Confidence Intervals (CIs)#
A range that would contain the true parameter a stated fraction of the time.
Important
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What it is#
A confidence interval is a range of plausible values for an unknown parameter — a mean, a proportion — computed from a sample together with a confidence level (typically 95%). It expresses the uncertainty in a point estimate: a wider interval means less precision.
What the level means#
The confidence level is a statement about the procedure, not any one interval. If you repeated the study many times, about 95% of the intervals you built would contain the true value — it is not a 95% probability that the parameter lies in this interval (in the frequentist view the parameter is fixed). Intervals narrow as the sample size grows.
How they’re built#
A CI is typically an estimate ± a margin of error (a critical value times a standard error), but for tricky quantities like a binomial proportion there are several methods — Wald, Wilson, Clopper–Pearson, bootstrap — that trade coverage against width.
Theme: Statistical Inference & Power · All terminology
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Mind map — connected ideas
Clopper–Pearson Interval · Wilson Score Interval · Bootstrap Confidence Intervals (CIs) · Standard Error (SE) · Statistical Tests · Normal Distribution
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More in Statistical Inference & Power
A Priori Power Analysis · Chi-square (χ²) Test · Clopper–Pearson Interval · Compromise Power Analysis · Effect Size (δ) · Hypothesis Testing · Kolmogorov–Smirnov (KS) Test · Minimum Detectable Lift (MDL) · P-Value (probability value) · Post Hoc Power Analysis · Power (1 – β) · Power Analysis · Sample size · Significance Level (α)
See also
Source article Adapted (context, re-expressed) in our own words from: Confidence Intervals (CIs) (insightful-data-lab.com).