The estimation of diversity indexes is considered when species abundance is estimated by means of plots, points or transects placed onto the study region in accordance with probabilistic schemes. Under uniform random sampling–that is when plots, points or transects are uniformly and independently located on the study region–the consistency and the large‐sample normality of diversity index estimators follow from the usual limit theorems as the sampling effort increases. In addition, variance estimation and finite‐sample bias reduction are achieved by means of standard results on the jackknife method. Despite its theoretical simplicity, uniform random sampling may lead to uneven coverage of the study region. In order to avoid this shortcoming, the use of one‐per‐stratum stratified sampling is usually considered. This sampling scheme involves partitioning the study region into subsets of equal size and uniformly selecting a plot, a point or a transect in each of these subsets. The present paper aims to show the consistency and the large‐sample normality of the diversity index estimators under one‐per‐stratum stratified sampling, as well as to deal with variance estimation and bias reduction. Copyright © 2015 John Wiley & Sons, Ltd.