Although the concentration index (CI) and the health achievement index (HAI) have been extensively used, previous studies have relied on bootstrapping to compute the variance of the HAI, whereas competing variance estimators exist for the CI. This paper provides methods of statistical inference for the HAI and compares the available variance estimators for both the CI and the HAI using Monte Carlo simulation. Results for both the CI and the HAI suggest that analytical methods and bootstrapping are well behaved. The convenient regression method gives standard errors close to the other methods, provided the CI is not too large (< 0.2), but otherwise tends to understate the standard errors. In our simulation setting, the improvement from the Newey–West correction over the convenient regression method has mixed evidence when the CI ≤ 0.1 and is modest when the CI > 0.1. Published 2011. This article is a US Government work and is in the public domain in the USA.