The statistical analyses were done in R (Faraway, 2005) using
the LMNE package. Given the sample design, the statistical analysis
of this study required a mixed effect model using two random
effects, where the second random effect, location, is nested within
the first random effect, county. The fixed effects examined were
region, well water, pickup date, different address, water softener or
other water treatment. The same general modeling procedure was
used in the analysis for each mineral. The first step was to fit the
full model and check for outliers. After the outliers were removed,
then the full model was set and reduced to the final model by first
dropping out one fixed effect at a time, then two fixed effects at a
time, etc. All testing was done using the likelihood ratio test.