Taxa differ widely in numbers of species, which may be due either to chance alone or to factors that cause differences in speciation and extinction rates between taxa. To test whether an observed distribution of species over taxa differs from the distribution expected from chance alone, one must take into account that neither speciation nor extinction rates are known. This paper introduces a way to estimate speciation and extinction probabilities from the distribution of extant species over families and to test whether the observed distribution is different from expected. Application of this procedure to the distributions of bird, hexapod, primate, and angiosperm species over taxa provides statistical evidence of differences in rates of cladogenesis between taxa.