What is the noncentrality parameter?

The noncentral distributions (t, F, and chi-square) can be derived from samples of normal random variables with a nonzero mean. These noncentral distributions are distinguished from the central distributions by a noncentrality parameter. The noncentrality parameter is useful in describing commonly used test statistics, where the noncentrality parameter represents the degree to which the mean of the test statistic departs from its mean when the null hypothesis is true.