Crustal stress orientations provide important information about the mechanics of regional deformation. Numerous methods exist for inverting earthquake focal mechanisms for stress orientation, and the more widely used methods usually obtain similar results for similar data sets. However, error estimates are highly variable, complicating the interpretation of results. The southern California stress field, for example, contains much statistically significant spatial and temporal variability according to the error estimates of one method (Michael, 1984, 1987b), but very little according to those of another (Gephart and Forsyth, 1984). To resolve whether the southern California stress field is generally homogeneous or heterogeneous, we must determine which of the error estimates best reflects the true inversion uncertainty. To do this, we tested both methods on a suite of synthetic focal mechanism data sets containing random errors. The method of Gephart and Forsyth (1984) usually provides more accurate estimates of stress orientation, especially for high-quality data sets, but its confidence regions are in most cases too large. The method of Michael (1984, 1987b) is more accurate for very noisy data sets and provides a more appropriate estimate of uncertainty, implying that the stress field in southern California is probably heterogeneous.