Primary uses of statistical methods in SHM include the following: (1) remove randomness or noise from measurements in an effort to uncover and estimate the values of underlying properties; (2) condense large data sets into less voluminous forms with higher information densities; (3) organize the data so as to test various hypotheses or to classify the state of the system or process; and (4) recognize underlying patterns or structures in the data. The first two of these-removal of randomness and data condensation-are the subject of this chapter. The second two-classification and pattern recognition-are primarily left to the next chapter.