Sensitivity Coefficients: Put Every Budget Contribution in the Result’s Units

Use the model to connect units

A sensitivity coefficient describes how a small input change affects the calculated result. Multiplying it by the input’s standard uncertainty expresses that contribution in the output’s units. The coefficient’s units therefore belong in the budget, alongside the source and uncertainty definition.

An invented temperature correction

Suppose an illustrative linear correction model has sensitivity 0.20 g/°C to temperature, and the temperature standard uncertainty is 0.50 °C. The resulting standard contribution is 0.10 g. Combining 0.50 directly with mass components would mix degrees Celsius and grams.

The coefficient here is invented for teaching. A real temperature effect must come from an applicable model or evidence; it cannot be copied from this example into a machine trial. A nonlinear model may also require more care than one local coefficient.

Check the budget dimensionally

Write each input, input unit, standard uncertainty, coefficient and converted contribution. Confirm that the converted terms have the result’s unit before combination. Keep dependence assumptions and the point at which coefficients were evaluated visible to the reviewer.

Primary references: NIST measurement handbook.

Measurement review worksheet

This blank worksheet is for your own project. It contains no H M machine trial result.

Customer Questions

Primary References

These references support the technical principles discussed in this guide. The worked examples and review questions are educational.

• NIST measurement handbook