I explored the effects of sampling on three measures of regional diversity: γ diversity (the number of species), β diversity (mean similarity among sites), and μ diversity (mosaic diversity and structure around mean similarity). Two sampling effects were modelled by computer simulation, number of sites sampled and intensity of sampling within sites, using plant community data from Michigan, North Carolina, and Costa Rica. Estimates of the number of species were sensitive to both sampling effects. Estimates of mean similarity were unaffected by the number of sites sampled but were sensitive to the intensity of sampling. Estimates of mosaic diversity were relatively unaffected by the number of sites sampled, if the number was above 30 sites and outlier sites were removed, and were not sensitive to the intensity of sampling. I offer mean similarity as a multi-gradient complement to β diversity measured as the turnover of species along a single gradient.