Margin of error vs. confidence intervals for data-driven decisions

When it comes to usability testing, numbers tell the story — but interpreting those numbers correctly can mean the difference between a solid product decision and a costly mistake.

Part of avoiding these mistakes involves knowing how to use and tell the difference between usability concepts. Two of the most misunderstood ones include margin of error and confidence intervals.

While they might sound like complex statistical jargon, the concepts behind them are simple and essential to understand if you’re conducting usability testing or any type of survey.

To help get you started, this post breaks them down and explores how they work in practice.

Don’t be 100 percent confident in your data

Imagine you’re in the vehicle leasing business and want to find out what percentage of Amsterdam residents have leased a car in the past two years.

Would you survey every single resident in the city? Probably not.

Instead, you’d take a sample — a smaller, randomly selected group of people that represents the population as a whole.

When it comes to usability testing or surveys, you rely on samples in the same way. A small group of participants stands in for the entire target audience.

But here’s the catch: because you’re only working with a portion of the population, your results can never be 100 percent accurate.

They’re always an estimate of the true value, with some degree of uncertainty — known as the margin of error.

You don’t need to be a math expert to understand the margin of error. But having a basic grasp of the concept can help you improve the reliability of your results and make better decisions.

Key testing concepts: Confidence level, margin of error, and confidence intervals

To understand the margin of error, you need to know three key terms: confidence level, margin of error, and confidence interval:

1. Confidence level

Your confidence level represents how certain you are that your results reflect the true value of your target group.

It’s a value you select — not something calculated by your data — and it reflects your tolerance for uncertainty.

• A higher confidence level means you want to be more certain, so you’re less willing to risk being wrong
• A lower confidence level is fine when precision is less critical and some uncertainty is acceptable

There a few common confidence levels used:

• 99 percent — Used in high-stakes situations where errors could have serious consequences, like testing the effectiveness of a new drug in medical research
• 95 percent — This is the standard choice in usability testing and research. It balances certainty and practicality
• 90 percent — Used for exploratory or early-stage testing, where early insights are more important than precision

2. Margin of error

Your margin of error (or margin error) is a calculated value that shows how much your sample results might differ from the true population value. It reflects the potential uncertainty in your data.

Unlike the confidence level (which you choose), the margin of error is derived from your data and depends on factors like the sample size, variability in the data, and your chosen confidence level.

Key points:

• A smaller margin of error means your results are more precise
• A larger margin of error reflects more variability or smaller sample sizes

The margin of error is expressed as a percentage. If the results of your testing are 60 percent with a margin of error of 3 percent, it means the true value is likely within ±3 percent of your result (between 57 percent and 63 percent).

3. Confidence intervals

Once you have the margin of error, you can calculate the confidence interval — the range within which the true value is expected to fall.

The confidence interval is calculated by adding and subtracting the margin of error from your result. It’s expressed as:

[X – margin of error and X + margin of error]

If your result is 60 percent with a margin of error of 3 percent, the confidence interval would be between 57 percent and 63 percent.

Examples of margin of error and confidence intervals in practice

Now, to see how the confidence level, margin of error, and confidence interval work together, read through the following scenarios.

Vehicle leasing survey

• Chosen confidence level: 90 percent
• Survey result: 60 percent of participants reported leasing a vehicle
• Calculated margin of error: ±3 percent
• Calculated confidence interval: [57 percent, 63 percent]

How to interpret this:
With 90 percent confidence, you can say that the true percentage of people in the overall population who leased a vehicle is between 57 and 63 percent.

This means that if you repeated the survey 100 times, the results would fall within this range 90 times out of 100.

Usability testing: Task completion

• Chosen confidence level: 95 percent
• Testing result: 80 percent of participants successfully completed the given task
• Calculated margin of error: ±2 percent
• Calculated confidence interval: [78 – 82 percent]

How to interpret this:
With 95 percent confidence, you can say the true percentage of users who would successfully complete the task is between 78 and 82 percent.

This means that if you conducted the usability test 100 times, the true result would fall within the range [78 – 82 percent] 95 times out of 100.

What influences the margin of error formula?

At this point, you might be thinking that you understand how the margin of error works in tandem with your confidence intervals but want to know more about how you actually calculate it:

The error margin is a function of three parameters:

• Z (Z-Score) — A fixed number calculated directly from your selected confidence level. The most commonly used confidence levels result in:
  • At a 95 percent confidence level, Z=1.96
  • At a 90 percent confidence level, Z=1.65
  • At a 99 percent confidence level, Z=2.58
• n (sample size) — This is the number of participants in your usability test or survey
• p (sample proportion) — The percentage or fraction of people in the test who meet the specific condition or answer the researched question positively
  • Example: If you’re testing a feature with 100 users and your goal is to observe how many will complete a certain task, and 60 of them successfully complete it, the sample proportion is 60 percent (p = 0.6)

A higher confidence level increases the margin of error

If you choose a higher confidence level (e.g., 99 percent), the margin of error increases.

For example, assume your result is 60 percent, and at a 95 percent confidence level, the margin of error is ±2 percent. This means you can be 95 percent confident that the true value falls within the range [58 to 62 percent].

However, if you want to state the same result with 99 percent confidence, you’ll need a wider range to account for the additional certainty. This results in a higher margin of error, meaning the range might expand to something like [57 to 63 percent] to include the true value with greater confidence.

A higher sample size means a lower margin of error

A larger sample size reduces the margin of error because it provides a more accurate representation of the target population. With more participants, the results are closer to what you’d get if the entire population were tested.

On the other hand, a very small sample size increases the margin of error, making the results less reliable.

The variability of the result affects margin of error

The variability in your results, reflected by the sample proportion p significantly influences the margin of error. The value p*(1−p) is largest when p is close to 50 percent and smaller when p is closer to 0 or 100 percent.

Results where p is close to 50 percent (e.g., 50 percent of users completing a task) result in a larger margin of error because the variability in the data is higher.

In contrast, results near the extremes (e.g., 90 or 10 percent) have lower variability, which reduces the margin of error.

What can you do to maximize results?

How can you achieve high precision in your results and reduce the margin of error?

While some factors are outside your control, like the confidence level (determined by the context of your work) or the variability in your data (the sample proportion p), there are two key steps you can take to improve your results:

1. Eliminate biased data

The margin of error formula assumes your data is unbiased.

What does that mean?

If you want to find out what percentage of Amsterdam residents have leased a car, it’s a bad idea to only survey people working at a car leasing company.

Why?

The data would be biased, as this group is much more likely to lease cars than the general population.

What should you do instead:

• Select your sample randomly so that every individual in the population has an equal chance of being included
• Make sure your sample isn’t skewed toward a specific group that doesn’t accurately represent the entire population

Without a representative sample, even a large sample size or high confidence level won’t give reliable results.

2. Adjust the sample size

The second important factor is the sample size.

A larger sample size reduces the margin of error and narrows the confidence interval, making your results more reliable.

Let’s say you’re working with a population of 10,000 users, a confidence level of 95 percent, and a sample proportion of 80 percent. Here’s how the margin of error decreases as you increase the sample size:

 

Sample size	Error margin
100	7.8 percent
200	5.5 percent
500	3.4 percent
1000	2.3 percent
2000	1.5 percent

 

But there’s a trade-off: larger samples require more resources, time, and costs.

Testing the entire population would provide perfectly accurate results, but it’s unrealistic and often unnecessary.

You need to balance resources and accuracy.

There isn’t a one-size-fits-all answer, but here are some tips to guide you:

• For exploratory research or initial usability tests, aim for a margin of error around 7 to 10 percent
• For key decisions like product launches or user satisfaction surveys, aim for a margin of error between 2 to 5 percent
• For high-stakes research, where precision is critical (e.g., medical testing or compliance studies), aim for a margin of error of 1 to 2 percent

Practical tips for usability testing

When conducting usability testing, these practical tips can help you maximize reliability and make the most of your resources:

• Use a sample size calculator — Many online tools are available to help you calculate the margin of error and determine the ideal sample size for your study. Use these calculators to experiment with different confidence levels, sample sizes, and error margins to understand how they impact your results
• Report with transparency — Always include error margins and confidence intervals in your reports. Providing stakeholders with this information ensures they understand the reliability and limitations of the results, avoiding overconfidence in findings
• Prioritize key metrics — If resources are limited, focus on the most critical metrics only and ensure they are supported by adequate sample sizes
• Leverage iterative testing — Start with smaller, exploratory tests, identify major issues, then scale up with larger tests to refine your findings. Iterative testing saves time and resources while helping you address the most significant problems early

Key takeaways

Understanding usability testing results requires grasping three key concepts: confidence level, margin of error, and confidence interval.

Here are some key takeaways:

• Ensure your sample is unbiased and large enough to achieve reliable results
• A higher confidence level increases the margin of error, requiring more sample data for greater precision
• Balance resources with accuracy and focus on critical metrics
• Always report results transparently, including margin of error and confidence intervals

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