The issue of permanent nondipole contributions to the time-averaged field lies at the very heart of paleomagnetism and the study of the ancient geomagnetic field. In this paper we focus on paleomagnetic directional results from igneous rocks of the southwestern U.S.A. in the age range 0–5 Ma and investigate both the time-averaged field and its variability about the mean value. Several decades of work in the southwestern United States have resulted in the publication of paleomagnetic data from over 800 individual paleomagnetic sites. As part of a new investigation of the San Francisco Volcanics, we collected paleomagnetic samples from 47 lava flows, many of which have been previously dated. The new data combined with published data are highly scattered. Contributions to the scatter were considered, and we find that removal of data sets from tectonically active areas and judicious selection according to Fisher's  precision parameter results in an axially symmetric data distribution with normal and reverse modes that are indistinguishable from antipodal. Monte Carlo simulations suggest that a minimum of 5 samples per site are needed to estimate the precision parameter sufficiently accurately to allow its use as a determinant of data quality. Numerical simulations from statistical paleosecular variation models indicate the need for several hundred paleomagnetic sites to get an accurate determination of the average field direction and are also used to investigate the directional bias that results from averaging unit vectors rather than using the full field vector. Average directions for the southwestern U.S.A. show small deviations from a geocentric axial dipole field, but these cannot be considered statistically significant. Virtual geomagnetic pole (VGP) dispersions are consistent with those from globally distributed observations analyzed by McElhinny and McFadden . However, a systematic investigation of the effect of imposing a cutoff on VGPs with large deviations from the geographic axis indicates that while it may reduce bias in calculating the average direction, such a procedure can result in severe underestimates of the variance in the geomagnetic field. A more satisfactory solution would be to use an unbiased technique for joint estimation of the mean direction and variance of the field distribution.