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Why repeated measurements can share an offset, why averaging does not remove it, and how calibration and correction help.
What is systematic error?
Systematic error is the component of measurement error that stays constant or changes predictably in repeated measurements under the stated conditions. A set of readings can agree closely while all being displaced from a reference. VIM: systematic measurement error.
Imagine a balance that reads 0.3 g when its pan is empty. If that uncorrected offset remains constant, it adds 0.3 g to each indication. Weighing the same object repeatedly does not make the offset disappear.
Must systematic error always be constant?
No. The effect may depend on the value being measured or on the operating conditions.
A zero offset adds a roughly constant amount. A scale-factor error changes readings in proportion to their size. A temperature-dependent effect may change as the instrument warms up.
These are examples of possible behaviour, not diagnoses from a single reading. The actual relationship needs evidence across the relevant range and conditions.
Why does averaging fail to remove an offset?
Suppose a stable reference is assigned 100.0 g. Three illustrative readings are:
100.2 g, 100.3 g and 100.4 g.
Their mean is 100.3 g, which is 0.3 g above the reference. Averaging has summarised the readings; it has not established why their mean is high.
If every reading contains the same +0.3 g offset, their mean contains it too. Many readings can give a very stable average that remains displaced. A small sample alone cannot establish the size or persistence of a systematic effect.
How can a systematic effect be investigated?
Compare the measuring system with suitable standards and examine its behaviour under the conditions in which it will be used.
Useful checks may include:
- Zero: does the instrument indicate correctly at zero?
- Range: does the discrepancy change with the value?
- Conditions: do temperature, alignment or loading affect the result?
- Method: does an independent suitable method reveal a shared problem?
Close agreement between two instruments is useful evidence, but both may share a reference or a method that introduces the same effect.
What is the difference between calibration and adjustment?
Calibration establishes relationships between standards, indications and measurement results, with associated uncertainties. Adjustment changes the measuring system so that it gives prescribed indications.
A calibration certificate does not necessarily mean the instrument was adjusted. Its information may instead need to be applied as a correction when interpreting a reading. VIM: calibration.
How does a correction work?
If a valid calibration establishes that an indication is high by 0.3 g in the relevant conditions, an additive correction is −0.3 g.
For an indication of 120.8 g:
Corrected value = 120.8 g − 0.3 g = 120.5 g.
That correction is appropriate only where the established relationship applies. Other instruments may require a factor or a calibration curve instead of a constant subtraction. VIM: correction.
The corrected result still has uncertainty, including uncertainty in the correction and any remaining effects.
What follows?
A small spread shows consistency under the tested conditions. It cannot establish that a common offset is absent. To investigate systematic effects, use references and comparisons that can reveal what repetition alone may hide.
Read Measurement Error for the wider distinction, or Random Error for unpredictable variation.
Ai disclosure: written with the help of AI (ChatGPT). You are encouraged to point out errors and omissions.
