Physics · Ch 1 — Nature of Physical World and Measurement
Errors in Measurement
Errors in Measurement
The uncertainty in a measurement is called an error; there are three fundamentally different kinds.
i) Systematic errors -- reproducible inaccuracies, always biased in the same direction, caused by a problem that persists throughout the experiment:
- Instrumental errors -- from an instrument not calibrated correctly at manufacture (e.g. a metre scale with a worn-out end); corrected by choosing/calibrating the instrument carefully.
- Imperfections in experimental technique/procedure -- limitations in the experimental arrangement itself, e.g. radiation losses from a poorly-insulated calorimeter; corrected with proper technique/corrections.
- Personal errors -- due to the individual performing the experiment: incorrect initial setup, or carelessness/lack of proper precaution while observing.
- Errors due to external causes -- changing external conditions (temperature, humidity, pressure) during the experiment shift the result.
- Least count error -- the smallest value an instrument can resolve (its least count) sets a floor on how finely it can measure; reduced only by using a higher-precision instrument.
ii) Random errors -- unpredictable, chance variations in experimental conditions (pressure, temperature, voltage supply, etc.), or personal variation between repeated trials by the same observer (e.g. successive screw-gauge readings of a wire's thickness coming out slightly different each time). Since these are genuinely random rather than one-directional, they are reduced by taking many readings and computing the arithmetic mean:
taken as the best estimate of the true value. …
| Type of error | Example | How to minimize it |
|---|---|---|
| Random error | Measuring the mass of a ring three times on the same balance: 15.46 g, 15.42 g, 15.44 g | Take more data; random errors can be evaluated statistically and reduced by averaging over many observations |