Measurement uncertainty Excel template: Nordtest and GUM
Measurement uncertainty is the range around a result where the value of the measured quantity can reasonably lie: 18.4 ± 1.2 mg/L (k = 2) puts it between 17.2 and 19.6 mg/L with about 95% confidence. This Excel template covers both routes for ISO/IEC 17025 §7.6: Nordtest TR 537 from control sample and proficiency test data, and a GUM budget.
Excel file (.xlsx), five sheets: how to use, u(Rw), u(bias), Nordtest result and GUM budget.
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One row per component, its contribution beside it
The table comes from the sample GUM budget in the file: a 1000 mg/L calibration standard, c = 1000 × m × P / V. Type your own components and the divisor, standard uncertainty and contribution recalculate.
| Component | Symbol | Value x_i | Unit | Uncertainty (U, a, s, u) | Distribution | k or n | ν (empty = ∞) | Divisor | u(x_i) | u(x_i)/x_i | Contribution, % |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Mass (weighing) | m | 100.28 | mg | 0.1 | Normal (U/k) | 2 | 2.0000 | 0.050000 | 0.000499 | 35.8% | |
| Purity | P | 0.9999 | 0.0001 | Rectangular (a/√3) | 1.7321 | 0.000058 | 0.000058 | 0.5% | |||
| Volume: flask calibration | V | 100 | mL | 0.1 | Triangular (a/√6) | 2.4495 | 0.040825 | 0.000408 | 24.0% | ||
| Volume: temperature effect | V | 100 | mL | 0.084 | Rectangular (a/√3) | 1.7321 | 0.048497 | 0.000485 | 33.9% | ||
| Volume: filling repeatability | V | 100 | mL | 0.02 | Type A (s/√n) | 1 | 9 | 1.0000 | 0.020000 | 0.000200 | 5.8% |
Nordtest's three numbers: u(Rw), u(bias), U
On the Nordtest route the uncertainty comes from the laboratory's own data. Values are relative, in percent.
- u(Rw)
- Within-laboratory reproducibility: the relative standard deviation of one control sample measured on different days. At least 20 results are recommended.
- u(bias)
- The share of systematic error. The root mean square of the proficiency test biases (RMS_bias) is combined with the uncertainty of the assigned values, u(Cref).
- U
- Expanded uncertainty: U = 2 × √(u(Rw)² + u(bias)²). k = 2 gives a level of confidence of about 95%. The report rounds it up to two significant digits.
Example: nitrate in drinking water
The sample data in the file: ion chromatography, 24 control results and 6 proficiency test rounds. The values come from the same calculation as the file's formulas.
| Measure | In the example | How it is calculated |
|---|---|---|
| u(Rw) | 1.53% | s / mean × 100 over the control results |
| RMS_bias | 2.13% | √(Σ bias² / n) over the rounds' percent biases |
| u(Cref) | 1.85% | s_R / √(number of labs) per round, averaged |
| u(bias) | 2.82% | √(RMS_bias² + u(Cref)²) |
| u_c | 3.21% | √(u(Rw)² + u(bias)²) |
| U (k = 2) | 6.42% | 2 × u_c |
| Reported U | 6.5% | Rounded up to two significant digits (GUM 7.2.6) |
| Result line | 18.4 ± 1.2 mg/L (k = 2) | U in units rounded up, the result rounded to the same decimal place |
Distribution and divisor
In a GUM budget each component's standard uncertainty is the given value divided by a divisor. In the file you pick the distribution from a list and the divisor follows.
| Distribution | Divisor | When to use it |
|---|---|---|
| Normal (U/k) | k from the certificate (usually 2) | A calibration certificate gives U and k: balance, pipette, thermometer. |
| Rectangular (a/√3) | √3 ≈ 1.732 | Only a ± a limit is known: purity, a manufacturer's tolerance, a temperature effect. |
| Triangular (a/√6) | √6 ≈ 2.449 | Values near the centre are more likely than near the limits: volumetric flask and pipette tolerance. |
| U-shaped (a/√2) | √2 ≈ 1.414 | The value is usually near the limits: a room temperature cycling between two set points. |
| Type A (s/√n) | √n | The standard deviation of repeated measurements; n is the number of readings averaged in the result. |
| Standard uncertainty (u) | 1 | u comes ready from another calculation. For a relative u (e.g. a repeatability RSD of 0.015), enter 1 as the value. |
Use the template in four steps
- 1
Paste the control results
Paste the results of one control sample, with their dates, into the intermediate precision sheet. Cover different days, analysts and instruments, and enter at least 20 results.
- 2
Enter the bias rows
Each proficiency test round is one row: assigned value, your result, s_R and the number of labs. For a reference material, enter the certificate's standard uncertainty in percent as s_R and 1 lab.
- 3
Read the Nordtest result
u_c, U and each component's share come from formulas. Enter the concentration level and unit to get the U to report and the result line.
- 4
Build a GUM budget if needed
For a model that multiplies and divides its inputs, write each source of uncertainty in a row and pick its distribution. Enter the result as y and U, ν_eff and k follow.
Excel file (.xlsx), five sheets: how to use, u(Rw), u(bias), Nordtest result and GUM budget.
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What is in the file
- How to use
- Steps, the formulas in words, the reporting rule and the sources.
- Intermediate precision u(Rw)
- 500 rows for control sample results. n, mean, s and u(Rw) sit beside them; below 20 results a warning appears.
- Bias u(bias)
- 50 rows for proficiency test rounds or certified reference materials. Bias and u(Cref) per row; RMS_bias and u(bias) beside them.
- Nordtest result
- u_c, U, each component's share and the reported U. Enter a concentration and unit to get U in units and the result line.
- GUM budget
- A 12-component budget: divisor, u(x_i), relative uncertainty, contribution, ν_eff, k and the result line. The distribution table sits below.
Uncertainty studies in PureField LIMS
PureField LIMS calculates measurement uncertainty inside the application: the team enters its own values in the same study, the result is approved with an e-signature, and the uncertainty applied to the method carries into results and reports. PureField LIMS
Frequently asked questions
What is the difference between Nordtest and the GUM method?
How many control results does u(Rw) need?
How do you report measurement uncertainty?
Can I use a certified reference material instead of proficiency tests?
Which programs open the template?
Why do you ask for an email address?
