Inference from individual streamflow records can be extremely misleading, even for large samples. One is often tempted to trust information available from a streamflow record rather than to exploit regional average statistics of those records. This study documents that regional average streamflow statistics usually contain much more information about the variability and persistence of streamflow at a particular site than does the individual streamflow record for that site. Experiments are performed using time series of annual streamflow at 1544 gauging stations across the continental United States. We document that 18 broad water resource regions of the United States are homogeneous in terms of the year-to-year persistence of streamflow, whereas much smaller regions are required to obtain homogeneity in terms of the variability of streamflow. Classical homogeneity measures ignore the serial correlation of streamflow. Instead, homogeneity is quantified using the sampling properties of at-site estimates of the coefficient of variation Cv and lag-one correlation &rgr;1 of annual streamflows. Additional experiments using the Hurst coefficient reveal that the long-term persistence structure of historical annual streamflow series is indistinguishable from the long-term persistence structure of either an AR(1) or ARMA(1,1) process. If historical flow series are generated from either an AR(1) or ARMA(1,1) process, then even given 1544 observed time series, we are unable to distinguish between those two processes. ¿ 1998 American Geophysical Union