In an earlier paper, we presented methods for estimating achievement gaps when test scores are coarsened into a small number of ordered categories, preventing fine-grained distinctions between individual scores. We demonstrated that gaps can nonetheless be estimated with minimal bias across a broad range of simulated and real coarsened data scenarios. In this article, we extend this previous work to obtain practical estimates of the imprecision imparted by the coarsening process and of the bias imparted by measurement error. In the first part of this article, we derive standard error estimates and demonstrate that coarsening leads to only very modest increases in standard errors under a wide range of conditions. In the second part of this article, we describe and evaluate a practical method for disattenuating gap estimates to account for bias due to measurement error.