Estimate analytical sigma performance

What sigma represents

This calculator expresses the remaining allowable error margin in units of analytical imprecision. Its formula is sigma = (TEa − |bias|) / CV, where TEa is allowable total error, bias is the estimated systematic difference from a suitable target, and CV describes imprecision. All three inputs must be percentages on a compatible basis. Mixing an absolute concentration allowance with percentage bias and CV gives a number without a useful interpretation.

Choose TEa before interpreting the output. Record its source, intended clinical use and applicability at the concentration being assessed. Different performance specifications can produce different sigma values for the same assay. A comparison between instruments or laboratories is only meaningful when the specifications, concentration levels and supporting data are sufficiently comparable. Do not choose a more permissive allowance simply to obtain a higher band.

Select representative input data

Estimate CV from stable control observations that reflect the period and operating conditions relevant to the decision. A brief repeatability experiment may underestimate the variability experienced across days, reagent lots and calibrations. Consider more than one concentration level when performance varies across the measuring interval. Review shifts or unresolved problems before using a pooled CV for planning.

Estimate bias against a defensible reference or comparison target. Consider the uncertainty and commutability of the material and whether the comparison represents patient samples. The calculation subtracts the absolute bias, so entering a negative value does not improve the result. A small estimated bias may still carry substantial uncertainty; the calculator does not propagate that uncertainty or provide a confidence interval for sigma.

Read the bands carefully

A sigma value of at least 6 is labelled World class. Values from 5 to below 6 are Excellent, from 4 to below 5 are Good, from 3 to below 4 are Marginal, and values below 3 are Poor. These are descriptive bands for this tool, not accreditation grades or universal guarantees of clinical suitability. The underlying unrounded value determines the band, so a displayed rounded value near a boundary can appear to sit in the adjacent category.

CV must be positive. If the absolute bias equals TEa, sigma is zero; if it exceeds TEa, sigma is negative. Neither result should be hidden or replaced with zero, because both indicate that the assumed error allowance has been exhausted before accounting for imprecision.

Translate the estimate into a QC review

Higher sigma performance may permit a simpler control strategy, while lower performance may require stronger error detection, shorter intervals between controls or improvement of the analytical process. This calculator does not prescribe a specific rule combination or control frequency. Consider patient risk, workload, stability, the number of control levels and the probability of false rejection. Document the chosen strategy and reassess it when the method, reagent lot, calibration behaviour or performance specification changes.

TEa = 10 %, bias = 2 %, CV = 1.5 %.

Sigma = (10 − |2|) / 1.5 = 5.33. The performance band is Excellent because the unrounded result is at least 5 and below 6. This estimate supports QC planning but does not by itself authorise patient-result release.