Testing whether some species traits have a significant effect on diversification rates is central in the assessment of macroevolutionary theories. However, we still lack a powerful method to tackle this objective. I present a new method for the statistical analysis of diversification with species traits. The required data are observations of the traits on recent species, the phylogenetic tree of these species, and reconstructions of ancestral values of the traits. Several traits, either continuous or discrete, and in some cases their interactions, can be analyzed simultaneously. The parameters are estimated by the method of maximum likelihood. The statistical significance of the effects in a model can be tested with likelihood ratio tests. A simulation study showed that past random extinction events do not affect the Type I error rate of the tests, whereas statistical power is decreased, though some power is still kept if the effect of the simulated trait on speciation is strong. The use of the method is illustrated by the analysis of published data on primates. The analysis of these data showed that the apparent overall positive relationship between body mass and species diversity is actually an artifact due to a clade-specific effect. Within each clade the effect of body mass on speciation rate was in fact negative. The present method allows to take both effects (clade and body mass) into account simultaneously.