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Guide: Confidence Intervals

A confidence interval (CI) is a range of plausible values for an unknown population parameter (such as the true mean or proportion), based on your sample data.

A 95% CI means: if you repeated your study 100 times, approximately 95 of those intervals would contain the true population parameter. It does not mean there is a 95% probability that the true value is in this specific interval.

CI for a mean: Use when your outcome is a continuous measurement (height, weight, test score, reaction time). Uses the t-distribution and requires raw data.

CI for a proportion: Use when your outcome is a count of successes out of n trials — a proportion or rate (e.g. "45 out of 100 patients recovered"). Enter the number of successes (x) and total sample size (n).

A narrower CI is more informative. The width depends on:

  • Sample size (n): Larger n → narrower CI. The CI width shrinks proportional to 1/√n.
  • Variability: Higher SD → wider CI.
  • Confidence level: 99% CI is wider than 95% CI, which is wider than 90% CI. More confidence requires a wider net.

Both carry similar information. The p-value tells you whether the effect is significant; the CI tells you both significance and the likely magnitude of the effect. Many journals now require CI reporting because it is more informative.

A key link: if a 95% CI for the difference between two means does not include 0, the corresponding two-sided p-value will be < 0.05.