G­
1
Appendix
G.
Hardness
Slopes
As
discussed
in
Section
5.1.1,
EPA's
earlier
freshwater
copper
criteria
recommendations
were
hardnessdependent
values.
Although
characterized
as
"
hardness­
dependent,"
EPA
recognized
that
these
adjusted
criteria
not
only
reflected
the
influence
of
hardness
on
copper
toxicity;
hardness
was
also
a
surrogate
for
other
covarying
water
quality
parameters.
In
order
to
compare
the
new
BLM­
based
criteria
with
updated
hardness­
dependent
criteria
an
overall
or
"
pooled
slope"
was
needed
to
normalize
the
acute
toxicity
data
to
a
standard
hardness
for
calculating
criteria.
A
pooled
hardness
slope
was
derived
using
all
appropriate
acute
toxicity
data,
regardless
of
the
quality
rating
assigned,
according
to
the
procedures
in
the
1985
Guidelines.

To
account
for
the
apparent
relationship
of
copper
acute
toxicity
to
hardness,
an
analysis
of
covariance
(
Dixon
and
Brown
1979;
Netter
and
Wasserman
1974)
was
performed
using
WINKS
statistical
software
(
WINKS
ETC)
to
calculate
the
pooled
slope
for
hardness
using
the
natural
logarithm
of
the
acute
value
as
the
dependent
variable,
species
as
the
treatment
or
grouping
variable,
and
the
natural
logarithm
of
hardness
as
the
covariate
or
independent
variable.
The
pooled
slope
is
a
regression
slope
from
a
pooled
data
set,
where
every
variable
is
adjusted
relative
to
its
mean.
The
species
are
adjusted
separately,
then
pooled
for
a
single
conventional
least
squares
regression
analysis.
The
slope
of
the
regression
line
is
the
best
estimate
of
the
all­
species
relationship
between
toxicity
and
hardness.

This
analysis
of
covariance
model
was
fit
to
the
data
contained
in
this
appendix
for
the
seven
species
for
which
definitive
acute
values
are
available
over
a
range
of
hardness
such
that
the
highest
hardness
is
at
least
three
times
the
lowest,
and
the
highest
is
also
at
least
100
mg/
L
higher
than
the
lowest.
Other
species
either
did
not
meet
these
criteria,
the
organisms
were
fed,
or
as
with
D.
pulex,
D.
pulicaria
and
H.
azteca
did
not
show
any
hardness­
toxicity
trend,
possibly
due
to
differences
in
exposure
methods
such
as
unusual
chemical
composition
of
the
dilution
water.

A
list
of
the
species,
acute
toxicity
and
hardness
values,
and
the
slopes
used
to
estimate
the
pooled
hardness
slope
are
included
in
this
appendix.
The
slopes
for
the
seven
species
ranged
from
0.4349
to
0.8963,
and
the
pooled
slope
for
these
seven
species
was
0.9584.
An
F­
test
was
used
to
test
whether
a
model
with
separate
species
slopes
for
each
species
gives
significantly
better
fit
to
the
data
than
the
model
with
parallel
slopes.
This
test
showed
that
the
separate
slopes
model
is
not
significantly
better,
and
therefore
the
slopes
are
not
significantly
different
than
the
overall
pooled
slope
(
P=
0.39).
