Systematic & random error

Error is the unavoidable, numerically expressed lack of accuracy in every measurement, the difference between the measured value and the true value, caused by the imperfections of instruments and methods. Not all errors are alike: they split into systematic and random, with different causes and different remedies.

Systematic error (bias)

It stays almost constant throughout the measurement and shifts the result in one direction (always +, or always −). It comes from a faulty or badly adjusted instrument, a wrong method, or environmental factors, and it makes the results genuinely wrong. Repeating the measurement will not reveal it (the readings come out consistently the same), and averaging will not remove it· that is what makes it the more dangerous of the two. It is reduced by calibration and correction.

The classic example is zero error: a micrometer that reads −0.04 mm when closed instead of zero. If you read 2.49 mm, the true value is 2.49 + 0.04 = 2.53 mm· you either correct it on the instrument or correct the result.

Random error (precision error)

It varies unpredictably from one measurement to the next, can be positive or negative, and is always present. It comes from objective causes (vibration, friction, play, the operator’s judgement when reading). Calibration will not correct it, but it is reduced by taking many measurements and averaging: the more readings you take, the closer the mean gets to the true value. Repeated values follow a normal (Gaussian) distribution around the true value and are quantified by the standard deviation. Random error is what limits precision.