Errors

Types of Errors

When performing procedures, experimental errors occur that impact the precision and accuracy of the collected data. Although always present, errors can be reduced with proper design and adherence to the procedure. 

Random errors are always present as there is always uncertainty associated with a measurement as each measurement can be slightly above or slightly below the true value. Random errors are based on the precision of the tool (e.g., the number of decimal places of a digital tool) and the number of measurements/trials. Repeating a measurement multiple times decreases random errors and increases accuracy as the average of the measurements SHOULD point to the true value.

Systematic errors affect the measurement in the same direction every time, either consistently making the measurement too high or too low. Repeating a measurement several times will not reduce the systematic error as it will always be too high or too low. Systematic errors require modifications to the procedure. Examples of systematic errors include using miscalibrated digital tools, always estimating an analog tool incorrectly and performing techniques incorrectly (e.g., not allowing a reaction to reach completion before taking a measurement).

Percentage Error

An experimental value can be compared to a theoretical (true) value by calculating the percentage (%) error.

% Error = |(experimental - theoretical) / (theoretical)| x 100%

The percentage error suggests whether the difference between the experimental and theoretical value is due to random or systematic errors.

• If the percentage error < total percentage uncertainty, the data suggests only random errors exist.

• If the percentage error > total percentage uncertainty, the data suggests systematic errors exist.

For example, if a student determines the density of a substance to be 0.94 g cm-3 and the true value of the substance is 0.89 g cm-3 , the percentage error is:

% Error = |(0.94 - 0.89) / (0.89)| x 100% = 5.6%

If the total percentage uncertainty of the measurement is 3%, the student can conclude that systematic errors existed that caused the experimental value to differ from the theoretical value.

Outliers

Outliers are points that do not fit a trend. Often, outliers can be identified in tables as the value does not agree with the others or on graphs as they do not fit the line of best fit of the data. Many outliers are caused by systematic errors but can not automatically be assumed to be the cause for the measurement. Advanced statistical tests must be applied to the data to determine the actual cause of the discrepency.