1.2 limitation of physical measurements

• Random errors

  • Affect precision
  • Cause readings to be spread about the true value
  • Unpredictable 
  • Cannot be corrected
  • E.g. measuring a random process
  • Caused by human error
  • Occurs in any measurement
  • Variety every time
  • Cannot keep control variables the same
• Systematic errors

  • Affect accuracy
  • Each reading is different by the same value
  • Shifts all results
  • Caused by environment
  • E.g. apparatus or experimental method
  • Unnoticeable 
  • Have to spot before testing to correct them
  • Correctable
  • Repeat the experiment with a different technique or apparatus and compare the results
• Precision - little spread around the mean value

  • Depends only on the extent of random errors - does not indicate how close to the true value the results are

  Accuracy - judged to be close to true value 

  • Applies to mean values rather than individual readings
• Repeatability - if the original experimenter repeats the investigation using the same method and equipment obtaining the same results

  Reproducibility - investigation can be repeated by another person or by using different equipment/techniques still obtaining the same results

  Resolution - smallest change in quantity being measured by a measuring instrument that gives a perceptible change in the reading

  • When starting values in a table that have been measured with a particular device, the values should not be stated to a higher resolution that can be measured
• Uncertainty

  • Uncertainty = (largest value - smallest value) / 2
  • If the resolution of the device can be improved, the uncertainty can be reduced
  • When using a device with a fixed resolution, make the measurement as large as possible to reduce percentage uncertainty
  • Absolute uncertainty - smallest degree of precision

  Percentage uncertainty = (absolute uncertainty / mean value) x 100
• Combining uncertainties

  • Adding or subtracting data - add absolute uncertainties
  • Multiplying or dividing data - add percentage uncertainties
  • Raising to a power - multiply percentage uncertainty by the power
• Uncertainties in graphs

  Error bars

  • Work out the final result using uncertainty in each measurement
  • When plotting a graph, show uncertainty in each measurement using error bars

  Gradient and intercept

  • Draw lines of best fit, lines with maximum and minimum gradient of error bars
  • Uncertainty in gradient is given by the difference between the largest and smallest gradients
  • Uncertainty in y-intercept is the difference between the greatest and least intercepts