We derive and test some assumptions and predictions of the Sampling Effect Hypothesis (SEH) by examining the relationship between the traits of species in monoculture and their relative abundance in mixture, and by comparing polyculture performance with single-species plots. Although we found a positive relationship between production in monoculture and dominance in mixtures as predicted by the SEH, the relationship had low explanatory power. Counter to predictions, the species with the highest monoculture biomass were not able to strongly dominate all mixtures; instead the dominance of these species decreased with increasing species richness. On average, polycultures did not achieve greater biomass than (transgressively overyield) the species in each mixture, or at each site, that was most productive in monoculture. However, mixture yields did transgressively overyield both the monoculture biomass of the dominant species in the mixtures, and the weighted average of all monocultures (non-transgressive overyielding), both of which were positively related to increasing species richness. The varying responses of different overyielding tests resulted because resource partitioning and positive interactions were often counter-balanced by selection for species with lower biomass than the highest-yielding monocultures. Judging whether or not mixtures overyield therefore depends in part upon which species is the basis for comparison. We present a new general framework for overyielding analysis where every monoculture provides a potential comparison and from which the most relevant tests can be selected.