About confidence intervals and independent results

Every estimate comes from a limited number of results, so it carries uncertainty. The counts, confidence levels and denominators each study uses are listed in Counts and denominators.

A confidence interval (CI) shows how precisely an estimate is known. A 95% CI of 2.1–9.9 mg/dL for a mean of 6.0 mg/dL means the data fit a true mean anywhere in that range. More independent results usually narrow the interval. A higher confidence level widens it without changing the estimate. You set the level before calculating; changing it later requires recalculation.

In method comparison, the CI of the mean bias tells you how precisely that average is known, and the limits of agreement show where 95% of individual differences fall. An SD or CV is a point estimate too: the true imprecision can be higher than the one observed, so a result close to its limit deserves a second look.

When an interval cannot be calculated, the study shows Not estimated with the reason, and any limit that depends on that interval stays Undecided.

Observations are rows; independent units are the specimens, subjects, materials, pools, days or runs they come from. Repeats add observations but no new units.

In method, instrument and lot comparison, and for reference interval subjects, the specimen is the experimental unit. Replicates are averaged first, and each specimen mean is one point. Replicates share the specimen's matrix and interferences. Counting them separately would overstate precision and give extra weight to specimens with more replicates.

The same reasoning applies to one material measured on several days. Those results all describe one material, so dividing their SD by √n would understate the uncertainty of the mean. A bias check on one material over five days therefore reports the bias without an interval. Results from one run describe that run's repeatability. Give a different ID only to a separate specimen. Replicates of one material keep its ID, even when that means no interval.

Reference interval studies use two different percentages. Target population coverage is the share of the healthy population the interval should contain: with 0.95 it runs from the 2.5th to the 97.5th percentile (see population coverage). The confidence level says how precisely each limit is known, as a CI around each limit.

In the example white blood cell study (female partition, 120 subjects, coverage 0.95, confidence 90%), the reference interval is 4.205 to 11.493 10⁹/L. It should hold 95% of healthy individuals. The 90% CIs on its limits, 3.700–5.000 and 10.300–14.000 10⁹/L, show how far each limit could move with another sample of 120.

A percentage is only comparable with another that uses the same denominator. In the example qualitative agreement study, overall agreement uses the 37 pairs reportable on both methods (34/37 = 91.9%), while all-pairs agreement uses all 40 paired specimens and counts nonreportable results as disagreement (34/40 = 85.0%). Check the denominator before comparing studies.