A fundamental problem using linear inverse theory to solve geophysical problems using eigenvalue decomposition algorithms is to determine how many eigenvalues to include in the solution. Of very small eigenvalues are included, the solution variance increases rapidly, particularly if zero-values eigenvalues are computed as positive small numbers and are misidentified. F-tests can be applied to a succession of solutions, each containing an incremental number of eigenvalues, to determine statistical significance of the data variance reduction. This methodology is widely used for multiple variable regression analysis, but has not been applied to eigenvalue problems. The F-test is a statistical criterion for choosing an 'optimal' solution along the trade-off curve of model resolution and model variance for a particular model parameterization. ¿American Geophysical Union 1991