Methods for Deriving Pesticide Aquatic Life Criteria - Reviews of Environmental Contamination and Toxicology - page 59

model offers a promising technique for generating toxicity estimates for untested
species, including threatened or endangered species. Estimates from ICE could be
used to supplement data sets so that important untested species may be included in
criteria derivations. Estimates may also be used to evaluate whether criteria derived
with tested species would protect untested species of particular concern.

6.5 Data Reduction

Data that are to be used in criteria calculation procedures often require preliminary
treatment. For example, if there are multiple data for a particular combination of
species, substances, and endpoints, some method is needed to reduce those data
into a single point for each species/substance/endpoint combination. Most method-
ologies utilize the geometric mean to represent the best estimate (central tendency)
of a toxicity or hazard value, but whether to use the geometric mean or the arithmetic
mean for environmental chemical data is somewhat controversial. Parkhurst (1998)
argues that, for environmental chemical concentrations, the arithmetic mean is
superior to the geometric mean because it is unbiased, easier to calculate, scientifi-
cally more meaningful, and more protective of public health (as a result of the low
bias of the geometric mean). He acknowledges a few cases in which a geometric
mean is preferable. One such case, pertinent to criteria derivation, is that of averaging
ratios, such as BCFs. Even for log-normally distributed data, Parkhurst states that
the arithmetic mean is preferable, because it is unbiased and makes more scientific
sense. He gives the example of two data sets, A = (10, 90) and B = (40, 50). The
arithmetic mean of A is larger, but the mean of the logarithms of B is larger. In such
a case, according to Parkhurst, a statistical comparison based on the log-transformed
data may be irrelevant or misleading.
The USEPA (1985) argues that for log-normally distributed data, the geometric
mean is preferred over the arithmetic mean. Parkhurst's argument, regarding the
low bias of geometric means not being protective, does not apply to toxicity data
(as opposed to environmental concentration data), because lower values are more
protective. With regard to Parkhurst's example of sets A and B, the possibility of
being misled by the geometric mean is not different than being misled by the arithmetic
mean, because the degree of variability between the raw and the log-transformed data
are not significantly different.
The USEPA (1985) requires that species mean acute values (SMAVs) are to be
calculated as the geometric mean of observed species values; similarly, GMAVs are
calculated as the geometric mean of all SMAVs for a given genus. If data indicate
that a particular life stage is at least a factor of 2 more resistant than another life
stage for the same species, then the data for the more resistant life stage is not used
to calculate the SMAV, because the goal is to protect all life stages. Similarly, if
acute toxicity values for a species or genus differ by more than a factor of 10, then
some or all of the values should be excluded (guidance on how to choose what to
keep or exclude is not given). The SMAV may be calculated from the result of one