Appendix
B
to
the
TSD
1
Appendix
B
to
the
TSD
Characterizing
Measurement
Variability
as
a
Function
of
Analyte
Concentration
for
a
Variety
of
Analytical
Techniques
Summary
EPA's
Office
of
Science
and
Technology
(
OST)
is
conducting
a
study
of
measurement
variability
as
part
of
an
assessment
of
detection
and
quantitation
limit
concepts.
The
study
utilizes
a
large
data
set
on
measurement
variability
generated
specifically
to
support
this
assessment
and
on
data
gathered
during
the
course
of
analytical
method
development.
The
purpose
of
the
study
reported
in
this
Appendix
B
to
the
Technical
Support
Document
(
TSD)
is
to
determine
if:
(
1)
appropriate
models
could
be
found
that
would
adequately
characterize
measurement
variability
and
support
the
estimation
of
detection
and
quantitation
limits;
and
(
2)
the
number
of
models
could
be
limited
in
order
to
minimize
complications
in
the
process
of
developing
detection
and
quantitation
limits.
Results
suggest
that
most
measurement
techniques
used
under
the
Clean
Water
Act
(
CWA)
could
be
described
by
a
general
two­
component
model.
The
model
describes
measurement
variability
as
a
function
of
concentration
in
terms
of
two
components:
an
additive
component
dominate
at
low
concentration
that
represents
variability
to
be
independent
of
concentration
and
a
multiplicative
component
dominate
at
higher
concentrations
that
represents
variability
as
proportional
to
the
concentration
of
the
substance
measured.
The
model
also
allows
for
a
smooth
transition
in
the
relationship
in
the
concentration
region
where
neither
component
is
dominate.
The
study
results
also
indicate
that
the
two­
component
model
may
not
be
applicable
to
all
analytes
for
all
methods.
In
some
cases,
measurement
variability
does
not
exhibit
a
pattern
that
would
suggest
a
particular
model.
In
other
cases,
measurement
variability
is
observed
to
be
effectively
constant
over
a
range
that
extends
beyond
the
low
concentration
range.
In
these
cases,
the
two
component
model
may
still
be
a
useful
tool
in
determining
detection
and
quantitation
levels
but
other
approaches,
e.
g.,
that
do
not
involve
the
use
of
a
particular
model
or
assume
that
variation
is
effectively
constant,
may
also
be
suitable.

1.
Introduction
In
1998,
EPA's
Office
of
Science
and
Technology
(
OST)
completed
several
studies
conducted
to
generate
data
that
would
characterize
measurement
variability
as
a
function
of
concentration
for
a
variety
of
analytical
techniques
(
see
Appendix
A).
These
studies
were
conducted
as
part
of
an
effort
to
address
criticism
by
the
academic
community,
regulated
industry,
and
others,
of
the
detection
and
quantitation
procedures
used
to
support
EPA's
Clean
Water
Act
(
CWA)
programs.
More
recently,
the
Agency
has
agreed
to
a
schedule
for
completing
this
work
and
applying
the
results
to
the
evaluation
and
selection
of
detection
and
quantitation
concepts
and
procedures.
This
document
uses
the
data
referenced
above
and
other
selected
data
to
characterize
measurement
variability
as
a
function
of
analyte
concentration
for
a
variety
of
measurement
techniques
This
Appendix
B
to
the
Technical
Support
Document
for
the
Assessment
of
Detection
and
Quantitation
Concepts
(
TSD)
was
drafted
before
assignment
of
letters
to
appendices
to
the
TSD.
This
resulted
in
duplication
of
appendix
letters
between
the
TSD
and
this
appendix.
To
avoid
confusion,
references
to
the
appendices
in
this
Appendix
B
to
the
TSD
are
used
without
further
defining
words,
whereas
references
to
this
appendix
as
an
appendix
to
the
TSD
are
used
with
the
words
"
this
Appendix
B
to
the
TSD."
The
appendices
to
this
Appendix
B
to
the
TSD
are
contained
on
a
CD­
ROM
that
supports
Appendix
B
to
the
TSD
2
the
TSD
and
are
not
physically
attached
to
this
document.
A
list
of
the
appendices
contained
on
the
CDROM
is
provided
at
the
end
of
this
Appendix
B
to
the
TSD.

2.
Data
EPA
has
conducted
an
extensive
review
of
the
published
literature
on
detection
and
quantitation.
Unfortunately,
the
published
literature
tends
to
focus
on
concepts
and
methodology
and
contains
little
actual
data.
No
data
were
found
on
the
key
issue
(
for
detection
and
quantitation)
of
the
characterization
and
modeling
of
measurement
variability
as
a
function
of
analyte
concentration.
In
order
to
fill
the
need
for
data,
EPA
embarked
on
an
effort
to
produce
data
that
would
support
the
characterization
of
variability
and
the
assessment
of
detection
and
quantitation.
The
first
phase
of
this
process
was
to
develop
data
sets
representative
of
the
most
commonly
used
analytical
technologies,
and
the
second
phase
was
application
of
statistics,
including
model
fitting,
to
these
data.

Four
data
sets
were
selected
to
support
the
analyses
presented
in
this
Appendix
B
to
the
TSD.
Three
were
developed
by
EPA
for
the
express
purpose
of
studying
the
relationship
between
measurement
variation
and
analyte
concentrations
across
a
wide
variety
of
measurement
techniques
and
analytes.
These
data
sets
are
referred
to
as
(
1)
EPA's
ICP/
MS
data,
(
2)
EPA's
Episode
6000
data,
and
(
3)
EPA's
Episode
6184
data.
In
all
three
data
sets,
replicate
measurement
results
from
each
combination
of
analyte
and
measurement
technique
were
produced
by
a
single
laboratory
over
a
wide
range
and
large
number
of
spike
concentrations.
The
fourth
data
set
was
developed
by
the
American
Automobile
Manufacturer's
Association
(
the
"
AAMA
Dataset")
for
the
purpose
of
estimating
a
specific
quantitation
value
referred
to
as
an
"
alternate
minimum
level"
(
AML)
[
see
Gibbons
et
al.
(
1997)].
For
development
of
the
AAMA
Dataset,
replicate
results
were
measured
at
a
limited
number
of
spike
concentrations
by
multiple
laboratories
using
EPA
Method
245.2
(
CVAA)
for
mercury
and
EPA
Method
200.7
(
ICP/
AES)
for
twelve
other
metals.
Details
of
these
four
data
sets
are
given
in
the
subsections
that
follow.

2.1
EPA's
ICP/
MS
Data
In
1996,
EPA
contracted
with
Battelle
Marine
Sciences
to
generate
data
to
support
the
assessment
of
measurement
variability
in
EPA's
draft
Method
1638
for
nine
metals
by
inductively
coupled
plasma
with
mass
spectroscopy
(
ICP/
MS).
The
nine
metals
were
silver,
cadmium,
copper,
nickel,
lead,
antimony,
selenium,
thallium,
and
zinc.
The
equipment
used
in
this
study
made
triplicate
readings
of
each
aliquot
of
each
sample
and
averaged
the
results.
Such
averaging
is
common
for
ICP/
MS
design
and
use.

In
preparation
for
this
study,
the
ICP/
MS
instrument
was
calibrated
using
one
sample
aliquot
at
concentrations
of
100,
1,000,
5,000,
10,000,
and
25,000
nanograms
per
liter
(
ng/
L).
Initially,
the
calibration
was
performed
using
the
default
instrument
software
to
produce
unweighted
least
squares
estimates
assuming
a
linear
calibration
function.
Subsequently,
the
analytical
results
were
adjusted
using
weighted
least
squares
estimates
in
place
of
the
unweighted
least
squares
estimates.
Weighted
least
squares
estimates
are
used
to
account
for
the
fact
that
measurement
variability
may
change
as
concentration
changes.
Usually,
variability
increases
as
analyte
concentration
increases
over
the
full
analytical
range.
Because
the
individual
readings
on
each
triplicate
were
not
retained;
the
only
data
available
to
EPA
are
average
intensity
results
for
the
aliquot.
Draft
EPA
Method
1638
specifies
the
use
of
an
average
response
factor
rather
than
least
squares
estimation
of
linear
calibration
curves,
although
it
does
allow
for
the
use
of
such
procedures.
Appendix
B
to
the
TSD
3
All
nine
metals
were
spiked
into
water
to
produce
solutions
at
concentrations
of:
10,
20,
50,
100,
200,
500,
1,000,
2,000,
5,000,
10,000,
and
25,000
ng/
L.
Each
solution
was
subsequently
divided
into
7
aliquots.
The
7
replicates
were
measured
in
order
of
decreasing
concentration.
Seven
replicates
at
0
concentration
(
what
chemists
term
a
"
blank")
were
also
measured
in
triplicate
for
all
nine
metals.
The
resulting
concentrations
were
converted
to
parts
per
trillion
(
ppt.)
for
ease
of
understanding
and
discussion.

Multiple
instrument
readings
(
at
multiple
mass
to
charge
ratios
or
m/
z's)
were
reported
for
most
metals,
although
draft
Method
1638
specifies
only
one
acceptable
m/
z
for
eight
of
the
nine
metals.
For
lead,
m/
z's
206,
207,
and
208
were
all
considered
to
be
acceptable
by
draft
Method
1638.
The
responses
at
the
other
m/
z
values
for
a
particular
metal
are
used
for
analyte
identification
purposes.
This
study
of
measurement
variation
used
only
data
associated
with
m/
z's
that
are
specified
by
draft
Method
1638.

2.2
EPA's
Episode
6000
Data
Episode
6000
data
were
collected
to
characterize
the
variability
of
measurement
results
from
0.1
times
an
initial
estimate
of
the
Method
Detection
Limit
(
MDL)
[
Glaser
et
al
(
1981)]
to
spike
concentrations
100
times
the
MDL.
Measurement
methods
studied
were:

°
Total
suspended
solids
(
TSS)
by
gravimetry
°
Metals
by
graphite
furnace
atomic
absorption
spectroscopy
(
GFAA)
°
Metals
by
inductively­
coupled
plasma
atomic
emission
spectrometry
(
ICP/
AES)
°
Hardness
by
ethylene
diamine
tetraacetic
acid
(
EDTA)
titration
°
Phosphorus
by
colorimetry
°
Ammonia
by
ion­
selective
electrode
°
Volatile
organic
compounds
in
water
by
purge
and
trap
capillary
column
gas
chromatography
with
photoionization
detector
(
GC/
PID)
and
electrolytic
conductivity
detector
(
GC/
ELCD)
in
series
°
Volatile
organic
compounds
by
gas
chromatography
with
a
mass
spectrometer
(
GC/
MS)
°
Available
cyanide
by
flow­
injection/
ligand
exchange/
amperometric
detection
°
Metals
by
inductively­
coupled
plasma
spectrometry
with
a
mass
spectrometer
(
ICP/
MS)

Details
of
the
study
design
are
described
in
EPA's
Study
Plan
for
Characterizing
Variability
as
a
Function
of
Concentration
for
a
Variety
of
Analytical
Techniques
(
July
1998).
The
design
is
summarized
below.

A
method
detection
limit
(
MDL)
study
was
conducted
for
each
combination
of
analyte
and
analytical
technique
as
an
initial
step
in
the
generation
of
the
Episode
6000
data.
The
study
plan
required
laboratories
to
calculate
these
initial
MDLs
using
the
procedure
in
Appendix
A.
Seven
replicates
were
then
run
at
100,
50,
20,
10,
7.5,
5.0,
3.5,
2.0,
1.5,
1.0,
0.75,
0.50,
0.35,
0.20,
0.15,
and
0.10
times
the
initial
MDL.

The
following
iterative
procedure
was
used
for
organic
compounds.
Methods
for
organics
normally
list
many
(
15
to
100)
analytes,
and
the
response
for
each
analyte
is
different.
Therefore,
to
determine
an
MDL
for
each
analyte,
the
concentration
of
the
spike
must
be
inversely
proportional
to
the
response.
The
process
of
making
spiking
solutions
with
15
to
100
different
concentrations
is
complicated
and
prone
to
error.
A
more
straightforward
approach,
and
one
used
in
this
study,
was
to
run
7
replicates
Appendix
B
to
the
TSD
4
at
decreasing
concentrations
until
signal
extinction
or
until
0.1
times
the
initial
MDL
was
reached,
whichever
came
first,
then
select
concentrations
appropriate
for
the
MDL.

Spike
concentrations
were
measured
in
order
from
the
highest
concentration
to
the
lowest
to
(
1)
to
minimize
carry­
over
effects
and
(
2)
to
prevent
the
collection
of
data
if
when
the
instrument
returned
zeros
for
three
or
more
of
the
replicates
at
a
given
concentration.
Carry­
over
can
occur
when
analysis
of
a
high
concentration
sample
is
followed
by
a
low
concentration
sample.
Carry­
over
is
usually
less
than
one
percent
but
can
be
a
few
percent
in
some
methods.
For
example,
if
a
sample
at
100
times
the
MDL
is
followed
by
a
sample
at
0.1
times
the
MDL,
the
sample
at
0.1
times
the
MDL
could
be
compromised
by
carry­
over
because
a
small
amount
of
carry­
over
from
the
100
MDL
sample
could
inflate
the
result
for
the
0.1
MDL
sample.
Running
the
samples
in
successive
decreasing
order
should
not
affect
successively
lower
measurements
because
the
amount
of
carryover
should
be
small
relative
to
the
measurement
at
the
next
lowest
level.

Further
details
are
described
in
EPA's
Study
Plan
for
Characterizing
Variability
as
a
Function
of
Concentration
for
a
Variety
of
Analytical
Techniques
(
July
1998).

2.3
EPA's
Episode
6184
Data:

Episode
6184
data
were
generated
to
determine
the
concentration
at
which
an
analyte
could
no
longer
be
identified
as
the
concentration
decreased.
Details
of
the
design
for
this
study
are
described
in
EPA's
Study
Plan
for
Characterizing
Error
as
a
Function
of
Concentration
for
Determination
of
Semivolatiles
by
Gas
Chromatography/
Mass
Spectrometry
(
December
1998).
Data
were
generated
for
82
semivolatile
organic
compounds
by
EPA
Method
1625C
(
semivolatile
organic
compounds
by
GC/
MS).
MDLs
were
not
determined
for
these
compounds.
Instead,
solutions
of
the
analytes
were
prepared
at
concentrations
of
50.0,
20.0,
10.0,
7.50,
5.00,
3.50,
2.00,
1.50,
1.00,
0.75,
0.50,
0.35,
0.20,
0.15,
0.10,
0.075
and
0.050
ng/
µ
L
(
or
µ
g/
mL).
The
solution
at
each
concentration
was
injected
into
the
GC/
MS
in
triplicate
with
the
mass
spectrometer
threshold
set
to
0,
and
again
in
triplicate
with
the
mass
spectrometer
threshold
set
to
a
low
level
in
the
signal
domain
typical
of
that
used
in
routine
environmental
analyses.
As
with
the
Episode
6000
dataset,
samples
were
analyzed
in
order
from
the
highest
to
the
lowest
concentration.

2.4
AAMA
Metals
Data
for
EPA
Methods
200.7
and
200.9
Data:

The
American
Automobile
Manufacturer's
Association
(
AAMA)
conducted
a
interlaboratory
study
of
EPA
Method
200.7
(
metals
by
ICP/
AES)
and
Method
245.2
(
mercury
by
CVAA).
Nine
laboratories
participated
in
the
study,
and
each
reported
data
for
the
following
13
metals:
aluminum,
arsenic,
cadmium,
chromium,
copper,
lead,
manganese,
mecury,
molybdenum,
nickel,
selenium,
silver
and
zinc.
Study
samples
were
analyzed
by
EPA
Method
200.7
for
12
of
the
metals;
mercury
was
determined
by
EPA
Method
245.2.

The
nine
laboratories
were
randomized
prior
to
the
start
of
the
study.
Five
matrix
types
(
including
reagent
water)
were
selected,
including
four
that
were
representative
of
the
automotive
industry.
Each
matrix
was
spiked
at
five
concentrations
in
a
predetermined
concentration
range.
Matrix
A
(
reagent
water)
was
analyzed
in
all
nine
laboratories,
and
three
laboratories
analyzed
each
of
the
other
four
matrices.
All
analyses
were
repeated
weekly
over
a
five
week
period.
As
a
result,
a
total
of
6825
observations
were
obtained,
which
includes
2925
observations
for
matrix
A
(
9
labs
*
13
metals
*
5
spike
concentrations
*
5
weeks)
and
975
(
3
labs
*
13
metals
*
5
spike
concentrations
*
5
weeks)
for
each
of
the
Appendix
B
to
the
TSD
5
other
four
matrices
(
6825
=
2925
+
[
975
*
4]).
There
were
two
missing
values
for
chromium
in
matrix
A
from
labs
1
and
9.

Starting
from
a
blank
or
unspiked
sample,
all
target
analytes
were
spiked
at
4
concentrations
to
yield
a
total
of
five
concentrations
per
matrix.
Concentrations
ranged
from
0.01
to
10
ug/
L
for
mercury
and
selenium,
respectively,
on
the
low
end,
and
from
2.0
to
1000
ug/
L
for
mercury
and
selenium,
respectively,
on
the
high
end.
In
addition,
the
concentrations
were
matrix­
dependent.
The
same
concentration
ranges
for
each
metal
by
matrix
combination
were
used
for
all
five
weeks
of
the
study.
A
copy
of
the
original
study
proposal
is
presented
in
Appendix
C.

3.
Statistical
methodology
The
study
data
were
first
analyzed
graphically
and
then
numerically.
Numerical
analyses
consisted
of
model
parameter
estimation
and
evaluation.

3.1
Graphical
Analysis
Techniques
Composite
plots
for
all
combinations
of
analyte
and
analytical
technique
were
produced.
These
sets
include:
(
1)
Measurement
Results
vs
Spike
Concentration
(
Appendix
B.
1),
(
2)
Log10
[
Measurement
Results]
vs
Log10
[
Spike
Concentration]
(
Appendix
B.
2),
(
3)
Observed
Standard
Deviation
vs
Spike
Concentration
(
Appendix
B.
3),
(
4)
Log10
[
Standard
Deviation]
vs
Spike
Concentration
(
Appendix
B.
4),(
5)
Relative
Standard
Deviation
vs
Log10
[
Spike
Concentration]
(
Appendix
B.
5),
and
(
6)
Standardized
Residuals
vs
Log10
[
Spike
Concentration]
(
Appendix
B.
6).
These
graphics
are
contained
on
the
CD­
ROM
in
the
file
Plot_
EPA_
AAMA.
pdf.

The
purpose
of
these
plots
is
to
allow
examination
of
the
relationship
between
two
numerical
variables
and
determine
if
the
data
fall
close
to
a
curve
describing
an
expected
model.

(
1)
The
first
set
of
plots
of
measurement
results
versus
spike
concentrations
can
be
used
to
evaluate
the
mean
recovery
model.
If
the
assumed
linear
model
were
true
then
the
relationship
outlined
by
the
plotted
data
would
be
approximately
linear.

(
2)
A
plot
of
log
measurement
results
versus
log
spike
concentration
will
show
an
approximately
linear
relationship,
similar
to
(
1),
if
the
relationship
between
measurement
results
and
spike
concentrations
is
well
behaved.
Otherwise,
the
log
transformations
used
in
these
plots
will
tend
to
exaggerate
deviations
from
the
linear
model.
In
particular,
a
positive
bias
in
measurement
results
will
show
as
an
almost
flat
line
at
low
concentrations
before
it
starts
to
increase
as
concentration
increases.
A
negative
bias
will
show
as
an
almost
perpendicular
drop
at
the
lower
concentrations.
The
primary
advantage
of
the
log­
log
plot
is
that
it
allows
for
easier
visualization
of
the
relationship
between
individual
measurement
results
spike
concentration
at
the
low
concentrations.
When
the
log­
log
plot
is
combined
with
an
indicator
that
identifies
which
data
came
from
which
calibration,
the
effect
of
changing
calibration
may
be
seen
clearly.

(
3)
The
plot
of
observed
standard
deviations
versus
spike
concentrations
can
be
used
to
evaluate
the
reasonableness
of
the
constant
and/
or
straight
line
models.
If
the
constant
model
for
standard
deviation
were
true
then
the
standard
deviation
would
be
approximately
the
same
regardless
of
concentration.
If
the
straight
line
model
for
standard
deviation
were
true
then
the
plots
are
expected
to
indicate
an
approximately
linear
relationship.
Appendix
B
to
the
TSD
6
(
4)
The
log­
log
plot
is
expected
to
display
an
approximately
linear
relationship
when
a
logarithmic
model
fits
the
data.
If
the
two­
component
model
were
true
then
we
would
generally
expect
to
see
a
relationship
that
looks
something
like
the
shape
of
a
hockey
stick.
That
is,
standard
deviation
would
be
approximately
constant
at
low
concentrations
and
would
increase
in
proportion
to
concentration
at
higher
concentrations.
However,
if
spike
concentrations
were
not
selected
at
sufficiently
low
concentrations,
the
two­
component
model
would
display
the
approximately
linear
relationship
of
a
loglog
model.

(
5)
The
plots
of
relative
standard
deviation
(
RSD)
versus
log
10
of
the
spike
concentration
are
generally
expected
to
show
high
RSD
for
the
lowest
concentrations
and
convergence
to
a
constant
RSD
at
higher
concentrations.
This
theory
may
be
used
to
describe
measurement
variation
in
terms
of
a
single
number.

(
6)
The
plots
of
standardized
residuals
versus
log
10
of
the
spike
concentration
show
how
well
variation
is
estimated
using
the
available
procedures
for
the
two
component
model.
A
residual
shows
how
much
a
measurement
result
has
deviated
from
the
model
of
the
relationship
between
measurement
results
and
spike
concentrations.
Standardized
residuals
are
generally
expected
to
be
within
plus
or
minus
3
standard
deviations
of
zero
and
are
expected
to
average
zero.
Residuals
at
each
spike
concentration
are
standardized
to
the
standard
deviation
estimated
using
the
two­
component
model.
When
residuals
spread
to
less
than
three
standard
deviations,
the
model
is
generally
overestimating
variability.
When
residuals
spread
to
more
than
three
standard
deviations,
the
model
is
generally
underestimating
variability.
The
exception
to
this
rule
is
an
apparent
outlier.
A
secondary
characteristic
of
this
type
of
plot
is
that
it
accentuates
any
deviation
from
the
expected
linear
relationship.

3.2
Model
Estimation
With
some
deviations,
the
two
component
model
(
Rocke
and
Lorenzato,
1995)
was
estimated
using
the
FORTRAN
program
provided
(
publicly
available
at
no
cost)
by
Professor
David
Rocke
(
http://
handel.
cipic.
ucdavis.
edu/~
dmrocke/).
Qualitative
output
and
plots
of
deviations
from
this
model
were
used
to
evaluate
the
fit
of
the
model
to
the
available
data.
The
model
is
expressed
as:

y
e
=
+
+
 
 
µ
 
 
where
the
parameters
are
defined
as:
y
=
observed
instrument
response
e
=
the
natural
exponential
function
=
the
intercept
of
a
linear
function
 
=
the
slope
of
a
linear
function
 
=
independent
errors
with
normal
distribution,
mean
zero,
and
fixed
variance
 
=
independent
errors
with
normal
distribution,
mean
zero,
and
fixed
variance
 
=
true
concentration
in
the
sample
measured
µ
In
this
Appendix
B
to
the
TSD,
two
deviations
from
the
two­
component
model
are
present.
These
deviations
are
that
results
have
been
substituted
for
instrument
responses
and
all
data
used
in
this
Appendix
B
to
the
TSD
have
entrained
dependencies
that
violate
the
assumption
of
independent
errors
within
the
domain
of
interest
(
e.
g.,
within
a
single
laboratory
or
within
a
group
of
laboratories).
For
Appendix
B
to
the
TSD
7
analytes
and
analytical
techniques
for
which
results
are
generated
by
a
linear
response,
substituting
results
for
responses
does
not
fundamentally
change
the
structure
of
the
model.
With
regard
to
independent
errors,
results
for
each
combination
of
analyte
and
measurement
technique
were
obtained
in
descending
order
of
concentration.
Hence,
any
event
that
happens
in
the
measurement
process
during
data
collection
has
effects
that
systematically
continue
throughout
the
remaining
portion
of
data
collection.
The
most
obvious
event
is
calibration,
which
can
be
linked
visually
to
systematic
changes
in
results.
It
is
not
clear
whether
the
AAMA
data
have
the
same
problem.
However,
the
AAMA
data
were
collected
in
sets
spaced
one
week
apart
and
each
set
contained
all
of
the
spike
concentrations
used
for
every
analyte
under
study.
Hence,
any
event
that
affects
any
one
result
at
a
given
spike
concentration
is
likely
to
affect
other
results
at
every
other
spike
concentration.
Again,
the
obvious
event
is
calibration.

Model
estimates
were
restricted
to
cases
for
which
at
least
5
spike
concentrations
were
available.
Because
the
two­
component
model
has
4
parameters,
the
extra
spike
concentration
is
required
to
have
a
real
indication
that
the
model
is
fitting
any
given
dataset.

4.
Results
4.1
Graphical
Evaluations
In
this
section,
we
provide
some
examples
of
diagnostic
plots.
Graphics
referred
to
in
the
text
are
shown
in
Section
4.1.7.
Complete
sets
are
provided
in
graphics
files
on
the
compact
disk
that
contains
the
attachments
to
this
document.

4.1.1
Results
vs.
Concentration
In
general,
the
observed
relationship
between
concentration
and
results
follows
a
straight
line
closely
(
see,
e.
g.,
Figure
4­
1
which
shows
measurement
results
versus
concentrations
for
WAD
Cyanide).
In
other
cases,
these
plots
help
identify
analytes
with
potential
outlier
observations
(
see,
e.
g.,
Figure
4­
2
which
shows
measurement
results
versus
concentration
for
1­
Chlorobutane).
In
still
others,
the
linear
relationship
is
not
well
demonstrated
in
the
EPA
data
(
see,
e.
g.,
Figures
4­
3
and
4­
4).
Although
more
difficult
to
visualize
because
of
fewer
spike
concentrations,
much
of
the
observed
AAMA
data
also
appear
to
follow
a
straight
line
(
see,
e.
g.,
Figure
4­
5
Cadmium
data
from
lab
3).
Because
one
complete
set
of
spike
concentrations
were
measured
each
week,
some
of
the
AAMA
data
show
an
effect
related
to
the
week
the
measurements
were
made.
An
extreme
example
is
shown
in
Figure
4­
6
Copper
from
lab
4.
The
highest
copper
measurement
result
at
each
spike
concentration
was
made
during
week
2
of
the
study.
The
complete
set
of
plots
for
measurement
results
vs.
spike
concentrations
is
provided
in
Sections
B­
1­
1
and
B­
1­
2
of
the
file
Plot_
EPA_
AAMA.
pdf
contained
on
the
compact
disk.

The
number
of
low
concentrations
included
in
the
EPA
data
made
possible
the
examination
of
patterns
of
variation
in
the
low
concentration
range.
The
rationale
for
this
was
the
importance
of
variation
in
the
low
concentration
range
from
theoretical
and
practical
perspectives.
We
specifically
focused
on
the
lowest
six
concentrations
reported
in
EPA
studies.
The
selection
of
six
was
based
on
the
judgment
that
six
was
large
enough
to
determine
a
departure
from
the
linear
model
and
small
enough
to
visually
resolve
the
individual
results
given
the
range
of
the
concentration
levels.
In
general,
the
plots
show
patterns
of
variation
not
related
to
concentration.
This
may
be
considered
evidence
of
the
constant
variation
property
in
the
low
concentration
and
also
may
be
due
to
the
fact
that
the
low
concentration
levels
in
the
EPA
studies
were
designed
to
demonstrate
the
performance
of
methods
below
their
Appendix
B
to
the
TSD
8
established
detection
levels.
Examples
of
these
plots
are
shown
in
Figures
4­
7
and
4­
8,
antimony
and
2,6­
dinitrotoluene.

4.1.2
Log10
[
Measurement
Result]
vs
Log10
[
Spike
Concentration]

For
the
EPA
data,
these
plots
indicate
that
discontinuities
in
the
relationship
between
results
and
spike
concentrations
can
occur
when
calibration
is
known
to
change
(
see,
e.
g.,
Figure
4­
9,
plot
for
1,3­
dichlorobenzene
and
Figure
4­
10,
2­
chlorotoluene).
No
remarkable
relationships
were
noted
among
the
AAMA
data,
though
it
would
be
difficult
to
discern
any
pattern
with
only
five
spike
concentrations.
The
complete
set
of
plots
for
Log10
[
Measurement
Results]
vs
Log10
[
Spike
Concentration]
can
be
found
in
Sections
B­
2­
1
and
B­
2­
2
of
the
file
Plot_
EPA_
AAMA.
pdf
contained
on
the
compact
disk.

4.1.3
Observed
standard
deviation
vs.
spike
concentration
These
plots
generally
indicate
that
measurement
variation
at
low
concentrations
may
be
approximately
constant
(
see,
e.
g.,
Figure
4­
11,
sodium).
However,
it
is
unusual
for
measurement
variation
to
remain
constant
throughout
the
range
of
spike
concentrations
considered
in
the
EPA
and
AAMA
studies.
At
some
point,
there
is
generally
an
indication
that
measurement
variation
increases
with
spike
concentration.
In
certain
cases,
the
plots
provide
some
indication
that
the
relationship
between
variability
and
concentration
may
be
increasing
linearly
(
see,
e.
g.,
Figure
4­
12,
Silver
[
Ag]
107).
On
the
other
hand,
other
graphics
indicate
both
convex
and
concave
curves
((
Figures
4­
13,
2­
chorophenol
and
Figure
4­
14,
1,4­
dicholobenzene).
With
only
five
spike
concentrations,
the
AAMA
data
do
not
appear
to
be
informative
in
these
plots.
The
complete
set
of
plots
is
provided
in
Sections
B­
3­
1
and
B­
3­
2
of
the
file
Plot_
EPA_
AAMA.
pdf.

4.1.4
Log/
log
plot
(
standard
deviation
vs
spike
concentration)

The
log­
log
plots
of
standard
deviation
versus
spike
concentration
display
three
general
patterns.
In
the
first,
measurement
variation
appears
random
within
an
approximately
oval
shaped
regions
that
does
not
suggest
a
relationship
between
log
standard
deviation
and
log
concentration
(
Figure
4­
15
WAD
Cyanide).
In
the
second,
lower
concentrations
exhibit
roughly
constant
variability
within
an
oval
shaped
region
but
higher
concentrations
show
an
increasing
linear
relationship
between
log
standard
deviation
and
log
concentration
(
Figure
4­
16
Ammonia
as
Nitrogen).
In
the
third,
all
concentrations
exhibit
log
standard
deviation
that
increases
linearly
with
the
log
concentration
(
Figure
4­
17
Mercury).
Note
that
the
approximately
linear,
concave,
and
convex
relationships
shown
in
the
figures
cited
in
Section
4.1.3,
above,
all
display
as
approximately
linear
in
the
log/
log
plots
(
Figure
4­
18
Silver
[
Ag]
107,
Figure
4­
19
2­
chorophenol
and
Figure
4­
20
1,4­
dicholobenzene).
This
suggests
that
the
apparent
relationships
shown
in
the
standard
deviation
versus
concentration
plots
were
artifacts
of
a
log/
log
relationship
that
is
approximately
linear.
The
complete
set
of
plots
is
provided
in
Sections
B­
4­
1
and
B­
4­
2.

4.1.5
Relative
Standard
Deviation
versus
Spike
Concentration
Relative
standard
deviation
(
RSD)
generally
appears
to
decrease
as
concentration
increases
throughout
the
range
of
concentrations
observed
in
this
study
although
there
are
some
exceptions
(
e.
g.,
Figure
4­
21
Chlorobenzene
and
Figure
4­
22
Dibromoethane).
The
more
typical
pattern
is
shown
in
Figure
4­
23
1­
Chlorobutane.
RSD
may
approach
asymptotically
some
limiting
value
but
it
does
not
generally
appear
to
become
constant
at
any
point.
Note
that
the
range
on
the
vertical
axis
changes
considerably
between
plots
and
that
the
larger
ranges
will
tend
to
hide
the
variation
that
continues
to
exist
at
higher
concentrations.
For
depicting
method
performance,
it
may
be
appropriate
to
select
the
lowest
Appendix
B
to
the
TSD
9
acceptable
result,
calculate
the
RSD,
and
describe
the
method
as
being
capable
of
meeting
or
doing
better
than
the
selected
standard.
Cases
where
RSD
increase
with
increasing
concentration
may
be
problematic.

4.1.6
Summary
of
the
Graphical
Analyses
The
primary
purpose
of
graphing
the
study
data
was
to
support
the
selection
of
models
for
relating
the
variability
of
results
to
spike
concentrations.
However,
artifacts
of
the
way
data
were
collected
are
also
visible
in
these
analyses.

The
classes
of
models
considered
include:
(
a)
constant
variability
(
not
related
to
spike
concentration),
(
b)
variability
increasing
linearly
with
concentration,
(
c)
log
variability
increasing
linearly
with
log
concentration,
and
(
d)
variability
increasing
proportionally
with
concentration
after
shifting
upward
some
fixed
amount.
The
data
seem
to
indicate
that
model
class
(
d)
is
able
to
describe
the
relationship
between
results
and
concentrations
across
a
wide
variety
of
measurement
techniques
and
analytes.
One
specific
model
in
this
class
is
the
two­
component
model
described
by
Rocke
and
Lorenzato
(
1975),
among
others.
Model
classes
(
a)
and
(
c)
can
be
considered
subsets
of
model
class
(
d)
that
appear
when
concentrations
do
not
cover
the
full
range
of
the
method.

The
effect
of
using
systematic
elements
in
the
sampling
design,
as
opposed
to
using
completely
random
sampling,
is
present
in
all
datasets
considered
here
and
clearly
demonstrated
in
the
Episode
6000
data
and
the
AAMA
data.
In
the
Episode
6000
data,
all
results
for
each
combination
of
analyte
and
measurement
technique
were
measured
in
order
from
the
highest
to
the
lowest.
Where
significant
changes
in
the
measurement
process
occurred,
such
as
instrument
re­
calibration,
visually
observable
effects
in
the
relationship
between
results
and
concentration
became
apparent.
In
the
AAMA
data,
every
spike
concentration
in
the
study
was
measured
once
a
week
for
five
weeks.
Where
significant
changes
in
the
measurement
process
occurred
between
weeks,
visually
observable
effects
in
the
relationship
between
results
and
spike
concentration
became
apparent.
Appendix
B
to
the
TSD
10
0
10
20
30
40
50
0
20
40
60
Classicals,
Method
1677
WAD
CYANIDE,
UG/
L
Measured
Concentration
Spike
Concentration
Figure
4­
1
0
50
100
150
200
0
200
400
600
800
1000
Organics,
Method
524.2
1­
CHLOROBUTANE,
UG/
L
Measured
Concentration
Spike
Concentration
Figure
4­
2
0
200
400
600
800
0
500
1000
1500
Metals,
Method
1620
IRON,
UG/
L
Measured
Concentration
Spike
Concentration
Figure
4­
3
0
2
4
6
8
10
0
5
10
15
20
Organics,
Method
502.2­
ELCD
DICHLORODIFLUOROMETHANE,
UG/
L
Measured
Concentration
Spike
Concentration
Figure
4­
4
0
20
40
60
80
100
0
20
40
60
80
Lab:
3
CADMIUM,
UG/
L
Measured
Concentration
Spike
Concentration
Figure
4­
5
0
50
100
150
200
0
50
100
150
200
250
300
Lab:
4
COPPER,
UG/
L
Measured
Concentration
Spike
Concentration
Figure
4­
6
4.1.7
Graphics
Appendix
B
to
the
TSD
11
0.0
0.05
0.10
0.15
0.20
0.1
0.2
0.3
0.4
Organics,
Method
1625:
T=
0
2,6­
DINITROTOLUENE,
NG/
UL
Measured
Concentration
Spike
Concentration
Figure
4­
8
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Metals,
Method
1620
ANTIMONY,
UG/
L
Measured
Concentration
Spike
Concentration
Figure
4­
7
0.05
0.10
0.50
1.00
5.00
10.00
0.05
0.10
0.50
1.00
5.00
10.00
Organics,
Method
502.2­
PID
2­
CHLOROTOLUENE,
UG/
L
Log­
10
of
Measured
Concentration
Log­
10
of
Spike
Concentration
Figure
4­
10
0.05
0.10
0.50
1.00
5.00
10.00
0.01
0.05
0.10
0.50
1.00
5.00
10.00
Organics,
Method
502.2­
PID
1,3­
DICHLOROBENZENE,
UG/
L
Log­
10
of
Measured
Concentration
Log­
10
of
Spike
Concentration
Figure
4­
9
0
1000
2000
3000
4000
20
30
40
50
60
70
Metals,
Method
1620
SODIUM,
UG/
L
Observed
Standard
Deviation
Spike
Concentration
Figure
4­
11
0
5000
10000
15000
20000
25000
0
50
100
150
200
250
Metals,
Method
ICP/
MS
Ag
107,
ppt
Observed
Standard
Deviation
Spike
Concentration
Figure
4­
12
Appendix
B
to
the
TSD
12
0
20
40
60
80
100
0.0
0.1
0.2
0.3
0.4
0.5
Organics,
Method
1625:
T=
0
2­
CHLOROPHENOL,
NG/
UL
Observed
Standard
Deviation
Spike
Concentration
Figure
4­
13
0
50
100
150
200
0
2
4
6
8
10
Organics,
Method
524.2
1,4­
DICHLOROBENZENE,
UG/
L
Observed
Standard
Deviation
Spike
Concentration
Figure
4­
14
0.001
0.005
0.010
0.050
0.100
0.500
1.000
0.005
0.010
0.050
Classicals,
Method
350.3
AMMONIA
AS
NITROGEN,
MG/
L
Log­
10
of
Observed
Standard
Deviation
Log­
10
of
Spike
Concentration
Figure
4­
16
0.5
1.0
5.0
10.0
50.0
0.06
0.07
0.08
0.09
0.10
0.20
0.30
0.40
Classicals,
Method
1677
WAD
CYANIDE,
UG/
L
Log­
10
of
Observed
Standard
Deviation
Log­
10
of
Spike
Concentration
Figure
4­
15
0.005
0.010
0.050
0.100
0.500
1.000
5.000
10.000
0.005
0.010
0.050
0.100
Metals,
Method
200.8
MERCURY,
UG/
L
Log­
10
of
Observed
Standard
Deviation
Log­
10
of
Spike
Concentration
Figure
4­
17
10
100
1000
10000
0
0.5
1.0
5.0
10.0
50.0
100.0
Metals,
Method
ICP/
MS
Ag
107,
ppt
Log­
10
of
Observed
Standard
Deviation
Log­
10
of
Spike
Concentration
Figure
4­
18
Appendix
B
to
the
TSD
13
0.01
0.10
1.00
10.00
100.00
0.005
0.010
0.050
0.100
0.500
Organics,
Method
1625:
T=
0
2­
CHLOROPHENOL,
NG/
UL
Log­
10
of
Observed
Standard
Deviation
Log­
10
of
Spike
Concentration
Figure
4­
19
0.1
0.5
1.0
5.0
10.0
50.0
100.0
0.005
0.010
0.050
0.100
0.500
1.000
5.000
10.000
Organics,
Method
524.2
1,4­
DICHLOROBENZENE,
UG/
L
Log­
10
of
Observed
Standard
Deviation
Log­
10
of
Spike
Concentration
Figure
4­
20
­
1.0
­
0.5
0.0
0.5
1.0
0
1
2
3
4
5
6
Organics,
Method
502.2­
ELCD
DIBROMOMETHANE,
UG/
L
Relative
Standard
Deviation
Log­
10
of
Spike
Concentration
Figure
4­
22
­
1.0
­
0.5
0.0
0.5
1.0
0
2
4
6
8
Organics,
Method
502.2­
ELCD
CHLOROBENZENE,
UG/
L
Relative
Standard
Deviation
Log­
10
of
Spike
Concentration
Figure
4­
21
­
1
0
1
2
0
100
200
300
Organics,
Method
524.2
1­
CHLOROBUTANE,
UG/
L
Relative
Standard
Deviation
Log­
10
of
Spike
Concentration
Figure
4­
23
1
10
100
­
2
­
1
0
1
2
Lab:
6
ALUMINUM,
UG/
L
Standardized
Residuals
Log­
10
of
Spike
Concentration
Figure
4­
24
Appendix
B
to
the
TSD
14
1
10
100
­
3
­
2
­
1
0
1
2
3
Classicals,
Method
160.2
TOTAL
SUSPENDED
SOLIDS,
MG/
L
Standardized
Residuals
Log­
10
of
Spike
Concentration
Figure
4­
25
0.001
0.01
0.1
1
­
3
­
2
­
1
0
1
2
3
Classicals,
Method
350.3
AMMONIA
AS
NITROGEN,
MG/
L
Standardized
Residuals
Log­
10
of
Spike
Concentration
Figure
4­
27
10
100
1000
10000
0
­
2
0
2
Metals,
Method
ICP/
MS
Ni
60,
ppt
Standardized
Residuals
Log­
10
of
Spike
Concentration
Figure
4­
26
Appendix
B
to
the
TSD
15
4.2
Two­
component
Model
fitting
This
section
considers
the
results
of
fitting
the
two­
component
Rocke­
Lorenzato
Model
to
the
EPA
and
AAMA.
The
basic
approach
was
to
use
maximum
likelihood
estimation
to
estimate
parameters
of
the
Rocke­
Lorenzato
model
using
software
developed
by
Professor
Rocke
which
is
available
at
no
cost
on
his
web
site
http://
www.
cipic.
ucdavis.
edu/~
dmrocke/
software.
html.
The
software
implements
a
numerical
optimization
algorithm
that
solves
for
the
maximum
likelihood
estimates
of
the
parameters
of
the
model.
The
results
for
the
EPA
data
are
summarized
in
Table
4­
1
which
lists
the
number
of
analytes
by
method
and
the
number
of
times
the
software
was
run
and
the
number
of
times
that
the
software
was
not
able
to
obtain
a
solution,
i.
e.,
failures.
Failure
to
obtain
a
solution
is
usually
the
result
of
poor
fit
of
the
data
to
the
data.
That
is,
the
data
are
so
discrepant
with
regard
to
the
assumed
model
that
the
algorithm
fails
to
converge
to
a
solution.
For
the
EPA
data,
47
of
371
cases
(
about
13%)
failed
to
obtain
a
solution.
There
were
no
failures
for
the
AAMA
data.
The
appendices
to
this
document
contained
on
the
companion
CD­
ROM
include
tables
with
results
of
the
maximum
likelihood
estimation
including
parameter
estimates
along
with
recorded
optimization
failures
by
study,
class,
technique,
and
analyte.
Plots
of
residuals,
useful
for
evaluating
model
fit
are
shown
in
Plot_
EPA_
AAMA.
pdf
which
is
also
on
the
CD­
ROM.

Table
4­
1:
Optimization
Failures
for
Two­
Component
Model
Estimates
EPA
Study
Measurement
Method
Number
of
Analytes
Measured
(
Analytes
x
Labs)
Number
of
Failures
Episode
6000
130.2
1
0
Episode
6000
160.2
1
0
Episode
6000
1677
1
0
Episode
6000
350.3
1
0
Episode
6000
365.2
1
0
ICP/
MS
ICP/
MS
11
2
Episode
6000
1620
26
0
Episode
6000
200.8
21
9
Episode
6000
502.2
63
4
Episode
6000
524.2
80
0
Episode
6184
1625
167
32
Total
371
(
13%)
47
The
two­
component
model
can
be
judged
to
fit
the
EPA
and
AAMA
data
since
the
maximum
likelihood
algorithm
was
able
to
obtain
parameter
estimates
for
the
large
majority
of
the
data
sets.
Evaluation
of
model
fit
should
also
include
examination
of
residual
plots.
The
two­
component
model
Appendix
B
to
the
TSD
16
appears
to
fit
the
AAMA
data
well
but
the
fit
is
inconsistent
for
the
EPA
data.
For
the
AAMA
data,
the
maximum
likelihood
algorithm
had
no
difficulty
obtaining
parameter
estimates
for
the
two
component
model
and
plots
generally
indicate
the
expected
random
pattern
of
the
residuals
about
zero
(
e.
g.,
Figure
4­
24
Aluminum,
Lab
6).
For
the
EPA
data,
some
analytes
have
residual
plots
that
indicate
a
reasonable
fit
and
others
have
residuals
that
indicate
questionable
fits.
For
example,
the
results
indicate
that
the
fit
for
Method
160.2
seems
reasonable
(
Figure
4­
25
Total
Suspended
Solids).
For
other
methods
in
the
EPA
studies,
the
model
fit
is
inconsistent
with
some
analytes
showing
reasonable
residuals
and
others
indicating
problems
with
model
fit
(
e.
g.
Figure
4­
26
Nickel
60).
For
many
of
the
analytes
it
was
possible
to
assess
the
effect
of
changes
in
calibration
on
model
fit.
For
a
number
of
analytes,
plots
of
results
vs.
concentration
were
generated
by
calibration
sequence.
For
example,
residuals
shown
in
Figure
4­
27
Ammonia
as
Nitrogen
indicate
the
presence
of
four
different
calibrations.
The
complete
set
of
plots
is
presented
in
Plot_
EPA_
AAMA.
pdf.
Also,
in
addition
to
performing
diagnosis
and
analysis
based
on
the
full
set
of
available
spike
concentrations
for
each
analyte,
model
parameters
were
estimated
based
on
calibration
sequences.
Tables
contained
in
the
appendices
contained
on
the
companion
CD­
ROM
to
this
document
show
the
estimated
parameters
by
calibration
sequence.
Information
was
not
available
to
allow
diagnostics
and
the
plotting
of
organics
by
calibration
sequence.

5.0
On
Designing
Studies
of
Results
versus
Concentration
Based
on
evaluation
of
the
data
generated,
four
improvements
are
suggested
to
the
original
EPA
study
design.

The
first
suggestion
is
directed
towards
instruments
that
report
no
value
or
a
constant
value
below
some
fixed
spike
concentration.
In
these
cases,
perform
a
preliminary
assessment
of
instrument
capabilities
prior
to
selecting
the
lowest
concentrations
for
the
tests.
The
assessment
would
include
a
limited
number
of
measurements
at
low
concentrations
to
determine
the
capability
of
the
instrument
to
generate
low
level
measurements.
Then,
in
conducting
the
study,
restrict
the
selection
of
spike
concentrations
in
the
experiment
to
those
concentrations
high
enough
to
generate
suitable
measurements.

A
second
suggestion
would
be
to
include
replicate
measurements
at
increasing
concentrations
until
the
upper
end
of
the
calibration
range
is
achieved.
Data
at
the
highest
possible
concentrations
would
allow
enhanced
definition
of
the
proportional
error
region.

The
third
suggestion
would
be
to
create
all
study
samples
and
aliquots
from
the
samples
prior
to
measurement
and
to
completely
randomize
the
order
in
which
aliquots
are
measured.
The
possibility
of
carryover
would
exist
but
it
would
be
handled
the
same
way
it
is
handled
by
a
laboratory
using
a
measurement
method
in
production,
i..
e,
by
re­
analysis
of
a
low
concentration
sample
that
follows
analysis
of
a
high
concentration
sample
after
analysis
of
a
blank
to
demonstrate
that
the
analytical
system
is
essentially
free
from
carryover.
This
could
increase
the
analytical
cost
by
an
order
of
magnitude.

The
fourth
suggestion
would
be
to
use
multiple
laboratories.
This
assumes
that
inter­
lab
objectives
are
consistent
with
study
goals.
Of
course,
depending
on
how
many
and
which
measurement
methods
are
selected
for
study,
the
cost
of
such
a
study
using
multiple
laboratories
could
easily
run
into
several
million
dollars.
Appendix
B
to
the
TSD
17
6.0
Conclusions
The
study
data
suggest
that
measurement
variation
for
most
measurement
techniques
used
under
the
Clean
Water
Act
can
be
described
by
two
models.
Those
models
are
the
two­
component
model
and
the
constant
model.
Though
the
pure
lognormal
model
could
be
used
to
fit
data
that
do
not
show
a
constant
component,
this
model
implies
the
unacceptable
condition
that
measurement
variation
may
become
zero
at
some
low
concentration.
Graphics
of
the
variability
associated
with
EPA's
data
combined
with
both
the
graphics
and
the
two­
component
estimates
from
the
AAMA
data
makes
the
suggestion
of
these
two
models
fairly
strong
for
metals
data.
Although
the
two­
component
model
has
an
appealing
physical
basis
(
see
Rocke
and
Lorenzato
[
1995]),
the
available
data
do
not
provide
strong
support
for
or
organic
analytes..
Graphics
of
variability
versus
concentration
in
many
cases
suggest
the
two­
component
model
but
the
actual
fit
of
this
model
using
the
maximum
likelihood
algorithm
sometimes
fails.
We
assume
that
the
cases
where
the
two­
component
model
does
not
work
well
for
the
organics
data
in
this
study
are
due
to
the
lack
of
a
response
at
low
concentrations
or
because
of
problems
in
the
design
and
implementation
of
the
procedures
used
to
generate
the
data.

Unfortunately,
problems
associated
with
the
design
of
the
studies
considered
in
this
assessment
make
it
unclear
whether
the
estimation
procedures
associated
with
the
two­
component
model
can
be
relied
on
to
routinely
produce
estimates
under
the
necessary
conditions.
More
than
10%
of
the
analyte/
measurement
technique
combinations
considered
here
have
failed
to
produce
maximum
likelihood
estimates
for
the
two­
component
model.
More
of
these
combinations
appear
to
fail
the
graphical
examination
of
the
fit.
For
our
purposes,
the
true
test
of
the
model
is
how
well
it
can
be
used
in
practice
to
produce
detection
or
quantitation
estimates.
If
a
simpler
model
produces
estimates
on
a
more
reliable
basis,
trade
offs
in
terms
of
precision
and
bias
would
have
to
be
considered.
Appendix
B
to
the
TSD
18
References
(
1)
EPA
(
1995),
Appendix
B
to
Part
136
­
Definition
and
procedure
for
the
Determination
of
the
Method
Detection
Limit
­
Revision
1.11,
40
Combined
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Register,
U.
S.
Goverment
Printing
Office,
Washington.

(
2)
Glaser,
J.
A.,
Foerst,
D.
L.,
McKee,
G.
D.,
Quane,
S.
A.,
and
Budde,
W.
L.
(
1981),
Trace
Analyses
for
Wastewaters.
Environmental
Science
and
Technology,
15,
pp.
1426­
1435.

(
3)
Rocke,
D.
M.,
and
Lorenzato,
S.
(
1995),
A
Two­
Component
Model
for
Measuremnt
Eroor
in
Analytical
Chemistry,
Technometrics,
69,
pp.
3069­
3075.

(
4)
Gibbons,
R.
L,
Coleman,
D.
E.
and
Maddalone,
R.
F.
(
1997),
An
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for
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and
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pp.
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2077.
Appendix
B
to
the
TSD
19
Appendix
B
Appendices
and
Tables
on
CD­
ROM
Graphics
(
Sorted
by
Study,
Class,
Measurement
Technique)
in
Plot_
EPA_
AAMA.
pdf
B.
1.
Measurement
vs.
Spike
Concentration
B.
1.1
EPA
B.
1.2
AAMA
B.
2
Log
Measurement
vs.
Log
Spike
Concentration
B.
2.1
EPA
B.
2.2
AAMA
B.
3
Observed
Standard
Deviation
vs.
Spike
Concentration
B.
3.1
EPA
B.
3.2
AAMA
B.
4
Log
Standard
Deviation
vs.
Spike
Concentration
B.
4.1
EPA
B.
4.2
AAMA
B.
5
Relative
Standard
Deviation
(
RSD)
vs.
Log
Spike
Concentration
B.
5.1
EPA
B.
5.2
AAMA
B.
6
Standardized
Residuals
vs.
Log
Spike
Concentration
B.
6.1
EPA
B.
6.2
AAMA
B.
6.3
EPA
(
by
Calibration)

Tables
(
Sorted
by
Study,
Class,
Measurement
Technique)
in
wpd
files
Table
1_
AAMA.
wpd
Table
1_
EPA.
wpd
Table
2_
EPA.
wpd
