GIFSQ Tools · Module 15 — Metrology, Validation & Laboratory Accreditation · Tool 293 of 500
Summarise an interlaboratory comparison: grand mean, standard deviation, median and the largest laboratory z-score, so outlying laboratories stand out at a glance.
Try sample values — fills the form with the worked example below.
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Grand mean
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Standard deviation
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Median
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Largest |z|
Equation: Grand mean = Σx ÷ n. Sample SD = √[Σ(x − mean)² ÷ (n − 1)]. Median = middle value (mean of the two middle values for even n). Laboratory zᵢ = (xᵢ − mean) ÷ SD; largest |z| is the maximum.
Method: Interlaboratory comparison summary per ISO 5725-2 and ISO 13528: the consensus mean and spread describe the group, and the largest |z| flags the laboratory furthest from the consensus.
Assumptions: each laboratory contributes one result; the results are approximately normally distributed; no laboratory result is a known blunder.
Limitations: the consensus mean is pulled by an outlier — use the median and a robust SD (for example the median absolute deviation) when the group is small or skewed.
Rounding: mean, SD and median to 2 decimal places; largest |z| 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: Interlaboratory comparison summary per ISO 5725-2 and ISO 13528: the consensus mean and spread describe the group, and the largest |z| flags the laboratory furthest from the consensus.
Assumptions: each laboratory contributes one result; the results are approximately normally distributed; no laboratory result is a known blunder.
Limitations: the consensus mean is pulled by an outlier — use the median and a robust SD (for example the median absolute deviation) when the group is small or skewed.
Rounding: mean, SD and median to 2 decimal places; largest |z| 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 results 10.1, 10.3, 10.2, 10.6, 10.0 mg/kg: grand mean = 10.24, SD = 0.23, median = 10.20, largest |z| = 1.56 (the 10.6 mg/kg laboratory).
Enter values above to see results.
A laboratory with |z| above 2 deserves a look; above 3 it is an outlier for the purpose of the comparison. Tool 293 of 500 — GIFSQ
