Procedures introduced here make it possible, first, to show that background (piecemeal) extinction is recorded throughout geologic stages and substages (not all extinction has occurred suddenly at the ends of such intervals); second, to separate out background extinction from mass extinction for a major crisis in earth history; and third, to correct for clustering of extinctions when using the rarefaction method to estimate the percentage of species lost in a mass extinction. Also presented here is a method for estimating the magnitude of the Signor-Lipps effect, which is the incorrect assignment of extinctions that occurred during a crisis to an interval preceding the crisis because of the incompleteness of the fossil record. Estimates for the magnitudes of mass extinctions presented here are in most cases lower than those previously published. They indicate that only ∼81% of marine species died out in the great terminal Permian crisis, whereas levels of 90-96% have frequently been quoted in the literature. Calculations of the latter numbers were incorrectly based on combined data for the Middle and Late Permian mass extinctions. About 90 orders and more than 220 families of marine animals survived the terminal Permian crisis, and they embodied an enormous amount of morphological, physiological, and ecological diversity. Life did not nearly disappear at the end of the Permian, as has often been claimed.