Confidence Intervals

How to use this category

An interval is a range built from a critical value and a standard error. Mean intervals use t. Proportion intervals lead with Wilson and show Wald so the choice is not hidden. Two-proportion intervals do not pool the way the matching hypothesis test does. The margin-of-error page will also solve for a sample size. If you only needed the range for a mean you already summarised, open the dedicated mean interval rather than the chooser.

An interval without a stated critical value is a slogan. Mean intervals on this shelf use t, so the margin shrinks only as the sample grows and as the estimated spread settles. Proportion intervals lead with Wilson because the Wald interval misbehaves when the proportion is near zero or one or the sample is modest. We still show Wald, since many courses teach it first and a reader needs to see the gap rather than be told to forget it. Two-proportion intervals keep the variances separate. The hypothesis test pools. If you mix those standard errors you will get a range that does not match the test you think you ran. The margin-of-error page is the one that solves backward for n. Use it when the question is how many people, not what range you already earned. A mean-difference interval and a paired interval are not the same construction either: one compares independent samples, the other stays on differences from matched pairs. Open the page that matches the design you actually ran. Confidence level is not a probability that today's interval covers the true mean; it is a property of the procedure across repeated samples. Say the level, the sample size, and the critical value family in the same sentence as the endpoints. If you only needed a point estimate, leave this shelf and open the descriptive page that matches the summary. If you needed a yes-or-no decision at alpha, leave this shelf and open the matching test. The interval is the range. It is not a substitute for either of those jobs.

The cards above are the whole category, with one sentence on the job each page actually does. Open a page when that sentence matches the decision in front of you. If the sentence is close but the assumption is wrong, read the comparison section on the page before you copy a number into a report, a bid, or a lesson plan.

Worked examples are prefilled so the first result is auditable. Change one input and the ticket updates. The essay under the ticket walks the same arithmetic in sentences, then a second example, then the move that most often breaks the definition. Five questions at the end answer the objections a careful reader raises after seeing the figure. That structure is repeated because the habit of checking is the point, not because the formulas are the same.

Internal links leave this category only when the next formula genuinely lives next door. A standard deviation page may point at variance and at a t test. It should not point at a decking calculator. If you arrived from search on a broad word, use the one-sentence descriptions to discard the near misses. Near misses are how people report a p-value from a test they did not run.

Each worksheet in Confidence Intervals keeps one H1, a canonical URL that matches the tool name, and meta text sized for search snippets. The steps are part of the page, not a hidden modal. If you teach from these pages, project the ticket and the assumptions together so students see the same definition you graded against.

When two tools in Confidence Intervals look alike, read the blurb under each name before you commit. The difference is usually a divisor, a critical value, a waste percent, or a caution that belongs on one page and not the other. That difference is why the URLs stay separate.

Reviewed 21-10-2026. Pages in Confidence Intervals currently include Confidence Interval Calculator, Margin of Error Calculator, Mean Confidence Interval Calculator, Mean Difference Confidence Interval Calculator, Paired T-Test Confidence Interval Calculator, Proportion Confidence Interval Calculator, Two Proportion Confidence Interval Calculator.

Every confidence intervals page

• Confidence Interval Calculator Builds a mean confidence interval from summary stats using a t critical value.
• Margin of Error Calculator Finds a margin of error for a mean or proportion, or solves for the sample size that buys a target margin.
• Mean Confidence Interval Calculator Confidence interval for a mean from raw data or from summary statistics.
• Mean Difference Confidence Interval Calculator Interval for the difference of two independent means using pooled or Welch SE.
• Paired T-Test Confidence Interval Calculator Interval for the mean of paired differences from raw pairs or summary stats.
• Proportion Confidence Interval Calculator Wilson score interval for a single proportion, with Wald shown underneath for comparison.
• Two Proportion Confidence Interval Calculator Interval for the difference between two independent sample proportions.