Shannon entropy is often a quantity of interest to linguists studying the communicative capacity of human language. However, entropymust typically be estimated from observed data because researchers do not have access to the underlying probability distribution. While entropy estimation is a well-studied problem in other fields, there is not yet a comprehensive exploration of the efficacy of entropy estimators for use with linguistic data. In this work, we fill this void, studying the empirical effectiveness of different entropy estimators for linguistic distributions. In a replication of two recent information-theoretic linguistic studies, we find evidence that the reported effect size is over-estimated due to over-reliance on poor entropy estimators. We end this paper with a concrete recommendation for the entropy estimators that should be used in future linguistic studies.