3. Calibration Error
3.1. Examples
A thermometer that reads 2 °C too high across its entire range due to incorrect calibration at the factory
A set of masses labelled 100 g that actually weigh 98 g, causing all mass measurements to be consistently underestimated
A pH meter that has not been calibrated against a buffer solution, giving readings that are offset from the true pH
A force sensor that drifts over time and no longer matches its original calibration, giving readings that are consistently too low
A pressure gauge that has been dropped and bent, causing all readings to be offset by a fixed amount
Calibration Error: A Four-Step Analysis
Use the four-step framework to analyse calibration error:
- Step 1 — Identify the source
Instrumental — the measuring device has not been correctly set against a known standard, or has drifted from or been damaged since its last calibration.
- Step 2 — Classify the behaviour
Consistent, one-direction shift → Systematic error → affects accuracy. Every reading is displaced from the true value by a consistent or proportional amount across the instrument’s range.
- Step 3 — Explain the impact
All results are shifted consistently too high or too low. The error cannot be detected by repeating measurements, as every repeat is affected equally. Precision is unaffected — results will agree with each other — but none will reflect the true value.
- Step 4 — Suggest an improvement
Calibration error is eliminated, not averaged out — verify the instrument against a known standard before use and recalibrate if necessary.
3.2. Effects
Calibration error produces a consistent or proportional offset across all measurements. Because every reading is displaced by the same instrument fault:
results will appear precise (repeats agree with each other),
but accuracy is reduced — all values are displaced from the true value in the same direction,
repeating measurements does not help, as the error affects every reading equally,
the offset may be fixed (the same amount across the range) or proportional (larger at higher values), depending on the nature of the fault.
3.3. Improvements
To eliminate calibration error, verify instruments against a known standard before use and recalibrate or replace them if they are found to be faulty.
Calibrate the instrument against a known standard before collecting data — for example, check a thermometer in an ice-water bath (0 °C) and boiling water (100 °C at sea level).
Use buffer solutions of known pH to calibrate a pH meter before and during data collection.
Record the calibration check as part of the method so the instrument’s accuracy can be verified if results are questioned.
If a fixed offset is known and stable, apply a correction factor to all readings.
Replace or have the instrument professionally serviced if calibration cannot be restored.
Structured Question: Calibration Error
A Year 8 class is investigating how the weight of different objects compares when measured on two different spring balances. One group uses a spring balance that was dropped earlier in the year, bending the internal spring slightly. When the group hangs a 100 g standard mass from the spring balance, it reads 112 g. The group does not report this and proceeds to use the spring balance to measure the weight of five different objects.
(a) Identify the type of error present in this investigation and classify it as random, systematic, or personal. (2 marks)
(b) Explain how this error would affect the group’s weight measurements. In your answer, refer to the direction of the error and its effect on the accuracy and precision of the results. (3 marks)
(c) The group repeats each measurement three times and calculates a mean. Evaluate whether this would reduce the effect of the error identified in part (a). (2 marks)
(d) Describe one improvement the group could make to identify and address this error before collecting data. (1 mark)
Reveal Answer Key
(a)
The error is a calibration error, classified as a systematic error.
(1 mark for naming calibration error; 1 mark for systematic)
(b)
Because the spring balance consistently reads higher than the true value — reading 112 g when the true mass is 100 g — every measurement made with it will be consistently overestimated. Every reading is displaced in the same direction by a similar proportion across the range of the instrument. (1 mark)
The accuracy of the results is reduced, as all recorded values are higher than the true weight of each object. (1 mark)
The precision is unaffected — because the same faulty spring produces a consistent offset for every reading, the repeated measurements will agree closely with each other. (1 mark)
(c)
Repeating measurements and calculating a mean would not reduce the effect of this error. (1 mark)
Because the spring balance is faulty, every repeat produces the same consistent overestimate. Averaging does not cancel a consistent offset — it only reduces the effect of random errors, which vary unpredictably between trials. (1 mark)
(d)
Before collecting data, the group should verify the spring balance against a known standard mass — for example, hang a 100 g mass and check whether the reading matches. If it does not, the instrument should be replaced with one that reads correctly. (1 mark)
Part (a): accept “calibration error” or “the spring balance is incorrectly calibrated.” Do not accept “zero error” — the instrument was not giving a false zero reading, it was giving a consistently incorrect reading across its range due to physical damage. Do not accept “human error” or “mistake” — the fault is in the instrument itself.
Part (b): award the direction mark only if the student identifies overestimation specifically, not just “the results are wrong.” The question states the balance reads 112 g for a 100 g mass, so the direction can be reasoned directly from the stem. Award the precision mark only if the student correctly states precision is unaffected and provides a reason. A response that states precision is also reduced should not receive the precision mark.
Part (c): a response that simply states “repeating reduces error” without explaining why it does not apply here should not receive full marks. The key reasoning is that the faulty spring produces the same offset in every trial.
Part (d): accept “apply a correction factor based on the known offset” as an alternative valid response. Do not accept “repeat measurements” as this has already been evaluated in part (c) as ineffective.