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Positive relationships between species richness and sampling area are perhaps the most pervasive patterns in nature. However, the shape of species–area relationships is often highly variable, for reasons that are poorly understood. One such source of variability is the “small-island effect”, which refers to a decrease in the capacity of sampling area to predict species richness on small islands. Small-island effects have been attributed to a variety of processes, including spatial subsidies, habitat characteristics and ocean-born disturbances. Here, we show that small-island effects can be generated by logarithmic data transformations, which are commonly applied to both axes of species–area relationships. To overcome this problem, we derive several null models to test for non-random variability in the capacity of island area to predict species richness and apply them to data sets on island plant communities in Canada and New Zealand. Both archipelagos showed evidence for small-island effects using traditional breakpoint regression techniques on log-log axes. However, null model analyses revealed different results. The capacity of sampling area to predict species richness in the Canadian archipelago was actually lowest at intermediate island size classes. In the New Zealand archipelago, island area was similarly capable of predicting species richness across the full range of island sizes, indicating the small-island effect detected by breakpoint regression is an artifact of logarithm data transformation. Overall results show that commonly used regression techniques can generate spurious small-island effects and that alternative analytic procedures are needed to detect non-random patterns in species richness on small islands.