What is Confidence Interval?
ELI5 — The Simple Version
Imagine you're trying to find the perfect time to bake cookies. You've baked them ten times, and each batch turned out great when baked between 10 and 15 minutes. This range, 10 to 15 minutes, is like a confidence interval. It shows the time frame where you can be pretty sure the cookies will be perfect. Now, picture testing two cookie recipes to see which one your friends like more. You give them both recipes and count the thumbs up each one gets. The confidence interval here is the range of votes each recipe might receive if you asked even more people. It helps you predict which recipe is likely the favorite beyond just your friends. This is important because when deciding which recipe to bake for a party, you want to be confident in your choice. Using a confidence interval means you're not just guessing; you have a good idea based on evidence.
Technical Deep Dive
Definition
A confidence interval is a statistical tool used to estimate the range within which the true value of a parameter lies, given a certain level of confidence (usually 95% or 99%). In A/B testing, it indicates the reliability of the observed difference in conversion rates.
How It Works
- 1.Conduct an A/B test to collect data.
- 2.Calculate the sample mean and standard deviation.
- 3.Determine the desired confidence level (e.g., 95%).
- 4.Use a statistical formula or tool to calculate the confidence interval.
- 5.Interpret the interval: if it does not include zero, the difference is statistically significant.
Key Characteristics
- Range: Indicates variability and uncertainty.
- Confidence Level: Typically 95% or 99%.
- Margin of Error: Width of the interval.
Comparison
| Concept | Definition |
|---|---|
| Confidence Interval | Range for estimating a parameter with confidence |
| P-Value | Probability of observing the test results under null hypothesis |
| Standard Error | Measure of statistical accuracy of an estimate |
Real-World Example
In a VWO A/B test, a company tested two landing page designs. Design A had a conversion rate of 8%, while Design B had 10%. The confidence interval for the difference in conversion rates was calculated as 1% to 3%, confirming Design B's superiority.
Best Practices
- Use tools like Google Optimize or Optimizely for automated calculations.
- Ensure sample sizes are adequate to avoid wide intervals.
- Interpret intervals contextually with business goals.
Common Misconceptions
- Myth: A wider interval means the result is unreliable.
Truth: It reflects more variability and less precision.
- Myth: Overlapping intervals mean no difference.
Truth: Overlap doesn’t always imply non-significance.