‘Chance variation’ or ‘chance error’ or ‘random error’ is the inherent error in any predictive statistical model. It is defined as the difference between the predicted value of a variable (by the statistical model in question) and the actual value of the variable. For a fairly large sample size, these errors are seen to be uniformly distributed above and below the mean and cancel each other out, resulting in an expected value of zero.
The factors influencing the behaviour of a variable in question usually behave in a random way. So the outputs and the resulting chance errors also appear in a somewhat random fashion. Thus, chance errors cannot be controlled, however accurate the model be. The presence of this error hence does not reduce the credibility of a model.
This error is in sharp contrast to the other modelling error, called the ‘sampling error’. This is a systematic error, which has crept into the system due to biases in assumption or the experimentation arrangement. This error has a direct defined relationship with the variable, hence its expected value is not zero, resulting in severely erroneous models.
An example of a random experiment will be measurement of pulse-rates of 100 random people on the street. However, a biases set-up may be measuring pulse-rates of 100 joggers on the street, which will definitely contain an up-side bias.