StatReason

Confidence Interval Calculator

"Confidence interval" is not one formula; it is a family of methods, each appropriate for a different design. Answer one question below and this page routes you to the exact calculator built for your situation, rather than giving one generic answer that silently picks a method for you.

What this answers

This page answers "which confidence interval calculator on this site actually matches my design?" A mean, a proportion, and a difference between groups each need a different standard error formula and, in several cases, a different reference distribution entirely. Picking the wrong one produces a technically computable but statistically wrong interval.

How the routing works

Each option above maps to exactly one canonical engine on this site, listed in full below. There is no separate calculation happening on this page itself; it exists purely to save you the trouble of knowing this site's category structure in advance, and to make sure you land on a method whose assumptions actually match your data.

The four supported designs

A single mean uses the Mean Confidence Interval Calculator, built on the t distribution. A single proportion uses the Proportion Confidence Interval Calculator, built on the Wilson score interval rather than a plain normal approximation. Two independent groups' mean difference uses the Difference in Means Confidence Interval, built on Welch's method by default. Matched pairs use the Paired Mean Difference Confidence Interval, built directly from the paired differences.

Assumption audit

Calculated from your data: nothing on this page itself; the destination calculator you land on performs its own full assumption audit once you arrive.
Evidence to review: whether your actual data structure genuinely matches the design you selected here. A common source of error is treating naturally paired data (the same subjects measured twice) as if it were two independent groups, which throws away information and can give a misleadingly wide interval.
You must verify: your study design before selecting an option here; no router can infer from raw numbers alone whether two lists are independent groups or matched pairs.

Common mistakes

Selecting "two independent group means" for data that is actually matched pairs is the single most common design error this router exists to prevent; if your two lists have a genuine row-by-row correspondence, use the paired option instead. A second mistake is wanting a difference in proportions or an odds ratio, which are not listed here since they have their own dedicated engines under this same category on the site's directory.

Limitations

This router only covers the four most common designs by search volume; less common designs such as a difference in proportions, an odds ratio, or a bootstrap interval for a statistic without a closed form each have their own standalone engines, browsable from the Confidence Intervals & Estimation category page.