| Describes | Uncertainty of an estimate under a procedure |
|---|---|
| Requires | Parameter, method, and assumptions |
| Is not equivalent to | Dispersion of individual observations |
Definition and context
A confidence interval is constructed using a statistical procedure to estimate a parameter. Its confidence level describes the behavior of the procedure over hypothetical repetitions under the model conditions, not the proportion of observations that fall within the interval.
For a mean, its width depends on factors such as variation, sample size, and the assumptions of the calculation. Interpreting an interval requires knowing these elements. An expression such as a 95 % interval is incomplete if it does not state which parameter it estimates and how it was obtained. Nor does it automatically allow a 95 % probability to be assigned to any explanation proposed by the authors. It is an inference tool with a specific scope.
What we know and its limits
Introductory reference sheet. Properties and applications depend on measurement conditions; consult the sources before making comparisons.
Follow the evidence
The original sources for exploring this explanation and its limits.
- Engineering Statistics Handbook · Confidence Limits for the Mean
NIST / SEMATECH
Confidence intervals and conditions for their calculation.
Image credits
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