Simple Precision Statistical Guidelines
Simple Precision — Statistical Calculations
Simple Precision calculates the following for each concentration level. Pass/fail is determined by comparing the Observed SD to the Goal SD:
Observed Mean
x̄ = Σxᵢ / n
The arithmetic mean of all measurements at this concentration level. Used as the basis for converting between absolute SD and %CV, and for calculating allowable absolute imprecision when TEa is expressed as an absolute value.
Observed SD
s = √[Σ(xᵢ − x̄)² / (n − 1)]
The sample standard deviation of all measurements at this level. This is the primary precision estimate compared against the Goal SD to determine pass/fail status.
Observed CV%
CV% = (s / x̄) × 100
The coefficient of variation — expresses imprecision as a percentage of the mean. Useful for comparing precision across concentration levels because it is unitless.
95% Confidence Interval for Observed SD
CI = s × √[(n−1) / χ²] for upper and lower bounds
A chi-square–based confidence interval around the Observed SD. This quantifies the statistical uncertainty of the SD estimate given the sample size. A wide CI indicates limited precision of the estimate itself.
Allowable Imprecision
Allowable CV% = TEA% × Imprecision Allocation%
The portion of Total Allowable Error (TEa) allocated to random error (precision). Derived by multiplying the configured TEa percentage by the imprecision allocation percentage. For absolute TEa formats, the equivalent CV% is computed from the observed mean. Each concentration level is evaluated independently using the appropriate TEa rule for that level's observed mean.
Goal SD
Goal SD = (Allowable CV% / 100) × Observed Mean
The maximum allowable standard deviation at this concentration level. Derived in two steps: (1) calculate Goal CV% from TEa and imprecision allocation; (2) convert to an absolute SD using the observed mean. When comparing against manufacturer claims rather than TEa, the Goal SD is taken directly from the manufacturer's published specification.