Interval estimators of parameters for normal one sample and balanced one-way random effects models when data are rounded

In standard statistical analysis, data are typically assumed to be essentially exact. But in fact, all real data are reported to some smallest unit of measure related to the precision of the device used to produce them. We might call such data “rounded” because they are really obtained by “rounding to something.” We first discuss the interval estimation of the parameters μ and σ, when a single rounded sample comes from the N(μ, σ 2) distribution with both parameters unknown. Then we discuss the interval estimation of variance components σ and σ_τ if rounded data are from a balanced one-way normal random effects model. For each problem rounded-data likelihood-based methods are compared to naive calculations made as if observations were exact. We find that with some modifications the likelihood-based methods provide an effective way to analyze such data.