One of the major aims in community ecology is to understand the processes that underlie the species diversity and abundance in a community. It is now well accepted that the species abundance distributions (SADs) of various natural communities can be well explained by Hubbell's neutral model, while it has been traditionally considered that some deterministic process could be important. In fact, for many datasets, deviations from the neutral model are not sufficiently large to reject the neutrality. This would be potentially because that the commonly used tests focus on less informative summary statistics. Here, we explored the power of statistical tests of the neutral model by extensive simulations. In practice, we developed a simple niche model that incorporates stochastic demography of individuals as well as non-random replacements of individuals, i.e. niche differentiation. Under this niche model, a large number of SADs were simulated, to which the common model-fitting approach is applied. We also examined the neutrality test based on species richness, Shannon's index as well as Etienne's exact tests. It was found that a neutral model was well supported by simulated SADs of niche-structured communities. Particularly, a neutral model showed a good fit not only when niche overlap is large among species but when the number of niche is large.