move beyond just spotting correlations and start understanding what's really driving our metrics. Whether we're tweaking a product feature or rolling out a marketing campaign, using these approaches helps us get better results.

Applying causal inference in practice

So, what does all this look like in the real world? Misreading correlation and causation can lead you down the wrong path. For instance, you might see that users who use advanced features are less likely to leave and think that adding more advanced features will reduce attrition. But unless you test this with a controlled experiment like A/B testing, you can't be sure.

When we're running experiments, we have to watch out for interaction effects. That's when two experiments overlap and affect each other's outcomes, messing up our results. Using techniques like hypothesis testing and Chi-squared tests helps us spot these interactions so we can trust our findings.

Here are some tips for making causal inference work in practice:

• Keep it simple: Complex experiments can hide what's really causing changes.

• Focus on the "what": Even if you don't fully get the "why" behind your results, knowing what works is valuable.

• Use your judgment: Data isn't everything. Combine formal methods with your own intuition and experience.

By following these principles, you can navigate the tricky world of data and make choices based on real cause-and-effect relationships. Remember, tools like correlation analysis and linear regression are helpful, but they don't prove causation on their own. Controlled experiments are still the best way to figure out what's really going on.

At Statsig, we're all about helping teams run effective experiments and make data-driven decisions. We hope these insights help you on your journey to better understand your users and build amazing products.

Closing thoughts

Understanding the difference between correlation and causation isn't just academic—it's essential for making smart decisions based on data. By being aware of pitfalls like selection bias and using methods like controlled experiments, we can uncover the real drivers behind our metrics. Whether you're in product development, marketing, or any field that relies on data, applying these principles will help you avoid mistakes and achieve better outcomes.

If you're interested in learning more, check out the links we've included throughout the blog. And if you're looking for tools to help you run experiments and make sense of your data, Statsig is here to help. Happy experimenting!