Calculadora de Intervalo de Confianza

Calculadora de Intervalo de Confianza

The Confidence Interval Calculator turns a single sample into a defensible range estimate for an unknown population parameter. Feed it your sample size, sample mean and sample standard deviation (or, for survey-style data, your sample size and number of “yes” responses) and it returns the lower bound, upper bound, margin of error and the exact critical value used — all computed in your browser using the same Z and Student-t distributions that statistics textbooks rely on.

Two modes are supported. Mean mode auto-selects the t-distribution for small samples (n < 30) and the Z-distribution otherwise, with an override switch for cases where the population sigma is known. Proportion mode defaults to the Wilson score interval, which holds up better than the textbook Wald formula on small samples or proportions near 0% / 100%.

Cómo Usar

1. Pick what you are estimating — a mean (continuous data like weight, time, score) or a proportion (yes / no outcomes).
2. For a mean: enter the sample size, sample mean and sample standard deviation. The distribution selector defaults to Auto; leave it unless you genuinely know the population sigma.
3. For a proportion: enter the sample size and the number of successes. Keep the Wilson method unless your stats class specifically requires Wald.
4. Choose a confidence level (80%, 90%, 95%, 99%, 99.9%, or any custom value between 50% and 99.99%).
5. Read the result — the green verdict box shows the interval in plain English, and the breakdown table below it lists every intermediate number (standard error, critical value, margin of error, bounds).

Características

• Two estimation modes — sample mean (Z or Student-t) and one-proportion (Wilson score or Wald).
• Auto distribution selection — picks t for n < 30 and Z for larger samples, with manual override.
• Exact critical values — inverse normal CDF (Beasley-Springer-Moro) and inverse Student-t (numerical inversion of the regularized incomplete beta), so any confidence level and any df work without lookup tables.
• Wilson score for proportions — the default method, robust even at p̂ = 0%, p̂ = 100% or tiny n where the Wald interval breaks down.
• Custom confidence levels — the five common presets plus any custom level from 50% to 99.99%.
• Visual interval band — the point estimate and the confidence band rendered on a number line so the width is immediately readable.
• Copy-friendly summary — a monospace block with every input, calculation step, and the resulting interval, ready to paste into a notebook or report.
• Quick examples — one-click presets for adult height, political polling, A/B conversion, and small lab samples.
• 100% del lado del cliente — your numbers never leave the browser; calculations run instantly with no server round-trip.

When to Use a Confidence Interval

Reach for a confidence interval whenever you need to communicate an estimate plus its uncertainty. Reporting a single number (a sample mean of 4.2, a conversion rate of 6.4%) hides the fact that another sample would have given a slightly different value. A confidence interval makes that variation explicit: “we are 95% confident the true value is between 3.50 and 4.90”. That framing is essential for A/B tests, opinion polls, lab measurements, medical studies, manufacturing tolerances and any decision that depends on whether a difference is real or just sampling noise.

Mean vs Proportion — Which Mode?

Usa mean mode when your sample is a list of numeric measurements — reaction times, blood pressure readings, monthly revenue figures, exam scores. You will need both the sample mean (x̄) and the sample standard deviation (s). Use proportion mode when each observation is a binary outcome — voted yes / no, clicked / did not click, recovered / did not recover. You only need the sample size and the count of “yes” outcomes; the calculator handles the rest.