Aim Quinn & Harrison (1988; Oecologia, 75, 132) suggested that several small, isolated islands generally bore a higher diversity than fewer (or single) larger islands. They proposed a method by which the cumulative diversity of islands arranged small-to-large (‘STOL’) and large-to-small (‘LTOS’) could be used to identify how island area and species distributions interact to produce the system-wide or ensemble diversity. From these curves, an ‘index of saturation’ (SI) was calculated to summarize the way in which diversity is generated on a given archipelago. Unfortunately, the method did not allow statistical judgements to be made. Our paper considers the reliability of the Quinn-Harrison approach, especially in light of the inconsistency of its implications compared with ‘nestedness’ analyses. Location Three example data sets are used: reptiles from the archipelagos of the Sea of Cortéz, breeding land-birds from the Canary Islands, and stream invertebrates occupying rocks in the Steavenson River of central Victoria, Australia. Methods We refine the Quinn-Harrison technique to produce a method by which the difference between the STOL and LTOS cumulative diversity curves can be gauged statistically (the ξ statistic). We also propose an alternative statistic (η)—which we believe to be more intuitive—that preferentially weights species occurring on few patches and that can be statistically assessed by using Monte Carlo simulation. Results The basic Quinn-Harrison technique is not reliable for diagnosing whether systems are characterized by STOL or LTOS patterns. The three example data sets provide the range of options for faunal-diversity generation (STOL overlies LTOS, LTOS overlies STOL, and coincident). However, statistical analyses indicate that the patterns all are generated by the rarer species occupying larger islands. The results of the revised ξ statistic and especially the η statistic are consistent with this deduction, which in turn relate well with faunal-nestedness analyses. Main conclusions There was a contradiction between the Quinn-Harrison analyses, which suggested that most rarer taxa occurred in impoverished, smaller islands, and results of nestedness analyses, which indicated that the rarer taxa occurred on more speciose, larger islands. The resolution to this dilemma is that the Quinn-Harrison diagram and saturation index are so flawed that they yield unreliable results vis a vis the generation of diversity on archipelagos.