How to Build Confidence Intervals for UX Metrics

By Philip Burgess | UX Research Leader

Understanding user experience (UX) metrics is crucial for making informed design decisions. However, raw numbers alone can be misleading without a sense of their reliability. Confidence intervals provide a way to express the uncertainty around UX measurements, helping teams understand how much trust to place in their data. This post explains how to build confidence intervals for UX metrics, making your analysis clearer and more actionable.

Confidence intervals displayed on a UX analytics dashboard

What Are Confidence Intervals and Why They Matter in UX

A confidence interval is a range of values that likely contains the true value of a metric. For example, if you measure the average time users spend on a page, the confidence interval tells you the range where the actual average probably lies. This range accounts for variability in your sample data.

In UX, confidence intervals help you:

• Understand the precision of your metrics

• Compare different designs or user groups reliably

• Avoid overreacting to small changes caused by random variation

  
  

Without confidence intervals, you might assume a change in a metric is meaningful when it could just be noise.

Key UX Metrics Suitable for Confidence Intervals

Not all UX metrics require confidence intervals, but many benefit from them. Common examples include:

• Task completion rate: The percentage of users who complete a task successfully

• Time on task: How long users take to finish a task

• Click-through rate: The proportion of users clicking a specific element

• System Usability Scale (SUS) scores: A standardized usability score from surveys

  
  

Each of these metrics comes from sample data, so their values vary depending on who participates in the test.

Step-by-Step Guide to Building Confidence Intervals

1. Collect Your UX Data

Start with a well-defined sample of users performing the tasks or interacting with your product. Ensure your sample size is large enough to provide meaningful results. For example, testing with only five users may not give reliable intervals, while 30 or more users usually provide better estimates.

2. Calculate the Metric of Interest

Compute the metric you want to analyze. For instance, if measuring task completion rate, count how many users succeeded and divide by the total number of users.

3. Choose the Right Statistical Method

The method to calculate confidence intervals depends on the type of metric:

• Proportions (e.g., task completion rate): Use a binomial proportion confidence interval, such as the Wilson score interval.

• Means (e.g., time on task, SUS scores): Use the t-distribution confidence interval if the sample size is small or the population standard deviation is unknown.

  
  

4. Calculate the Confidence Interval

For a mean metric, the confidence interval formula is:

```

Mean ± (t-value * standard error)

```

• Mean: Average of your sample data

• t-value: From the t-distribution table based on your confidence level (commonly 95%) and degrees of freedom (sample size minus one)

• Standard error: Standard deviation divided by the square root of the sample size

  
  

For proportions, use an appropriate formula or software function to get the interval.

5. Interpret the Interval

A 95% confidence interval means that if you repeated the study many times, 95% of those intervals would contain the true population metric. It does not mean there is a 95% chance the true value lies within this one interval.

Practical Example: Task Completion Rate

Imagine you test a new checkout flow with 50 users. Forty-five complete the task successfully. The task completion rate is 90%.

Using the Wilson score interval, the 95% confidence interval might be approximately 79% to 96%. This means the true completion rate for all users likely falls within this range.

This interval helps you understand that while 90% looks good, the actual success rate could be as low as 79%. If a previous design had a 70% completion rate, you can be confident the new design performs better.

Tools to Build Confidence Intervals

You don’t need to calculate confidence intervals by hand. Many tools and programming languages offer built-in functions:

• Excel: Use formulas or add-ins for confidence intervals

• R: Functions like `t.test()` for means or `binom.test()` for proportions

• Python: Libraries such as SciPy (`scipy.stats.t.interval`) or statsmodels

  
  

These tools simplify the process and reduce errors.

Python code snippet calculating confidence intervals for UX metrics

Tips for Using Confidence Intervals in UX Research

• Always report confidence intervals alongside point estimates to provide context.

• Use intervals to compare different designs or user groups rather than relying on single numbers.

• Remember that wider intervals indicate more uncertainty, often due to small sample sizes.

• Avoid overinterpreting small differences when confidence intervals overlap.

• Combine confidence intervals with qualitative insights for a fuller understanding.

  
  

Final Thoughts on Confidence Intervals for UX Metrics

Building confidence intervals for UX metrics adds clarity and trustworthiness to your data analysis. They help you see beyond single numbers and understand the range where the true user experience likely falls. This approach supports better decision-making and more reliable improvements to your designs.