About precision

Three studies estimate imprecision: Repeatability from one run, Multi-day precision across days and runs, and Descriptive summary from any set of results. Their SDs and CVs describe different sources of variation, which matters when one is compared with a limit or carried into sigma or measurement uncertainty.

Repeatability is the precision of one material measured repeatedly in one run. A repeatability study estimates only this within-run part; day-to-day and within-laboratory precision are not estimated. Within-laboratory precision is the total imprecision across runs and days. It is the figure to compare with a total imprecision goal, and the repeatability SD is its within-run part. Repeatability comes from one run and can overstate sigma; the sigma study's precision models copy within-laboratory SDs.

For each level, multi-day precision uses a random-effects analysis of variance to split imprecision into within-run, between-run and between-day parts. The within-laboratory SD combines them (calculations). One run a day combines run and day effects, so the study reports a single between-day/run SD. More runs a day separate them. The largest component shows where most of the variation arises. The how-to lists what to check for each (When a limit is not met).

A between-day SD reported as 0 means the day-to-day variation was too small to detect against the within-run scatter: the calculated component came out negative.

The confidence interval mean ± t × SD / √n counts every result as independent. In a descriptive summary the experimental unit is the specimen, and repeat measurements of one specimen aren't independent. That is why repeated specimen IDs turn off the mean interval and a limit needs at least 2 different specimens. In a repeatability study the same interval describes only the mean of that one run. Multi-day precision builds its interval for the grand mean from the day means, with D − 1 degrees of freedom for D days.

The SDs and CVs are point estimates. The true imprecision can be higher, so review a within-laboratory CV close to its limit. A confidence interval shows where the true mean is likely to lie. Few results give a wide interval: the five results in the descriptive summary example give 2.074–9.926 mmol/L around 6.000.

A laboratory acceptance limit asks whether the observed SD or CV is within the limit the laboratory set. A manufacturer claim comparison asks whether the observed SD is consistent with the manufacturer's stated SD. Its verification limit uses the claimed SD, the degrees of freedom of the observed SD and a one-sided confidence. Comparing the observed SD with that limit gives Consistent with the claim or Higher than the claim (repeatability, multi-day precision). The two answers can differ, and neither changes the other. Analyzer profiles also keep manufacturer claims separate from the laboratory's allowable error.