Expected Error Magnitude

Consider a series of N soil tests to be performed under nominally identical conditions. Before the experiments, the outcomes can be modeled as identically distributed random variables with (common) expected value E[R] and standard deviation . Before the experiments, the sample average is itself a random variable. Its realization after N experiments have been performed is denoted by .

Under the random sampling assumption, to compare the reliability of various types of experiments, a nondimensional (normalized) root-mean-square error is proposed, for the case of tests with strictly positive results. It is obtained by normalizing the root-mean-square error (standard deviation of ) with respect to the sample mean :

 

Since, in general, the value is not known a priori, it can be approximated by an unbiased estimator, the sample standard deviation:

 

Consequently, after the experiments have been performed, the normalized root-mean-square error in (4) can be estimated as:

 

The estimate will be refered as expected error magnitude.

It is obvious from (6) that, under the random sampling assumption, decreases with increasing number of tests.