Separating Measurement Error and Signal in Environmental Data: Use of Replicates to Address Uncertainty

Measurement uncertainty has long been a concern in the
characterizing
and interpreting environmental and toxicological measurements. We
compared statistical analysis approaches when there are replicates:
a Naı̈ve approach that omits replicates, a Hybrid approach
that inappropriately treats replicates as independent samples, and
a Measurement Error Model (MEM) approach in a random effects analysis
of variance (ANOVA) model that appropriately incorporates replicates.
A simulation study assessed the effects of sample size and levels
of replication, signal variance, and measurement error on estimates
from the three statistical approaches. MEM results were superior overall
with confidence intervals for the observed mean narrower on average
than those from the Naı̈ve approach, giving improved characterization.
The MEM approach also featured an unparalleled advantage in estimating
signal and measurement error variance separately, directly addressing
measurement uncertainty. These MEM estimates were approximately unbiased
on average with more replication and larger sample sizes. Case studies
illustrated analyzing normally distributed arsenic and log-normally
distributed chromium concentrations in tap water and calculating MEM
confidence intervals for the true, latent signal mean and latent signal
geometric mean (i.e., with measurement error removed). MEM estimates
are valuable for study planning; we used simulation to compare various
sample sizes and levels of replication.