Comparing diversities between groups is a task biologists are frequently faced with, for example in ecological field trials or when dealing with metagenomics data. However, researchers often waver about which measure of diversity to choose as there is a multitude of approaches available. As Jost (2008, Molecular Ecology, 17, 4015) has pointed out, widely used measures such as the Shannon or Simpson index have undesirable properties which make them hard to compare and interpret. Many of the problems associated with the use of these ‘raw’ indices can be corrected by transforming them into ‘true’ diversity measures. We introduce a technique that allows the comparison of two or more groups of observations and simultaneously tests a user-defined selection of a number of ‘true’ diversity measures. This procedure yields multiplicity-adjusted P-values according to the method of Westfall and Young (1993, Resampling-Based Multiple Testing: Examples and Methods for p-Value Adjustment, 49, 941), which ensures that the rate of false positives (type I error) does not rise when the number of groups and/or diversity indices is extended. Software is available in the R package ‘simboot’.