Calibration links an instrument's reading to a known standard. Without it, all measurements may be systematically shifted.
Types of systematic error
| Error | Description | Example |
|---|---|---|
| Zero offset | Instrument doesn't read zero at zero input | Scale reads with nothing on it |
| Scale factor | Readings are consistently too high/low | Ruler expanded by heat |
| Non-linearity | Error varies across the range | Spring beyond Hooke's law |
| Hysteresis | Reading depends on direction of change | Mechanical backlash |
Calibration procedure
- Measure a set of known standards spanning your range.
- Plot measured vs. true values.
- Fit a calibration curve (ideally linear: ).
- Use the inverse to correct all future readings.
Detecting systematic errors
- Compare your result with an accepted value.
- Use different methods or instruments to measure the same quantity.
- Look for trends in residuals (measured fitted values).
Accuracy vs. precision
- Accurate: close to the true value (low systematic error).
- Precise: measurements cluster tightly (low random error).
- A measurement can be precise but inaccurate (or vice versa).
Tip: Systematic errors do not decrease with more measurements. The only cure is to identify and remove the source.
Common pitfall: Averaging cures only random error. A miscalibrated instrument delivers beautifully repeatable wrong numbers — precision without accuracy. Calibration against a known standard is the only cure for systematic bias.