11.2.2 Processing Errors

• An error is the difference between a value or quantity obtained in an experiment and an accepted or literature value for an experiment
• There are two types of errors in experiments, random errors and systematic errors

Random Errors

• When you are reading an instrument and estimate the final digit, there is an equal chance that you may read it slightly too high or slightly too low
  • This is a random error

• Random errors are can be affected by:
  • How easily the instrument or scale is to read
  • The person reading the scale poorly
  • Changes in the environment, for example
    • fluctuations in the temperature of the lab
    • air currents in the room

• Random errors will pull a result away from an accepted value in either direction (either too high or too low)

Systematic Errors

• Systematic errors are errors that occur as a result of a faulty or poorly designed experimental procedure
• Systematic errors will always pull the result away from the accepted value in the same direction (always too high or always too low)
• For example,
  • If you forget to zero an electronic balance (using the tare button) the mass weighings will always be higher than they should be
  • If you don't read the volume in a burette at eye level, the volumes will always be smaller than they should be due to a parallax error
  • If you fail to keep a cap on a spirit burner in a calorimetry experiment, the alcohol will evaporate and give you a larger mass loss

Systematic errors

• Propagation of errors means the processing of errors so they are reflected appropriately in a final calculation based on experiment results
• There are a number of rules and processes to follow, beginning with percentage uncertainty

Percentage Uncertainties

• Percentage uncertainties are a way to compare the significance of an absolute uncertainty on a measurement
• This is not to be confused with percentage error, which is a comparison of a result to a literature value
• The formula for calculating percentage uncertainty is as follows:

• Some examples of percentage uncertainty calculations for common laboratory apparatus:

Calculating Percentage Uncertainty

Adding or subtracting measurements

• When you are adding or subtracting two measurements then you add together the absolute measurement uncertainties
• For example,
  • Using a balance to measure the initial and final mass of a container
  • Using a thermometer for the measurement of the temperature at the start and the end
  • Using a burette to find the initial reading and final reading

• In all these examples you have to read the instrument twice to obtain the quantity
• If each you time you read the instrument the measurement is 'out' by the stated uncertainty, then your final quantity is potentially 'out' by twice the uncertainty

Multiplying or dividing measurements

• When you multiply or divide experimental measurements then you add together the percentage uncertainties
• You can then calculate the absolute uncertainty from the sum of the percentage uncertainties