Complex Precision Statistical Guidelines
Complex Precision — Statistical Calculations
Complex Precision uses ANOVA (Analysis of Variance) to partition total variation into distinct sources. The components calculated depend on the study design:
Short-term (within-run + within-laboratory)
Within-Run Precision (Repeatability)
SR = √MS_within
Variation among replicate measurements within a single run under nearly identical conditions. Represents the baseline noise of the measurement system. Reported as df, SD, CV%, and 95% CI for CV%.
Within-Laboratory Precision (Total)
SWL = √(S²R + S²between-run)
The overall imprecision at this site combining repeatability and between-run effects. The most clinically relevant precision estimate for short-term multi-day studies — compared against the manufacturer's published claim or TEa-based allocation budget to determine pass/fail.
Long-term (within-run + between-run + between-day + within-laboratory)
Within-Run Precision (Repeatability)
SR = √MS_within
Variation among replicates within a single run. Computed from the ANOVA within-run mean square. Reported as df, SD, CV%, and 95% CI for CV%.
Between-Run Variance
S²between-run = (MS_between-run − MS_within) / nR
Additional variability introduced between runs within the same day. Computed from ANOVA mean squares. Elevated values may indicate within-day calibration or reagent handling issues. Reported as df, SD, CV%, and 95% CI for CV%.
Between-Day Variance
S²between-day = (MS_between-day − MS_between-run) / nR·nD
Variability across different days of testing. Captures drift from calibration, environmental factors, or operator-to-operator differences. Reported as df, SD, CV%, and 95% CI for CV%.
Within-Laboratory Precision (Total)
SWL = √(S²R + S²between-run + S²between-day)
The sum of all variance components — the most comprehensive precision estimate. Represents what a laboratory can expect to observe under routine conditions over time. Reported as df, SD, CV%, and 95% CI for CV%.
Manufacturer Claim Comparison — Upper Verification Limit (UVL)
Upper Verification Limit (UVL)
UVL = F × Claimed CV%
When comparing against a manufacturer's published precision claim rather than a TEa-derived budget, the pass/fail threshold is the UVL — not the claimed CV% directly. The F factor is a statistical multiplier derived from the degrees of freedom and the number of concentration levels tested. It accounts for the expected random variation in the CV% estimate itself and protects against falsely rejecting a method that actually meets the claim (~95% confidence). For the EP15-A3 5-day design with 2–3 concentration levels, F typically falls between 1.28 and 1.34.
- TEa-based: Within-Laboratory CV% < Allocation Budget CV% (TEa × Imprecision Allocation%) at every concentration level.
- Manufacturer claim: Within-Laboratory CV% ≤ UVL (F × Claimed CV%) at every concentration level. The UVL is used — not the raw claimed CV% — because random sampling variation means an acceptable method will occasionally produce a CV% slightly above the claim. Comparing to the UVL instead protects against false rejection at ~95% confidence.