Calculate confidence intervals for population parameters. Part of the DevTools Surf developer suite. Browse more tools in the Statistics collection.
Use Cases
Calculate margins of error for survey results before publishing
Determine precision of an A/B test metric before declaring a winner
Report results of user research with appropriate statistical uncertainty
Validate that a sample-based estimate is within acceptable error bounds
Tips
Choose the correct distribution: use z-score for large samples (n>30) or known population variance; use t-distribution for small samples (n<30) or unknown variance
The margin of error output directly answers how precise your estimate is — it equals half the confidence interval width
For proportions (like conversion rates), use the Wilson interval option instead of the normal approximation — it is more accurate near 0% and 100%
Fun Facts
The concept of confidence intervals was developed by Jerzy Neyman in 1937, who invented them as an alternative to the p-value approach of significance testing. Neyman and Karl Pearson's son Egon collaborated on much of classical statistics during this period.
A 95% confidence interval does not mean there is a 95% probability the true value is in the interval. It means that if you repeated the experiment 100 times, approximately 95 of those intervals would contain the true value — a subtle but important distinction.
In physics, 'five sigma' (99.99997% confidence) is the standard for claiming a new particle discovery — the level used when announcing the Higgs boson in 2012. The threshold is far stricter than social science's 95% because the implications of a false positive are vastly different.
FAQ
What is the difference between confidence level and confidence interval?
Confidence level (e.g., 95%) is the probability that the procedure produces an interval containing the true value. The confidence interval is the specific numeric range calculated from that procedure and your data. The level is a setting; the interval is the result.
Why use 95% and not 99%?
95% is the convention established in early 20th-century statistics. 99% gives a wider interval (more certain but less precise). The choice should match the consequences of error: medical trials often use 99%, while marketing tests commonly use 90% for faster decisions.
Does a wider confidence interval mean the data is bad?
A wide CI means the estimate is imprecise, usually because of a small sample size or high variance in the data. Collecting more data narrows the interval. 'Bad data' means biased or invalid data — that is a different problem than imprecision.
