Physics: Uncertainties and Errors

    This applies to both AS and A Level exams. You can find more examples in Appendix 10 in the Edexcel specification.

A10i Comparing results:

  • Validity: a measurement is valid if it measures what it's supposed to be measuring and if the measurement taken is only affected by one independent variable
  • True value: this is the value that should've been obtained if there were no experimental flaws or sources of error
  • Accuracy: a result is accurate if it is close to the true value - i.e. not influenced by random and systematic errors
  • Precision: how close together values from multiple repeats are
  • Repeatability: how similar results are when determined by different people with the same method
  • Reproducibility: how similar results are when determined by different people using a different method/different apparatus

A10ii Uncertainties and errors:

  • Uncertainty: the interval that the true value should lie in with a high level of confidence. Every measurement will have an uncertainty, e.g. ±0.5\pm 0.5 g\mathrm{g}
    - Absolute uncertainty is the 'plus or minus' value
    - Percentage uncertainty is the maximum percentage that the reading could be out by
    percentage uncertainty == absolute uncertaintymeasurement\frac{\mathrm{absolute\ uncertainty}}{\mathrm{measurement}} ×100\times 100
  • Error: the difference between the measurement result and the true value
    - Random errors are caused by unpredictable variation in the method or equipment
    - Systematic errors are caused by incorrectly calibrated equipment or an incorrect technique which is used throughout
  • Resolution: the smallest measuring interval in a reading (e.g. a ruler measurement would have a resolution of 1 mm1\ \mathrm{mm})

Compounding uncertainties:

  • Addition/subtraction of two measurements: add the absolute uncertainties
  • Multiplication/division of two measurements: add the relative uncertainties
  • Multiplying a constant by a measurement: multiply the absolute uncertainty by the constant. The relative uncertainty is not affected
  • Raising a measurement to a power: multiply the relative uncertainty by the power