Measurements and their Errors
Errors, Precision and Accuracy
OxfordAQA International AS and A-level Physics
Random and systematic errors
| Error | Effect on readings | Examples |
|---|---|---|
| Random | Scatters repeated readings either side of the true value | incorrect positioning of ruler, parallax error, misreading ruler, an irregular shaped surface |
| Systematic | Shifts every reading in the same direction by the same amount; repeating does not reduce it | incorrectly calibrated ruler, zero error on ruler (zero mark not at the end), zero error on voltmeter, voltmeter incorrectly calibrated, the weight of the tray ignored |
- Name the instrument with a zero error. Never write zero error on its own.
- Write incorrectly calibrated. Never write voltmeter not calibrated.
- Remove a systematic error by finding the reading with nothing measured and subtracting it from every reading.
- A straight-line graph: the systematic error only affects the intercept. The gradient is not affected by zero error, because the same error affects every measurement.
A ruler that is out of position or tilted gives a different error on each reading, so the error is random. Never write inaccurate ruler as a systematic error or ruler not vertical as a systematic error. A systematic error is the same on every reading: write incorrectly calibrated ruler or zero error on ruler.
Reducing random error
- Random errors are reduced by repeating and averaging: repeats and averages. Name the quantity that is repeated.
- Readings done in different locations on the specimen to take account of any lack of uniformity.
- Repeats and removes anomalies before the mean is calculated.
Parallax
- Placing eye level at the level of the reading to avoid parallax error.
- Use a set square placed against ruler.
- A vertical distance: set square placed against table and ruler, plumb line placed next to ruler, to ensure vertical distance is measured.
- A camera or phone arranged to prevent parallax error.
- Improving a length measurement: name the technique, such as putting ruler closer to the object or using set squares to avoid parallax. Never write just use larger l.
Data loggers and video
- A data logger: no variation in reaction time, and the datalogger allows simultaneous reading of two quantities, such as time and potential difference.
- A video: freeze frame allows the observer to take simultaneous readings.
- Never write records time more accurately.
Resolution
- Resolution is the smallest change in a quantity an instrument can show.
- Wire diameter: use a micrometer screw gauge. Width and thickness of a larger object: calipers.
- Write the resolution of the micrometer is better than the calipers, so using a micrometer leads to a smaller percentage uncertainty in the diameter.
Precision, accuracy and reproducibility
| Term | Meaning |
|---|---|
| Precision | Measurements are precise if there is only a small variation in repeated measurements: they lie within a small range of values |
| Accuracy | How close a measurement is to the accepted value; a result far from the accepted value is not accurate |
| Repeatability | The same results when the original experimenter repeats the measurement with the same method and equipment |
| Reproducibility | The same results by a different method, person or equipment; two methods whose ranges don't overlap do not give a reproducible value |
Compare the precision of two methods with numbers: the range of each set of readings.
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