Confidence Interval (CI)
Definition
A range computed from sample data using a procedure that, over many repetitions, would contain the true population parameter a stated percentage of the time. The percentage is the confidence level (commonly 90%, 95%, or 99%).
- Type
- Interval estimate from sample data
- Common levels
- 90%, 95%, 99%
- Basis
- Repeated-sampling (frequentist) interpretation
- Width drivers
- Sample size, variability, confidence level chosen
Common questions
What does a 95% confidence interval actually mean?+
It means that if the same sampling procedure were repeated many times, about 95% of the intervals produced would contain the true population parameter. It is not a 95% probability that this specific interval contains the true value, which is a common misreading.
Why does raising the confidence level widen the interval?+
A higher confidence level demands a greater margin of safety against missing the true parameter, so the interval must cover more possible values. A 99% interval is wider than a 95% interval computed from the same sample.
How does sample size affect a confidence interval?+
Larger samples reduce standard error, which narrows the interval for a given confidence level. This is why forensic statistical conclusions drawn from small evidentiary samples tend to carry wide, less useful intervals.
Related terms
- Bayesian Credible Interval
- An interval computed from the posterior distribution of a parameter, given a prior and the observed data. Unlike a confidence interval, a...
- Coverage Probability
- The true long-run proportion of intervals, from repeated sampling, that contain the parameter. If a procedure has 95% nominal coverage and its...
- Critical Value
- The value from a reference distribution (z or t) that cuts off the desired tail probability. For a 95% two-sided interval using...
- Margin of Error
- Half the width of a symmetric confidence interval, equal to the critical value multiplied by the standard error. Commonly reported in survey...
- Standard Error (SE)
- The standard deviation of the sampling distribution of an estimator. For the sample mean, SE equals the population standard deviation divided by...