It is common to find that authors use more than one diversity measure in published research without providing interpretation or explanation. We use a survey of the last three years of articles published in this journal along with a classic data set of Parker from the Gulf of Mexico to show that the familiar practice of citing multiple indices, e.g., Shannon’s and Simpson’s diversity indices and/or Fisher’s α, each calculated for the same samples, is redundant and singularly uninformative. In addition, authors often register surprise at the performance of indices when describing diversity over gradients such as depth or time. We show that there is no requirement that the values of the indices be concordant over any gradient and the behavior of a measure can be mathematically determined by the distribution of the observed species. The measures we found to be the most common in current use were S, α, H, λ, and max pi. The mathematical equivalence of measures is shown through simple plots and description and a standard set of non-redundant measures on a log scale, lnS, H, and ln (1/max pi) is recommended. Use of standardized analytical approaches to the study of problems of change in biodiversity removes limitations on the potential for inference concerning local as well as regional and global scales.