A bootstrap analysis for finite populations

Abstract: Bootstrap methods are increasingly accepted as one of the common approaches in constructing confidence intervals in bibliometric studies. Typical bootstrap methods assume that the statistical population is infinite. When the statistical population is finite, a correction needs to be applied in computing the estimated variance of the estimators and thus constructing confidence intervals. We investigate the effect of overlooking the finiteness assumption of the statistical population using a dataset containing all articles in Web of Science (WoS) for Delft University of Technology from 2006 until 2009. We regard the data as our finite statistical population and consider simple random samples of various sizes. Standard bootstrap methods are firstly employed in accounting for the variability of the estimates, as well as constructing the confidence intervals. The results unveil two issues, namely that the variability in the estimates does not decrease to zero as the sample size approaches the population size and that the confidence intervals are not valid. Both issues are addressed when accounting for a finite population correction in the bootstrap methods.