Random errors are errors manifesting independence: the error in one instance of a quantity is in no way predictable from knowledge of the error in another instance: the error in each instance is considered to be an independent draw from an underlying probability distribution; “random” implies in this context both “unpredictable” and “uncorrelated between measured values” (within a given processing level); random errors therefore tend to “average out” across many measured values, and the uncertainty in the average of the measured values decreases with more measurements; random effects may be operating at the same time as other types of effect, in which case only a component of the total error is random; an example of a random effect (an effect giving rise to random errors) is electronic noise in an amplifier circuit.

A complication arises in a chain of processing in which a quantity subject to random errors at a one level then influences many values in a higher level of processing: the originating effect may be random (or, “aleatoric”) but at the higher level the resulting errors across many values are not independent. For this reason, we use “random” to discuss the nature of an effect, and “independent” to signify “uncorrelated across measured values”.