GIFSQ Tools · Module 15 — Metrology, Validation & Laboratory Accreditation · Tool 289 of 500
Analyse reproducibility across laboratories: between-laboratory standard deviation, reproducibility standard deviation sᵣ and the reproducibility limit R of ISO 5725.
Try sample values — fills the form with the worked example below.
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Between-lab SD (sᴸ)
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Reproducibility SD (sᵣ)
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Reproducibility limit (R)
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Reproducibility RSD (%)
Equation: sᴸ = SD of the laboratory means (n − 1). sᵣ = √(sᴸ² + sᵣ²). Reproducibility limit R = 2.8 × sᵣ. Reproducibility RSD (%) = sᵣ ÷ grand mean × 100.
Method: Reproducibility conditions per ISO 5725-2: the same method applied in different laboratories, by different operators, on different equipment. sᵣ combines the between-laboratory component with the repeatability component.
Assumptions: each laboratory mean is based on the same number of replicates; the laboratories are a representative sample; results are approximately normally distributed.
Limitations: with few laboratories the between-lab estimate is imprecise; an outlying laboratory inflates sᴸ — screen with Grubbs or Cochran tests before pooling.
Rounding: sᴸ, sᵣ and R to 3 decimal places; reproducibility RSD to 2 decimal places; intermediates unrounded.
This is a calculation aid, not a laboratory report — confirm against your accredited method before citing a value.
Method: Reproducibility conditions per ISO 5725-2: the same method applied in different laboratories, by different operators, on different equipment. sᵣ combines the between-laboratory component with the repeatability component.
Assumptions: each laboratory mean is based on the same number of replicates; the laboratories are a representative sample; results are approximately normally distributed.
Limitations: with few laboratories the between-lab estimate is imprecise; an outlying laboratory inflates sᴸ — screen with Grubbs or Cochran tests before pooling.
Rounding: sᴸ, sᵣ and R to 3 decimal places; reproducibility RSD to 2 decimal places; intermediates unrounded.
This is a calculation aid, not a laboratory report — confirm against your accredited method before citing a value.
Worked example: Laboratory means 10.2, 10.5, 10.1, 10.4, 10.3 mg/kg with sᵣ = 0.10 mg/kg: sᴸ = 0.158, sᵣ = √(0.025 + 0.01) = 0.187, R = 0.524, reproducibility RSD = 1.82%.
Enter values above to see results.
Results from two laboratories should not differ by more than R in about 19 cases out of 20 when the method is in control. Tool 289 of 500 — GIFSQ
