Interpreting 95% confidence intervals in experiment results

Ever scratched your head over what a "95% confidence interval" really means? You're not alone. For many, it's a statistical concept that's shrouded in mystery and often misunderstood.

In this blog, we'll break down the 95% confidence interval in simple terms. We'll explore its role in experiments and how to interpret it correctly. So, let's dive in and demystify this fundamental statistical tool!

Demystifying the 95% confidence interval

So, what's all the fuss about the 95% confidence interval (CI)? Simply put, it's a range that, if you repeated your sampling process over and over, would contain the true population parameter 95% of the time. It tells us how precise and reliable our estimate is based on sample data. But here's a common misunderstanding: a 95% CI doesn't mean there's a 95% chance the parameter is within that interval.

This mix-up happens a lot, even among folks with a bit of statistical know-how. Just check out some discussions on Reddit. Getting a grip on CIs is key for making valid statistical inferences and smart decisions based on data.

In the world of online experiments, the 95% CI is like a gatekeeper. It helps us decide whether to reject the null hypothesis at a 5% significance level. It shows us the range of plausible values for the true effect and how precise our estimate is. Here at Statsig, we use different statistical tests, like the two-sample z-test and Welch's t-test, to crunch those CIs based on the data's quirks.

Understanding the role of the 95% CI is super important for experimenters and decision-makers alike. Even though it's a go-to standard, sometimes you might need to tweak the confidence level based on your experiment's needs and how much risk you're willing to take. No matter what level you choose, correctly interpreting CIs is vital for drawing accurate conclusions from your data.

The role of confidence intervals in experimental results

Confidence intervals (CIs) are like our statistical compass—they help us estimate population parameters based on our sample data. They give us a range that's likely to contain the true value. In online experiments, if a 95% CI doesn't include zero, it suggests there's a statistically significant difference between groups at a 5% significance level.

CIs are super helpful for decision-making because they quantify how precise and reliable our observed effects are. For instance, a 95% CI for a metric delta shows us the range of plausible values. If the CI is narrow, our estimate is more precise; if it's wide, there's more uncertainty.

We see CIs in action all the time:

• Evaluating how a website redesign affects user engagement

• Testing which marketing strategy boosts conversion rates

• Comparing different product features or algorithms

By giving us a measure of uncertainty, CIs help us make informed decisions based on data. They're crucial for interpreting results and figuring out the practical significance of our findings. And depending on your study's risk profile, you might adjust the confidence level (like using 90% or 99%) to suit your needs.

Interpreting confidence intervals correctly: avoiding pitfalls

Misinterpreting CIs can really mess things up. One big misunderstanding is thinking that a 95% CI means there's a 95% chance the true value is within the interval. That's not the case! Instead, it means that if we repeated the experiment many times, 95% of those intervals would contain the true value (see The correct interpretation of Confidence Intervals).

Another trap is focusing only on statistical significance and ignoring practical significance. Just because a result is statistically significant doesn't mean it's meaningful in the real world. For example, with a huge sample size, even tiny differences can be statistically significant—but they might not matter for your business (as discussed in The Surprising Power of Online Experiments).

To get CIs right, look at both the interval width and the effect size. A narrow CI means high precision; a wide one means more uncertainty. Always consider the context and use your domain knowledge—a statistically significant result might not be practically relevant.

Visualizing CIs can also help. Plotting the intervals with point estimates gives a clear picture of uncertainty and effect size. This is especially handy when comparing multiple groups or experiments.

Lastly, watch out when interpreting CIs for subgroups. Smaller sample sizes in subgroups can lead to wider CIs and more uncertainty. Make sure to apply appropriate corrections and consider the big picture when making decisions based on subgroup analyses.

Beyond the basics: advanced concepts and applications

Let's delve a bit deeper. While confidence intervals and credible intervals might sound similar, they come from different statistical philosophies. Confidence intervals are part of frequentist statistics, using methods like the Clopper-Pearson and Jeffreys methods to utilize quantiles of the Beta distribution. Interestingly, as we get more data or use less informative priors, these methods converge, making credible and confidence intervals look pretty much the same.

Another key point is that data quality is crucial for trusting experimental results. It takes time and effort to validate data and set up automated checks. Running A/A tests—testing the system against itself—helps ensure reliability by showing statistically insignificant differences 95% of the time. Companies like Microsoft have found lots of issues in experiments and incorrect formulas through rigorous testing.

Sometimes, you might consider adjusting the confidence interval from the standard 95%. Depending on your experiment's needs, tweaking the confidence level can make sense. For example, startups willing to take more risks might go for a 90% interval to catch more potential positives, while those working on critical systems might opt for 99% to reduce false positives. Just remember: make any adjustments before collecting data to avoid bias (more on this at Statsig's blog).

Lastly, there are challenges like experiment inference problems when estimating treatment effects or interpreting results across subgroups. Traditional p-value approaches can be tricky. Alternatives like empirical Bayes estimates use prior experiment data to better estimate true effects. But keep in mind, empirical Bayes isn't a magic bullet—it might miss unique details of your specific experiment.

Closing thoughts

Grasping the ins and outs of confidence intervals, especially the 95% CI, is key to decoding statistical results and making smart decisions. By interpreting these intervals correctly and watching out for common pitfalls, you can draw more accurate conclusions from your data. Remember, tools like CIs are here to guide us, but they need to be used wisely.

If you're keen to learn more, check out the resources linked throughout this post. And as always, Statsig is here to help you navigate the world of experimentation and data analysis. Hope you found this helpful!