When is a result statistically significant?

Ever looked at a set of data and wondered if the patterns you're seeing are real or just random chance? We've all been there—squinting at charts, trying to make sense of numbers that seem to have a mind of their own. That's where statistical significance comes into play.

In this blog, we'll dive into what statistical significance really means, how to make sense of p-values and significance levels, and why it's important not to confuse statistical significance with practical importance. We'll also share some best practices to ensure your results are reliable and meaningful—something we focus on at Statsig. Let's get started!

Understanding statistical significance

Statistical significance is all about figuring out whether the patterns we see in data are real or just random noise. It helps us tell true effects from random variations, making sure we're not fooled by chance. Essentially, we compare what we've observed to what we'd expect if there was no real effect—this idea is called the null hypothesis.

To decide if our results are statistically significant, we set a threshold known as the significance level, often set at 0.05. If the p-value, which is the probability of observing our data under the null hypothesis, is less than this threshold, we consider the result statistically significant. In simple terms, it means the effect we're seeing is unlikely to be just due to chance.

But here's the thing—statistical significance doesn't always mean the result is important in the real world. You might find a statistically significant effect, but if it's tiny, it might not be practically useful. That's why we also need to look at the effect size and clinical significance to really understand what our results mean.

When we're running online experiments (something we at Statsig are very familiar with), it's crucial to make sure our data is solid and free from issues that can mess up our conclusions. Techniques like A/A testing help confirm that our experimental setup is working correctly. We also need to watch out for outliers and heterogeneous treatment effects to keep our results trustworthy.

Interpreting results isn't just about the numbers. We also have to consider things like selection effects, subgroup outcomes, and multiple outcomes. By applying the right statistical techniques and being mindful of how different experiments might interact, we can make accurate conclusions. Understanding when a result is statistically significant—and knowing how to interpret that significance—is key to making confident, data-driven decisions.

The role of p-values and significance levels

Let's talk a bit more about p-values and significance levels—they're key players in statistical testing. A p-value tells us the probability of getting results as extreme as we did, assuming the null hypothesis is true. In other words, it's a way to measure how likely our data would be if there was no real effect.

The significance level, often denoted by alpha (α), is the threshold we set to decide whether to reject the null hypothesis. Common choices for alpha are 0.05 or 0.01, meaning we're willing to accept a 5% or 1% chance of a false positive. Deciding on an appropriate alpha level depends on the context of the study and the potential consequences of making an error.

But here's where things get tricky: p-values are frequently misunderstood. A lot of people think a p-value tells us the probability that the null hypothesis is true. It doesn't. Instead, it tells us the probability of our data given that the null hypothesis is true. And just because a result isn't statistically significant doesn't mean the null hypothesis is proven—it just means we don't have enough evidence to reject it.

Taking a look at p-value distributions can help us spot issues with our statistical tests. For example, interpreting p-value histograms can reveal problems like inappropriate test assumptions or too small sample sizes. When in doubt, getting input from a statistician can ensure we're interpreting the results correctly.

Statistical significance versus practical significance

Just because a result is statistically significant doesn't mean it's important in real life. A statistically significant result might not have much of an impact when you look at the bigger picture. For instance, a new medication might show a statistically significant improvement, but if the effect is tiny, it might not be worth the cost or side effects.

That's where practical significance comes in. It considers the actual size of the effect and whether it's meaningful in the real world. So, if you see a small but statistically significant increase in website conversion rates, you might decide it's not enough to justify a complete redesign.

To figure out practical significance, we look at the effect size, which measures how big the difference is between groups. Cohen's d is one way to do this, with values of 0.2, 0.5, and 0.8 representing small, medium, and large effects, respectively. A small effect size—even if it's statistically significant—might not be worth acting upon.

Context matters a lot here. In fields like physics, even tiny statistically significant differences can be a huge deal because measurements are so precise. But in areas like social sciences or business, where there's more variability, we usually need larger effect sizes to consider a result practically significant.

Best practices for reliable and meaningful results

To get reliable and meaningful results, ensuring data quality is a must. Using validation methods like A/A testing and setting up automated checks can help catch issues early and keep your data accurate. Investing time and resources here pays off in the long run.

It's also important to avoid common pitfalls that can mess up your interpretations. Things like data peeking, biases, and misusing statistical tests can lead you down the wrong path. Being aware of these traps—and knowing how to avoid them—is crucial.

A solid experimental design forms the backbone of meaningful results. This means careful planning, choosing the right sample sizes, and keeping an eye out for interaction effects. By doing so, your experiments are more likely to give you valid insights.

Interpreting your results accurately is essential for making informed decisions. Understanding things like p-value histograms, considering both statistical and practical significance, and effectively communicating your findings all play a part.

At Statsig, we're all about empowering teams to make data-driven decisions confidently. By following these best practices, you can trust the insights you gain and help your team succeed.

Closing thoughts

Understanding statistical significance is key to making sense of the data we encounter every day. By knowing how to interpret p-values, significance levels, and the difference between statistical and practical significance, you can make more informed, confident decisions. Whether you're running experiments or just analyzing data, these concepts are essential tools in your toolkit.

If you're interested in diving deeper, there are plenty of resources out there to explore. And remember, at Statsig we're here to help you navigate the world of data and experimentation. Hope you found this useful!