Overlap in species-accumulation curves ordered from small-large and large-small (aka SLOSS analysis) is an important line of evidence inferring weak positive diversity effects of fragmentation per se. Yet combining patches in small-large order maximises the probability of encountering new species for every patch, invalidating comparison with large-small order. Controlling for this using simulated null communities, I test species accumulation against a random expectation for 201 published datasets from islands, habitat islands and fragments and compare inference using both methods. SLOSS analysis found 67% positive, 7% negative and 26% no response among datasets. Using simulation, analogous values were 4%, 12% and 40% respectively with no clear outcome in the remainder. SLOSS analysis provides unreliable inference on the diversity effects of habitat subdivision. Accumulation of species in small-large patch size order is more likely to result in fewer than expected species than more, with no effect being the most probable result.