11.2 - Accuracy, Precision & Error
Accuracy and precision
| Term | What it means |
|---|---|
| Accurate | Close to the true value |
| Precise | Repeated readings are close to each other (a small spread) |
A set of results can be precise without being accurate. For example, weighing a 50.0 g mass on a balance not set to zero might give 52.0 g, 52.1 g, and 52.0 g. These readings are precise (they barely differ), but none is accurate (each is about 2 g too high).
Resolution
- Resolution is the smallest change an instrument can detect.
- A balance reading to 0.01 g has a higher resolution than one reading to 0.1 g.
- Use "higher resolution" for an instrument, not "more precise" - precise describes a set of readings that cluster closely, not an instrument.
Repeatable and reproducible
- Repeatable - You get similar results when you repeat the investigation yourself, with the same method and the same equipment.
- Reproducible - Someone else gets similar results, or you get them using a different method or different equipment.
- Reproducible results give more confidence than repeatable ones, because a similar result from a different set-up rules out a fault peculiar to one person or one piece of equipment.
Estimating uncertainty from the range of repeats
- Repeat readings scatter about a mean.
- Range - The largest reading minus the smallest reading.
- Uncertainty - Half the range of the repeat readings:
Example - Time for ten pendulum swings
Measured three times as 14.2 s, 14.6 s, and 14.4 s:
Range = 14.6 - 14.2 = 0.4 s
The result is written as the mean plus or minus the uncertainty: 14.4 ± 0.2 s.
Uncertainty on a graph
- On a graph, uncertainty is shown as a bar above and below the plotted point, stretching from the mean minus the uncertainty to the mean plus the uncertainty.
- A bigger range means a bigger uncertainty and less precise readings.
Random and systematic error
- Random error - An unpredictable difference between readings, such as slight differences in judgement when reading a scale.
- Systematic error - A fault that shifts every reading by the same amount in the same direction, such as a balance not set to zero (a zero error).
How errors link to precision and accuracy
- Random error scatters readings, so it reduces precision. Taking repeat readings and calculating the mean reduces the effect of random error.
- Systematic error shifts every reading the same way, so it reduces accuracy. Taking a mean doesn't reduce systematic error; the method or equipment must be corrected.
- A set of results that is precise but not accurate indicates a systematic error.
TermDefinition
AccurateDescribes a measurement that is close to the true value.
PreciseDescribes repeated measurements that are close to each other, with very little spread about the mean.
ResolutionThe smallest change an instrument can detect.
RepeatableDescribes results that are similar when the same person repeats the investigation with the same method and equipment.
ReproducibleDescribes results that are similar when someone else repeats the investigation, or when a different method or equipment is used.
RangeThe spread of a set of values from the smallest to the largest. For repeat readings, it is the largest reading minus the smallest.
UncertaintyHow far the true value may lie either side of a measured value. For repeat readings, it is often estimated as half the range.
Random errorAn unpredictable error that makes readings vary above and below the true value, so repeat readings differ from each other.
Systematic errorAn error that makes every reading differ from the true value by the same amount in the same direction.
Zero errorA systematic error caused by a measuring instrument that gives a reading other than zero when the true value is zero.
Key points to remember
How were these notes?