Random errors are errors in measurement that lead to measured values being inconsistent when repeated measures of a constant attribute or quantity are taken. The word random indicates that they are inherently unpredictable, and have null expected value, namely, they are scattered about the true value, and tend to have null arithmetic mean when a measurement is repeated several times with the same instrument. All measurements are prone to random error.

Random error is caused by unpredictable fluctuations in the readings of a measurement apparatus, or in the experimenter's interpretation of the instrumental reading; these fluctuations may be in part due to interference of the environment with the measurement process.

The concept of random error is closely related to the concept of precision. The higher the precision of a measurement instrument, the smaller the variability (standard deviation) of the fluctuations in its readings.

[edit] Systematic versus random error

Measurement errors can be split into two components: random error and systematic error.^[1]

Random error is always present in a measurement. It is caused by inherently unpredictable fluctuations in the readings of a measurement apparatus or in the experimenter's interpretation of the instrumental reading.

Whereas, systematic errors are predictable, and typically constant or proportional to the true value. If the cause of the systematic error can be identified, then it can usually be eliminated. Systematic errors are caused by imperfect calibration of measurement instruments or imperfect methods of observation, or interference of the environment with the measurement process, and always affect the results of an experiment in a predictable direction. Distance measured by radar will be systematically overestimated if the slight slowing down of the waves in air is not accounted for. Incorrect zeroing of an instrument leading to a zero error is an example of systematic error in instrumentation.:)

[edit] In-line citations and notes

[edit] See also

• Errors and residuals in statistics
• Observational error