Do small samples underestimate mean abundance? It depends on what type of bias we consider

Abstract

Former authors claimed that, due to parasites' aggregated distribution, small samples underestimate the true population mean abundance. Here we show that this claim is false or true, depending on what is meant by 'underestimate' or, mathematically speaking, how we define 'bias'. The 'how often' and 'on average' views lead to different conclusions because sample mean abundance itself exhibits an aggregated distribution: most often it falls slightly below the true population mean, while sometimes greatly exceeds it. Since the several small negative deviations are compensated by a few greater positive ones, the average of sample means approximates the true population mean.