Margin of Error: The Number Clients Always Ask About

"What's the margin of error?" is the single most common statistical question clients ask. Usually right before a board presentation where they need to defend a data point. The answer is almost always larger than they want to hear, especially for subgroups.

n=1,000 at 95% confidence gives you ±3.1% for a 50/50 proportion. That's the headline number. But if you're reporting on the 18-24 age group and only 120 respondents fall into that cell, the MOE jumps to ±8.9%. That's the number the client needs to understand before they put "Young adults prefer our brand by 5 points" on a slide.

What the tool shows

Input your sample size and observed proportion. The tool calculates MOE at 90%, 95%, and 99% confidence levels and renders visual confidence interval bands so you can actually see the range of uncertainty around your result. There's also a reference table showing how MOE changes across different sample sizes, which is useful for the "how many more completes do we need to tighten this up?" conversation.

The visual CI bands are the most useful part. Telling a client "the margin of error is plus or minus 5 points" is abstract. Showing them a chart where the confidence band visually overlaps with the competitor's result makes the statistical uncertainty tangible. "See how the bands overlap? That means we can't say with confidence that there's a real difference."

Tech stack

React 18.2 + Babel CDN. Z-scores from standard normal distribution tables. The confidence interval bands are rendered in SVG. The reference table pre-computes MOE for common sample sizes from n=50 to n=5,000 so you can eyeball the trade-off between additional sample and tighter precision.