Confidence Intervals

Definition & interpretation

• Definition — A confidence interval (CI) is a range of values, computed from sample data, within which the true (unknown) population parameter is expected to lie with a stated level of confidence — conventionally 95%. It is an interval estimate of the parameter, in contrast to the single point estimate (sample mean, proportion, difference, OR), and it conveys the precision of that point estimate.
• Confidence limits — The interval is bounded by the lower and upper confidence limits; the distance between them is the interval's width and indexes precision — a narrow CI is a precise estimate, a wide CI an imprecise one.
• Correct frequentist interpretation — If the sampling-and-estimation procedure were repeated many times, 95% of the CIs so constructed would contain the true parameter. For any single computed interval we cannot know whether it is one of the 95% that captures the parameter or one of the 5% that misses it — of every 100 independently constructed 95% CIs, on average 95 bracket the truth and 5 do not.
• Not unique — A CI is not unique — different investigators sampling the same population obtain different point estimates and hence different 95% CIs, though ~95% of those intervals will include the true parameter.