WHEN LEAST-SQUARES SQUARES LEAST

There is a general lack of awareness among 'lay' professionals (geophysicists included) regarding the limitations in the use of least-squares. Using a simple numerical model under simulated conditions of observational errors, the performance of least-squares and other goodness-of-fit criteria under various error conditions are investigated. The results are presented in a simplified manner that can be readily understood by the lay earth scientist. It is shown that the use of least-squares is, strictly, only valid either when the errors pertain to a normal probability distribution or under certain fortuitous conditions. The correct power to use (e.g. square, cube, square root, etc.) depends on the form of error distribution. In many fairly typical practical situations, least-squares is one of the worst criteria to use. In such cases, data treatment, 'robust statistics' or similar processes provide an alternative approach.