Measurements and their Errors
Errors, Precision and Accuracy
AQA A-level Physics
Random error
- Random error scatters repeated readings either side of the true value.
- Repeat measurements at different points along a wire and in different directions, then calculate a mean, to reduce the effect of random error.
- Repeat readings to detect anomalies, then reject anomalous readings before calculating the mean.
- Repeats reduce random error. Never write repeats eliminate random error or an average eliminates the effect of anomalies.
- Data logging reduces impact of statistical error in reading and recording data manually, and data can be collected at a high rate.
- Record raw data to a consistent number of decimal places.
Systematic error and zero error
- A systematic error shifts every reading in the same direction, by the same amount or the same proportion. Repeating does not reduce it.
- Callipers: tare the callipers before use.
- Micrometer: close jaws using ratchet with nothing between them to find the zero error, then subtract zero error from each reading.
- Meters: check and correct for any zero error before use. Timing: ensure stopwatch is zeroed before use.
- Mass: tare the balance with empty beaker on pan.
- Bench not level: repeat experiment with track direction reversed and calculate the average, to account for the effect of non-level bench.
- Micrometer reading: use of ratchet, because tightening the thimble directly can change the diameter of the object and give a reading smaller than true value.
Parallax
- Scale: view at right angles to the scale, at eye level, to reduce parallax error.
- Vertical distance: use of set-square with edge made vertical to read the ruler.
- Liquid: eye level with the bottom of the meniscus to avoid parallax error.
Resolution
- Resolution is the smallest change in a quantity an instrument can show.
- The micrometer has a smaller resolution than a ruler, so its readings have a smaller percentage uncertainty.
- Wire diameter: use a micrometer screw gauge. Never write vernier callipers for a wire diameter.
- A meter whose readings use only a small part of its range: the resolution of the meter is not satisfactory.
- A finer scale: write resolution is smaller. Never write resolution is better.
Accuracy and precision
| Term | Meaning |
|---|---|
| Accuracy | How close a measurement is to the true value |
| Precision | How little repeated measurements scatter about their mean |
| Repeatability | The same results when the original experimenter repeats the measurement with the same method and equipment |
| Reproducibility | The same results when the measurement is repeated by a different person or with different techniques and equipment |
A mean of repeated readings gives a more accurate value.
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