This paper compares the traditional methods of statistical inference on the data from biomedical studies with a proposed index of fragility in the results. In general, for any given study there are 8 possible combinations of conclusions regarding statistical significance, quantitative significance and fragility. The 8 possibilities are considered in turn with respect to how studies in each group might be interpreted. Numerical examples show that not all 8 possibilities need be attainable with a given study design, and that the relative likelihood of them occurring can vary widely. It is concluded that the fragility index may be a useful adjunct to conventional statistical inference, with certain intuitive appeal, but that more empirical experience is needed with the fragility method.