Document ID: EPA-HQ-OAR-2003-0072-0042
Agency: epa
Document Type: Supporting & Related Material
Title: 
Posted Date: 2002-09-20T04:00Z

IL
t
I,
AN
ASME
REPORT
CRTD
Vol.
60
REFERENCE
METHOD
ACCURACY
AND
PRECISION
(
ReMAP):
PHASE
1
Precision
of
Manual
Stack
Emission
Measurements
Prepared
by:

W.
Steven
Lanier
GE
Energy
and
Environmental
Research
Corporation
Charles
D.
Hendrix
Statistical
Consultant
under
the
auspices
of:
American
Society
of
Mechanical
Engineers
Research
Committee
on
Industrial
and
Municipal
Waste
February
200
1
Disclaimer
(
hereinafter
referred
to
f,
make
any
warranty,

owned
rights.

Reference
herein
to
any
preparation
or
review
of
this
report,
or
any
agency
thereof.

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from
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by­
laws
of
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or
opinions
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other
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01923.
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Telephone:
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(
7.1.3).

or
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r
'
1
,

6"
I
I.­%
Section
1
.
o
2.0
3.0
4.0
5.0
6.0
7.0
TABLE
OF
CONTENTS
Page
Executive
Summary
................................................................................................................
S­
I
Introduction
........................................................................................................................
1
Background
.......................................................................................................................
.3
.
.
The
Analysis
Procedure
­
A
Layman's
Descnphon
..............................................................
1
1
Measures
of
Precision
................................................................................................
1
1
Estimating
Standard
Deviation
..................................................................................
13
The
Relationship
Between
S
and
C
.....
1
.....................................................................
17
Summary
of
ReMAP
Analysis
Procedure
.................................................................
21
3.1
3.2
3.3
3.4
Confidence
Intervals
..................................................................................................
18
3.5
EPA
Particulate
Matter
Methods
­
Method
5
and
5i
.............................................................
25
4.1
Method
5
Data
and
Precision
Analysis
......................................................................
28
4.2
Method
5i
Data
..........................................................................................................
50
4.3
Discussion
of
Particulate
Matter
Measurement
Results
............................................
61
EPA
Method
23
for
Measuring
Dioxin
and
Furan
Emissions
...............................................
67
5.1
5.2
Available
Multi­
Train
Data
for
Method
23
as
Total
PCDDPCDF
...........................
69
Analysis
of
Method
23
Data
for
Total
Dioxin
and
Furan
..........................................
70
5.3
Available
Multi­
Train
Data
for
Method
23
as
ITEQ
.................................................
8
1
EPA
Method
26
for
Hydrochloric
Acid
.................................................................................
9
1
EPA
Methods
29,
10
1
a
and
10
1
b
for
Mercury
......................................................................
103
TABLE
OF
CONTENTS
(
Cont.)

8.0
EPA
Method
29
for
Multi­
Metals
..........................................................................................
1
19
8.1
EPA
Method
29
Data
for
Antimony,
Arsenic,
Beryllium,
Cadmium,
,
I
Chromium,
and
Lead
.......*.........,..............................................­................................
l
19
8.1.1
Antimony
Data
..............................................................................................
.119
~

I
r
L
8.1.2
Arsenic
Data
...................................................................................................
126
8.1.3
Beryliium
Data
...............................................................................................
126
8.1.4
Cadmium
Data
...............................................................................................
126
??

8.1.5
Chxnium
Data
..............................................................................................
122
8.1.6
Lead
Data
...............................
...................................................................
I22
EPA
Method
29
Regression
Analyses
.......................................................................
138
??

8.2
9.0
Other
Measurement
Methods
.................................................................................................
167
10.0
Conclusions
........................................................................................................................
169
BNDi
References
........................................................
.........................................................
*.
I72
Appendix
­
Statistical
Analysis
Procedures
for
the
ReMap
Program
c
_*

...
111
TABLE
OF
CONTENTS
(
Cont.)

Figure
'
Page
1
2
3
4
5
6
7
8
9
10
11
I2
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
Illustration
­
The
Difference
Between
Precision
and
Accuracy
............................................
7
Normal
Distribution
of
Field
Results
....................................................................................
.12
Simulated
Data
.......................................................................................................................
16
Regression
Line
and
Confidence
Interval
for
Simulated
Data
..............................................
19
Schematic
of
Method
5
Sampling
Train
................................................................................
26
EPA
Method
5
Data
­
Standard
Deviation
(
Fig.
6A)
............................................................
37
EPA
Method
5
Data
­
Relative
Standard
Deviation
(
Fig.
63)
.............................................
..
3
8
thod
5
.......................................
42
d
5
(
Front
Half
Only)
...........
48
..............................................
5
1
.............................................
­
56
eviation
(
Fig.
11B)
............................................
57
..............................................
60
..............................................
62
..............................................
68
viation
.........................................
.72
Deviation
..........................
..
7
....................................................
.76
nts
Using
EPA
Method
23
............
78
ion
................................................
83
....................
92
Method
26
.....................................
10
1
........................................................
104
iv
TABLE
OF
CONTENTS
(
Cont.)

Fimre
Page
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
Schematic
of
Method
29
Sampling
Train
..............................................................................
105
Schematic
of
Method
l
0
l
b
Sampling
Train
..........................................................................
106
EPA
Method
29/
10
1
all
0
1
b
Data
­
Total
Mercury
Standard
Deviation
.................
......
......
...
1
1
1
EPA
Method
29/
10
1
a
/
l
O
1
b
Data
­
Total
Mercury
Relative
Standard
Deviation
..........
........
1
12
Regression
Line
and
95%
Confidence
Interval
­

EPA
Method
29
Data
for
Antirn
ata
for
Antimon
ata
for
Arsenic
­

.....................................
140
......,............
143
Regression
Line
and
95%
C
Regression
Line
and
95%
EPA
Method
29
Precision
EPA
Method
29
Precision
d
29
­
Chromium
................
146
d
29
­
Lead
..........................
147
Precision
Estimates
for
Mea
Precision
Estimates
for
Mea
EPA
Method
29
Precision
Metrics
­
Composite
Data
.........
....
.
................._......
.....................
165
V
­
Table
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
TABLE
OF
CONTENTS
(
Cont.)

Paae
EPA
Method
5
Data
­
Hamil
and
Camann,
1974
and
1974b
................................................
29
EPA
Method
5
Data
­
Dade
County
MWC,
Hamil
and
Thomas,
1976
................................
3
1
EPA
Method
5
Data
­
Pittsfield
MWC,
E
g
o
and
Chandler,
1997
.......................................
32
SPC
Factors
for
Identification
of
Data
Outliers
.....................................................................
33
Consolidated
Method
5
Data
Set
...........................................................................................
34
Factors
for
Calculating
Unbiased
Estimates
of
sigma
ts
Based
on
S
.....................................
35
Method
5
­
Small
Sample
Bias
Correction
to
Standard
Deviation
.......................................
36
Method
5
Regression
Analysis
Results
..................................................................................
40
EPA
Method
5i
Data
and
Standard
Deviation
­
Eli
Lilly
Data,
(
Table
9A)
..........................
53
andard
Deviation
­
EPA
DuPont
Data,
(
Table
9B)
..................
55
Regression
Analysis
for
Method
5i
Data
..............................................................
58
Data
as
Total
Mass
of
Tetra
through
Octa
Dioxin
pIus
Furan
.............................
71
ate
of
Method
23
Standard
Deviation
...................................................................
79
Data
as
ITEQ
.......................................................................................................
82
Data
and
Standard
Deviation
for
HC1
...............................................
93
uture
HC1
Data
..................................................................................
102
a
for
Mercury
(
Table
16A)
.............................................................
109
a
for
Mercury
(
Table
16B)
.............................................................
1
10
cipated
Future
Mercury
Data
...........................................................................
1
18
ata
and
Standard
Deviation
for
Antimony
.....................................
120
ata
and
Standard
Deviation
for
Arsenic
.........................................
121
ata
and
Standard
Deviation
for
Beryllium
.....................................
122
ata
and
Standard
Deviation
for
Cadmium
......................................
123
ain
Data
and
Standard
Deviation
for
Chromium
....................................
124
ain
Data
m
d
Standard
Deviation
for
Lead
..............................................
125
gression
Analysis
for
Various
Metals
............................................
13
8
­
I
f
Measured
PCDDRCDF
Concentration
Based
on
Range
of
Anticipated
Future
Metals
Data
­
Antimony,
Arsenic,
Beryllium,
Chromium,
or
Lead
............................................................................................................
166
Vi
This
page
IntentionaIly
left
blank.
Reference
Method
Accuracy
and
Precision
(
ReMAP
Phase
I)
An
Assessment
of
the
Precision
of
EPA
Manual
Stack
Emission
Measurements
Executive
Summary
This
report
documents
results
from
the
first
phase
of
a
study
co­
sponsored
by
the
American
Society
of
Mechanical
Engineers
(
ASME)
to
assess
the
accuracy
and
precision
of
manual
test
methods
adopted
by
the
US
Environmental
Protection
Agency
(
EPA)
for
determining
the
stack
concentration
of
selected
air
pollutants.
The
program
is
entitled
Reference
Method
Accuracy
and
Precision
and
is
referred
to
by
the
acronym
ReMAP.
The
Phase
1
effort
addresses
the
precision
of
the
selected
measurement
methods.
The
formal
Purpose
Statement
for
the
program
is:

"
To
determine
the
precision
of
pollutant
emission
measurements
based
on
analysis
of
available
simultaneous
­
sample
test
data
which
were
generated
using
EPA
Manual
Reference
Test
Methods
5
and
5i
(
Particulate
Matter),
23
(
Dioxin
and
Furan),
26
(
HCI),
29
(
multi­
metals),
1Ola
and
lOlb
(
mercury)
and
108
(
arsenic)
at
a
number
of
stationaty
air
sources."

As
used
in
the
Re
rogram,
precision
is
defined
as
random
error
that
inadvertently
enters
the
measurement
process.
This
error
may
enter
at
any
stage
of
the
measurement
le
recovery,
or
sample
analysis.
The
impact
of
deviate
from
the
true
stack
concentration.
any
manual
test
of
the
selected
ibution.
This
distribution
is
xpected
indicating
measured
Because
these
e
Precision
of
a
curve.
One
c
o
r
n
dicated
by
the
horizontal
spread
of
the
bell
&
e
bell
curve
shape
is
to
determine
the
(
c)
of
the
distribution.
Alternately,
the
bell
distributian
also
peated
application
of
the
the
best
estimate
of
the
ators
of
data
quality
that
two
additional,
directly
measurement
99
out
of
100
future
single
measurements.
If
the
is
repeatedly
applied
to
a
stack
with
a
given
concentration,
this
nes
the
upper
and
lower
concentration
bounds
for
99%
of
measurement
ES­
1
2.
The
anticipated
range
for
99
out
of
100
future
triplicate
measurements.
Since
most
environmental
regulations
define
the
re
able
stack
concentration
as
the
average
of
three
repeated
test
runs,
this
metric
defines
the
anticipated
range
of
results
in
triplicate
(
3
single
time
series)
measurements
due
to
random
error
in
the
measurement
process.

For
each
of
these
precision
metrics
it
is
important
to
note
the
inherent
assumption
that
faciiity
operation.

100
single
measurements
will
fall
withi
anticipated
range
for
the
average
of
repea
to
the
true
concentration.
More
precisely,

standard
deviation
of
concentration.

lities
must
be
assumed
to
of
method
precision
mu
trains
are
used
to
sim
deviation
of
the
particula­
measurement
at
the
specific
stack
concentration.

ES­
2
97
E
l
LJ
The
ReMAP
program
procedures
required
to
performed
a
careful
assessment
estimate
the
precision
of
Manual
of
the
statistical
analysis
Reference
Methods
using
multi­
train
sampling
data
(
see
Appendix).
To
assure
the
quaiity
of
data
used
in
the
statistical
anaiysis,
an
extensive
effort
was
expended
in
gathering
data
from
the
original
sources
and
carefilly
evaluating
them
to
assure
that
consistent
data
reduction
procedures
were
used.

Conceptually,
the
ReMAP
statistical
analysis
procedure
is
straightforward.
First,
data
fiom
a
multi­
train
test
run
are
averaged
to
provide
an
estimate
of
the
average
C
run
(
Ci).
The
standard
deviation
for
the
test
run
(
Si)
is
also
C
a
calculated
standard
deviation
fiom
a
single
test
using
a
dual
sampling
probe
provides
a
relatively
poor
estimate
of
the
true
standard
deviation
of
the
method
(
0)
at
the
true
concentration
(
p)­
However,
after
accounting
for
various
biases,
a
significant
array
of
data
from
multi­
train
tests
should
provide
a
reasonable
basis
for
estimating
the
true
standard
deviation
as
a
function
of
concentration.
The
ReMAP
procedure
is
to
ass
at
the
standard
deviation
varies
with
concentration
according
to
a
power
functio
nship
and
then
to
fit
the
data
to
that
equation
using
regression
analysis.

regression
analysis
represent
the
best
estimate
av
able
on
the
standard
measurement
method
at
any
given
concentration
ReMAP
analysis
procedure
also
provides
for
calculation
of
confidenc
s
define
the
upper
and
lowe
lyses
are
summariz
i
for
Particulate
Matter
­
Front
Half
Only
frdm
the
true
ave
h
tacks
with
particulate
concentrations
ual­
train
sampling
and
ep
the
simultaneous
measurements.
eliminate
test
results
reening,
coupled
with
the
ReMAP
anaiysis
ant
variation
of
standard
deviation
with
concentration.

ES­
3
Based
on
a
pooled
analysis,
the
characteristic
standard
deviation
for
Method
5i
was
found
to
be
1.43
mgdscm.
Based
on
this
best
estimate
of
standard
deviation,
the
ReMAP
analysis
indicates
that
99
out
of
100
Method
5i
single
measurements
should
deviate
from
the
true
concentration
by
no
more
than
f
2.68
mg/
dscm.
For
triplicate
measurements
99
out
of
100
Method
ata
results
should
deviate
from
the
true
concentration
by
no
more
than
f
2.12
rng
rs
ranging
from
zero
a
were
reported
in
both
forms.
Even
nts,
the
ReMAP
results
suggest
that
though
the
same
data
were
used
for
both
Table
ES­
I
.
Anticipated
Range
o
analysis
found
no
statistically
significant
variation
of
standard
deviation
with
ES­
4
r
I;

P
L1
r:
Li
concentration.
Pooled
analysis
indicates
that
the
best
estimate
of
standard
deviation
is
27
ng
ITEQ/
dscm.
when
the
emission
concentration
is
in
the
range
of
0.02
to
0.9
ng
ITEQ/
dscm.
This
further
indicates
that
99
out
of
100
future
single
measurements
shoufd
fall
with
50.069
ng
ITEQ/
dscm
of
the
m
e
concentration
and
99
out
of
100
triplicate
measurements
should
fall
within
50.04
ng
ITEQ/
dscm
of
the
true
concentration.

99
out
of
100
Single
Concentration
I
Measurements
Truestack
HCl
The
absolute
value
of
anticipated
range
for
future
Method
25
measurements
(
as
ITEQ)
are
quite
small
in
absolute
t
ut
they
are
on
the
same
order
as
regulatory
emission
limits
being
considered
in
regions.
As
indicated
above,
the
best
estimate
of
standard
deviation
is
0.027
ng
ITEQIdscm.
However,
at
95%
confidence,
the
standard
deviation
may
be
as
large
as
0.037
ng
ITEQ/
dscm
and
the
potential
range
for
99
out
of
100
future
measurements
might
deviate
from
the
true
concentration
by
as
much
as
Q/
dscm.
ReIying
upon
a
single
measurement
has
the
potential
to
create
mission
limits
were
set
at
0.095
ng
ITEQ/
dscm,
to
be
assured
confidence
level,
measurement
resuits
could
not
exceed
zero.
results
must
be
above
0.19
ng
ITEQ/
dscm
e
true
stack
concentration
exceeded
the
emissio
95%
confidence
Most
regulations
and
permit
limits
establish
compliance
based
on
averaging
results
from
triplicate
measurem
icipated
range
for
99
out
of
100
fkture
triplicate
to
single
measurements,
by
43.
Thus,
compliance
EQ/
dscm
is
assured
(
at
the
95%
codidence
level)
or
below
0.04
ng
ITEQ/
dscm.
Similarly,
at
95%
95
ng
ITEQ/
dscm
limit
is
assured
when
the
three
run
confidence,
exceeden
99
out
of
100
Triplicate
Measurements
I
Method
26
for
Hydrochloric
Acid
ReMAP
analysis
of
available
data
for
Method
26
for
HCI
indicated
that
RSD
is
typically
in
the
range
of
5%
to
10%.
RSD
does
increase
when
the
method
is
applied
to
stacks
with
very
low
concentration.
Table
ES­
2
summarized
the
anticipated
upper
and
lower
bounds
for
99
out
of
100
Method
26
measurements
as
a
hction
of
true
stack
HCI
concentration.

TabIe
ES­
2.
Anticipated
Range
of
HC1
Measurement
Results
Due
to
Random
Error
in
Application
of
Method
26.

I
20
16.1
23.9
17.7
22.3
50
41.9
58.1
45.3
54.7
100
85.8
1
14.2
91.8
108.2
I
I
I
I
I
J
ES­
5
Methods
29,
lOla
and
lOlb
for
TotaI
Mercury
Several
measurement
methods
have
been
de
concentration
and
for
mercury
speciation,
multi­
train
mercury
data
collected
using
Me
data
for
total
mercury
concentration.
concentration
range
of
50
to
78
9.6
to
12.4%.
As
concentration
from
12.4%
to
for
99
out
of
10
ped
for
measurement
of
rota1
emission
lysis
took
ail
availabIe
The
data
analysis
i
Results
Due
to
Random
Method
29
for
Multi­
Metals
Method
29
is
also
used
for
measurement
of
several
other
metal
emissions.
Precision
analysis
was
completed
for
six
other
metals
including
antimony,
arsenic,
beryllium,
cadmium,
chromium,
and
lead.
With
exception
of
cadmium,
the
analysis
indicates
that
these
metals
behave
similarly
wi
to
measurement
method
precisio
composite
andysis
was
performed
for
the
g
metals
and
the
results
indicate
that
use
of
Method
29
provides
an
RSD
that
tween
13
and
18%
when
the
individual
metal
concentrations
are
b
pg/
dscm.
Table
ES­
4
summarizes
the
anticipated
upper
and
1
9
out
of
100
Sb,
As,
Be,
Cr,
and
Pb
measurements
using
Method
e
stack
total
metal
concentration.

As
regards
cadmium
measurements
using
M
9,
the
analysis
indicates
that
standard
deviation
is
a
weaker
fiction
of
conce
at
least
at
higher
concentration
ranges.
The
best
estimate
of
R
oncentration
is
80
pg/
dscm
and
18.7
%
when
the
concentr
However,
at
5
pg/
dscm,
predicted
RSD
is
38.
to
exceed
75%.

ES­
6
h­
a
L
100
65.7
134.3
"
PLY
­
,
­
4
80.2
119.8
I
c
,
I
L
u
r
1
ES­
7
This
page
Intentionally
left
blank.
REFERENCE
METHOD
ACCUR4Cl
PHASE
I
ZIYD
PRECISION
(
R
e
m
)

PRECISION
OF
MANUAL
STACK
EMISSION
MEASUREMENTS
1.0
Introduction
An
integral
part
of
efforts
to
regulate
and
control
air
pollution
emissions
is
collection
and
analysis
of
exhaust
stream
samples
to
determine
the
concentration
and
flow
rate
of
pollutants
released
to
the
atmosphere.
The
U.
S.
Environmental
Protection
Agency
(
EPA)
and
its
counterparts
in
other
countries
have
developed
formal
methods
defining
the
hardware
and
procedures
for
collecting
and
analyzing
samples
to
quanti
emissions
of
individual
pollutants.
A
significant
number
of
these
methods
involve
manual
extraction
of
a
sample
from
a
facility's
exhaust
stack,
sample
recovery
and
subsequent
laboratory
analysis
to
quantify
concentration
of
a
specific
pollutant(
s)
in
the
sample.
All
manual
processes,
inc
ing
the
various
EPA
measurement
methods,
are
subject
to
random
variations,
which
ultimately
impact
the
end
results.
Relatively
minor
variations
in
the
skill
of
the
sampler,
as
well
as
the
equipment
and
procedures
used
to
extract
the
sample
can
influence
the
indicated
quantity
of
sample
extracted
from
the
stack
and
the
eficiency
with
which
the
pollutant
of
interest
is
colIected
or
recovered.
Similarly,
minor
variation
in
laboratory
hardware
and
procedures
influence
quantification
of
the
mass
or
volume
of
pollutant
in
that
sample.
The
net
result
of
such
random
variation
is
imprecision
in
measurement
results.
The
current
report
documents
a
study
where
available
data
have
been
gathered
and
analyzed
to
quantify
the
precision
of
key
EPA
manual
measurement
methods.
The
study
has
been
conducted
under
the
auspices
of
the
American
Society
of
Mechanical
Engineers
(
ASME)
and
is
entitled
Reference
Method
Accuracy
and
Precision1
(
ReMAP),
Phase
1.
S
The
purpose
of
the
R
e
m
­
Phase
1
program
is
"
to
determine
the
precision
of
pollutant
emission
measurements
based
on
anaiysis
of
available
simultaneous­
sample2
test
data
which
were
generated
1
Precision
is
defined
here
as
"
Random
Error"
according
to
the
new
ASME
PTC
19.1­
1998.
2
Dual­
train,
quad­
train,
and
simultaneous­
samples
from
different
sample
locations
at
a
stationary
emission
source.

1
using
EPA
Manual
Reference
Test
Merhods
5
and
j
i
(
PM).
23
(
dioxin
andfiran),
26
(
HCI).
29
(
multi­
metals,
lOla
and
IOIb
(
mercury),
and
108
(
arsenic)
at
a
number
of
srationary
air
sources."

ASME
intends
ReMAP
to
be
a
multi­
phase
effort
with
the
first
phase
focusing
exclusively
on
assessment
of
measurement
method
precision.
Consideration
o
sues
associated
with
measurement
accuracy
is
reserved
for
a
later
phase
of
ReMAP.

Three
major
groups
have
sponsored
the
ReMAP­
Phase
1
effort.
First,
the
U.
S.
EPA
has
provided
funding
and
personnel
support
to
the
project.
Second,
several
industrial
groups
representing
manufacturing
companies
and
the
waste
combustion
industry
have
provided
program
funding.

Finally,
the
ASME's
Committee
on
Industrial
and
Municipal
Waste
has
provided
both
financial
support
and
overall
program
direction.

Although
Phase
I
results
indicate
that
th
Methods
provide
differing
levels
of
precision
and
that
the
precision
typically
varies
utant
concentratio
MAP
does
not
reach
conclusions
relative
to
p
be
used.
Answering
those
questions
is
appro
the
public.
The
role
o
rifically
sound
d
facilitate
meaningful
policy
debate
and
decisi
lated
industries,
an
It
is
important
to
note
from
the
outset
that
a
variety
of
stack
emission
concentrations.
In
addition
to
measure
skill
of
the
stack
tester),
variation
of
process
feed
mat
operations
impact
stack
emission
A
compliance
test
impacted
by
process
variation
over
time
and
will
potentially
indicate
greater
variability
method
itself.
ntribute
to
variability
in
measured
thod
precision
(
which
includes
the
luding
combustion
fuels)
and
unit
ngle
samples
will
be
ssion
concentrations
the
precision
of
fhe
measurement
2
2.0
Background
The
US
EPA
has
developed
and
published
a
wide
variety
of
methods
for
determining
the
concentration
of
pollutants
in
process
effluent
streams.
The
manual
air
sampling
methods
typically
invoIve
a
probe
for
extracting
a
representative
sample
of
stack
effluent
and
means
for
physically
capturing
or
chemically
extracting
selected
pollutants
from
that
sample.
The
methods
further
define
procedures
for
determining
the
volume
of
sample
gas
extracted
and
for
recovering
the
coIIected
pollutant(
s)
from
the
sampling
apparatus.
Finally,
the
methods
specify
laboratory
procedures
to
use
for
determining
the
quantity
of
pollutant
collected.

In
developing
new
measurement
procedures,
 PA
has
traditionally
conducted
extensive
laboratory
and
field
validation
studies
including
tests
to
define
the
precision
and
biases
of
the
method.

Procedures
empioyed
by
EPA
have
evohecl
over
the
years
but
generally
conform
to
those
described
in
a
1977
paper
entitled,
"
How
 PA
Validates
NSPS
Methodology"
(
Midgett,
1977).
Mos
procedures
discussed
by
Midgett
have
been
incorporated
into
EPA
Method
301
which
"
is
used
whenever
a
source
owner
or
operator
proposes
a
test
method
to
meet
a
U.
S.
Environmental
Protection
Agency
(
EPA)
requirement
in
the
absence
of
a
validated
method."(
EPA,
1992)
In
validation
of
a
new
method
or
in
tests
to
evaluate
an
alternate
method,
EPA
suggests
use
of
four
sampIing
trains
to
simultaneously
extract
samples
from
nominally
the
same
location
in
a
source
stack.
This
is
commonly
referred
to
as
a
quad­
train.
For
method
validation,
two
of
the
four
trains
are
configured
and
operated
in
strict
accordance
with
the
proposed
method,
while
the
other
two
trains
are
spiked
with
known
quantities
of
the
target
analyte.
Comparison
of
data
from
the
two
unspiked
trains
provides
an
indication
of
measurement
precision
while
data
from
the
spiked
trains
provides
an
indication
of
measurement
bias.
Data
from
a
significant
number
of
repeated
multi­
train
runs
provide
an
indication
of
the
precision
and
bias
of
the
method
itself.
Method
301
states
that
"
The
precision
of
the
method
at
the
level
of
the
standard
shall
not
be
greater
than
50
percent
relative
standard
deviation."

Several
of
the
EPA
measurement
methods
were
developed
and
validated
in
the
early
days
of
the
Agency.
 PA
Method
5
for
measuring
stack
particulate
concentration
was
published
in
the
FederaI
Register
on
December
23,
1971
(
36FR
25876).
Tests
to
validate
that
method
were
performed
on
3
sources
with
particulate
emissions
ranging
from
45
to
240
mddscm.
In
that
time
period,
the
majority
of
Federal
particulate
emission
standa
were
established
at
180
mg/
dscm
(
0.08
gr/
dscf)

corrected
to
7%
02.
Thus,
the
me
ver
a
range
that
included
the
prevailing
regulatory
limits.
At
this
emission
limit,
the
EPA
validation
studies
indicate
that
precision
of
Method
5
,
expressed,
as
a
relative
standard
deviation
was
on
the
order
of
10%.

Passage
of
the
Clean
Air
Act
Amendments
of
1990
ushered
in
new
era
in
both
scope
and
stringency
of
environmental
regulations.
Rules
erning
release
of
Hazardous
Air
PolIutants
(
HAPS)
called
for
regulation
of
I79
specific
pollutants
from
both
new
and
existing
emission
sources.

Provisions
in
the
law,
stipulate
that
standards
must
consider
the
"
Maximum
Achievable
Control
Technology"
(
MACT).
For
existing
sources,
MACT
standards
shall
not
be
less
stringent
than
the
average
emission
performance
achieved
by
the
subcategory.
Implementation
of
this
congressional
mandate
has
resulted
in
many
new
emission
regulations
that
are
dramatically
more
stringent.
F
mple,
in
1999
the
particulate
emission
limit
for
hazardous
waste
incinerators
was
tig
t
performing
12%
of
the
sources
in
a
catego
ed
from
180
to
34
mg/
dscm
(@
7%
02).

Stringent
emission
standards
raise
numerous
concerns
a
methods.
The
particulate
standards
can
be
used
to
highli
method
validation
studies
assessed
acceptably
precise
over
a
rather
broad
applied
and
results
used
for
regulatory
for
which
it
was
validated.
Method
5
mav
be
ac
mgldscm)
but,
prior
to
ReMAP
Phas
meant
all
environmental
stakeholders
EPA
measurement
s.
As
noted,
initial
the
Method
to
be
for
Method
30
1.

Particulate
matter
is
not
the
only
EPA
Reference
measurement
Method
for
which
there
is
concern.

Another
example
is
 PA
Method
23
for
determining
diox
d
furan
emission
concentration.
The
published
method
validation
studies
concentrated
almo
clusively
on
pre
on
and
bias
of
4
1
analytical
procedures
and
largely
ignored
the
sample
collection
portion
of
the
overall
method.
No
Agency
method
validation
data
were
provided
examining
the
precision
of
the
entire
sampling
and
analysis
procedure.
Method
23
does
provide
for
extensive
spiking
of
the
sampling
train
with
labeled
compounds
and
includes
tests
to
quantify
recovery
of
those
standards.
However,
data
are
considered
acceptable
if
the
fractional
recovery
of
the
labeled
compounds
falls
within
the
range
of
40%
to
130%.
With
such
broad
allowable
recoveries
and
in
the
absence
of
full
system
precision
analysis,
it
is
anticipated
that
Method
23
may
provide
results
with
exceedingly
wide
precision
bands.

The
above
noted
issues
do
not
imply
that
Methods
5
and
23
are
technically
unacceptable
procedures,

Instead,
these
issues
are
typical
of
senera1
concerns
that
develop
when
method
validations
are
incomplete
or
out
of
date.
In
the
absence
of
well­
documented
assessments
of
measurement
method
precision,
many
reasonable
questions
are
formed
and
nurtured.
Typical
questions
include:

In
light
of
the
economic
and
public­
perception
consequences
associated
with
a
failed
compIiance
test,
are
the
current
EPA
measurement
methods
technically
acceptable
procedures
for
determining
compliance
with
standards
that
have
become
more
stringent
over
time?

If
a
method
is
highly
imprecise,
will
indication
of
a
failed
compliance
test
withstand
scrutiny
of
a
legal
challenge?

Do
data
indicating
emission
concentrations
below
the
regulatory
limit
really
imply
Databases
used
to
establish
MACT
standards
are
generally
developed
based
on
reports
from
tests
using
published
EPA
methods.
A
critical
portion
of
these
data
­
data
from
facilities
defining
the
best
performing
12%
of
the
facilities
­
is
extracted
to
define
the
MACT
technology
or
the
MACT
based
emission
limits.
Do
these
data
characterize
exceotionallv
well
designed
and
operated
facilities
or
do
the
key
data
represent
imprecision
in
the
measurement
methods?
This
concern
applies
to
any
analysis
where
the
best
12%
of
the
data
are
selected
for
examination
but
it
is
even
more
critical
when
those
data
indicate
results
below
the
range
for
which
the
method
was
validated.

5
Concerns
extend
beyond
regulatory
compliance
and
regulatory
development.
Are
the
EPA
methods
acceptable
procedures
for
determining
whether
a
new
air
pollution
control
device
is
meeting
its
performance
guarantees?
is
the
indicated
performance
representative
of
the
control
device
or
do
the
test
results
reflect
significant
imprecision
in
the
method?
I
The
above
lists
of
issues
and
concerns
are
far
from
exhaustive.
However,
almost
invariably,
the
response
to
such
questions
is
that
the
measurement
methods
may
not
be
perfect
but
they
are
the
best
that
we
have.
That
answer
does
not,
however,
alleviate
stakeholder
fears.
The
sponsors
of
ReMAP,

including
the
US
EPA,
have
entered'into
the
program
to
provide
tools
that
might
be
used
to
develop
better
answers.
This
report
is,
however,
not
intended
methods
addressed
herein
or
as
a
substitute
for
Method
301.

APPROACH
There
is
often
confusion
concerning
the
terms,
precision
and
accuracy.
Figure
1,
adapted
from
a
presentation
by
Dr.
Greg
Rigo
at
a
meeting
of
ASME's
Committee
on
Industrial
and
Municipal
Waste
clearly
illustrates
what
the
two
terms
imply.
Imagine
shooting
at
a
target.
The
illustration
on
the
left
shows
a
wide
scattering
of
results,
almost
equally
distributed
around
the
bull's
eye.
The
illustration
on
the
right
shows
a
tightly
grouped
set
of
shot
in
these
results
is
an
indication
of
precision
while
proximity
to
the
bull'

accuracy.
The
target
on
the
left
illustrates
poor
precision
but
good
accuracy.
The
target
on
the
right
illustrates
highly
precise,
but
inaccurate
shooting.
Phase
I
of
ReMAP
is
concerned
with
precision.

Accuracy
is
an
issue
for
later
phases
of
ReMAP.

Many
facilities
have
Iarge
quantities
of
data
from
repeated
single­
train
stack
tests.
These
resu
important
to
the
facility
but
typicaIly,
they
shed
little
light
on
the
precision
of
EPA
measurement
Methods.
Variation
in
repeat
measurements
is
in
also
influenced
by
variations
in
facility
operation.
Unfortu
for
separatinz
these
two
effects.
Determination
of
measurement
method
precision
must
be
based
on
simultaneous
determinations
of
stack
emission
concentrations,
preferably
with
co­
located
probes.

6
­
k,

p9""

'
k
­?­
a
7
Results
from
two
or
more
simultaneous
measurements
provide
information
to
calculate
a
sample
standard
deviation
of
that
measurement.
Two
data
points
­
a
single
indication
of
standard
deviation
­
are
not.
however,
a
sufficient
basis
for
defining
the
precision
of
the
measurement
method.
Repeated
simultaneous
data
from
a
given
source
provide
an
improved
indication
of
method
precision.

Repeated
simultaneous
measurements
from
a
v
ty
of
facilities
further
improves
the
data
base
for
assessing
method
precision
since
the
data
co
tack
concentrations
and
a
broader
range
of
personnel
applying
the
method.

The
Re
assembled
a
database
consisting
of
available
multi­
train
data
from
a
variety
of
selected
EPA
methods.
A
key
source
of
these
data
are
published
and
unpublished
EPA
reports
addressing
method
validation.
Additionally,
a
limited
number
of
industry
sponsored,
multi­

train
studies
have
been
conducted
and
documented.
These
industry
reports
provide
significant
expansion
to
the
scope
of
available
multi­
train
data.
Finally,
the
 PA
has
sponsored
a
limited
number
of
studies
where
multi­
train
tests
were
performed
to
expand
the
range
of
data
for
validation
of
previously
published
methods.
The
ReMAP
program
has
gathered
available
multi­
train
data
sets
for
the
following
EPA
measurement
methods:

9
Methods
5
and
5i
for
particulate
matter
(
PM)
emissions
Method
23
for
dioxin
and
furan
emissibns
Method
26
for
hydrochloric
acid
and
chlorine
gas
Method
29
for
multi­
metals,
and
9
9
9
c:

9
Methods
IO
1
a
and
10
1
b
for
mercury.

A
search
was
made
for
validation
data
on
the
follo
discovered:
ods
but
no
multi­
train
results
were
Method
108
for
arsenic
Method
0030
and
00
10
for
volatile
and
semi­
volatile
organics
respectively,
and
Method
00
1
1
for
formaldehyde.

8
After
the
initial
data
collection
activity,
the
ReMap
program
took
two
parallel
paths.
One­
path
provided
for
detailed
validation
of
the
gathered
data.
Wherever
possible,
validation
began
with
the
original
field
run
sheets
and
continued
through
a
complete
re­
reduction
of
the
data.
This
tedious
process
improved
the
database
by
providing
consistency
in
such
key
factors
as
use
of
consistent
standard
reference
conditions
and
blank
correction
procedures.
The
parallel
effort
involved
identifLing
and
refining
mathematical
procedures
for
analyzing
simultaneously
sampled
concentration
data
to
determine
measurement
precision
at
various
appropriate
concentrations.

Finally,
after
validating
the
database,
the
selected
statistical
analysis
procedures
(
see
Appendix)

were
applied
to
the
validated
database
to
determine
the
precision
of
the
selected
EPA
methods
at
appropriate
concentrations.

A
final
preliminary
point
concerns
the
issue
of
correcting
data
to
a
fixed
percentage
of
excess
oxygen.
Environmental
regulations
almost
always
set
a
limit
on
the
concentration
of
pollutants
in
the
stack
and
require
that
the
concentration
be
adjusted
to
reflect
a
standard
stack
excess
oxygen
(
typically
7%
oxygen).
For
several
reasons
the
ReMAP
study
does
not
include
oxygen
correction
in
the
analysis
of
measurement
method
precision.
The
primary
rationale
is
that
the
various
chemical
analyses
determine
the
quantity
of
a
specific
analyte
in
the
overall
sample
matrix.
If
the
quantity
of
analyte
is
low,
it
makes
little
difference
to
the
chemical
analysis
whether
the
loading
is
the
result
of
effective
air
pollution
control
or
if
the
stack
has
high
excess
air.
A
more
pragmatic
consideration
comes
from
the
available
data.
Several
of
the
key
EPA
method
validation
studies
failed
to
record
the
stack
oxygen
concentration
during
the
tests,

The
following
material
develops
estimates
of
measurement
method
precision
as
a
function
of
the
average
pollutant
concentration.
Both
the
concentration
and
the
precision
metrics
(
when
expressed
in
concentration
terms)
can
be
adjusted
to
a
fixed
oxygen
level
by
applying
the
following
0
2
correction
equation:

This,
of
course,
requires
that
one
have
knowledge
of
the
actual
stack
oxygen
level
as
well
as
the
desired
reference
oxygen
level.
More
specifically,
the
precision
of
a
measurement
method,

9
referenced
to
a
fixed
percent
excess
iir
(
say
7%
02)
will
vary
with
the
02
concentration
in
the
stack.

This
issue
will
be
discussed
in
further
detail
in
later
portions
of
the
report
Report
0
rganiza
tion
This
report
is
divided
into
two
different
sections
front
portion
of
the
repon
has
been
written
for
readers
with
only
a
passing
familiarity
with
st
a1
analysis.
Included
are
descriptions
of
the
measurement
methods
and
the
database
of
multi­
train
results.
It
also
includes
a
layman's
presentation
of
the
data
analysis
procedures
and
a
presentation
of
the
study
results.
The
last
portion
of
the
report
(
actually
an
appendix)
provides
a
detailed
description
of
the
statistical
analysis
procedures
used
in
ReMAP.
A
serious
attemp
ade
10
make
the
main
body
ofthe
report
and
the
appendix
readable
and
understandable
to
non­
statisticians.
3.0
The
Analysis
Procedure
­
A
Layman's
Description
Material
presented
in
this
section
provides
a
brief
summary
of
statistical
analysis
procedures
used
in
ReMAP
to
assess
precision
of
the
selected
EPA
measurement
methods.
The
presentation
is
written
for
the
statistical
layman
and
may
seem
overiy
simpiistic
ta
those
skilled
in
the
statistical
sciences.

Such
readers
are
referred
to
the
report's
Appendix
which
includes
detailed
development
of
the
.

statistical
analysis
procedures.

3.1
Measures
of
Precision
As
indicated
earlier,
imprecision
in
a
measurement
method
implies
that
random
error
in
the
sampling
ry
analysis
result
in
random
variation
in
the
indicated
emission
concentration.

otherical
stack
that
emits
a
nearly
constant
concentration
of
some
pollutant.

Imprecision
from
the
measurement
method
will
result
in
measured
concentrations
deviating
from
the
true
stack
concentration.
If
the
hypothetical
stack
is
sampled
many
times,
a
plot
of
the
results
should
such
as
the
one
illustrated
in
Figure
2.
The
average
of
a
large
number
of
ach
the
true
concentration
and
most
of
the
data
points
will
be
relatively
If
the
average
does
not
approach
the
true
concentration,
the
sed.
Individual
measurements
that
are
significantly
removed
from
the
decreasing
frequency.
The
core
objective
of
the
ReMAP
program
is
in
anticipated
results
for
different
manual
measurement
methods
and
measurements
should
concentrafion.

determination
of
how
that
spread
varies
with
the
stack
concentration.

There
are
a
variety
of
parameters
that
may
be
used
to
characterize
the
precision
of
a
method.
The
U.
S.
EPA
has
historically
used
standard
deviation
or
relative
standard
deviation
to
define
precision.

There
are,
however,
several
other
parameters
that
may
be
equally
valid
precision
indicators.
In
Figure
2,
standard
deviation
(
denoted
by
the
symbol
0)
is
indicated
as
a
distance
on
either
side
of
the
mean
value
in
the
distribution.
The
area
under
the
bell
shaped
curve
bounded
by
f
cr
has
special
mathematical
significance
but
for
current
purposes
it
is
sufficient
to
note
that
this
area
covers
68.2
percent
of
the
total
area
under
the
curve.
In
the
example
discussed
11
12
S
0
IIJ
C
.
I
.)
111
L
­
b.
0
I­­­

.
above
relative
to
Figure
2,
the
bell
shaped
curve
represents
the
expected
frequency
of
many
future
measurements.
Sixty
eight
percent
of
those
future
measurements
are
expected
to
indicate
concentrations
within
k
one
standard
deviation
of
the
mean.
If
the
value
of
Q
is
small
relative
to
the
mean,
then
the
majority
of
the
measurement
results
will
occur
close
to
the
true
value.
Conversely,
if
the
relative
value
of
G
is
large,
a
larger
portion
of
the
measurement
results
will
deviate
significantly
from
the
true
concentration.

A
second
approach
for
describing
measurement
precision
is
to
define
a
data
spread
expected
to
encompass
the
majority
of
future
measurements.
A
convenient
approach
is
to
define
concentration
bounds
capturing
99%
of
the
future
data.
This
parameter
may
hold
special
significance
to
facility
owners
and
operators
who
must
comply
with
emission
regulations.
Essentially,
this
parameter
defines
the
expected
concentration
bounds
for
99
out
of
100
future
measurements.
Where
as
68.2
%

of
measurements
fall
within
A
1.0
(
r
of
the
mean,
99%
of
the
measurements
fall
within
k
2.567
G
of
the
mean.
Both
the
standard
deviation
and
99%
concentration
bounds
represent
the
spread
in
future
measurements
from
random
variation
of
the
measurement
method.
The
standard
deviation
and
99%

concentration
bounds
do
not
include
variation
of
the
emission
source.

A
third
precision
metric
is
the
expected
spread
in
the
average
of
triplicate
measurements.
That
parameter
may
have
special
significance
to
facility
owners,
since
compliance
with
emission
regulations
is
typically
based
on
the
average
of
three
runs.
All
three
precision
metrics
are
related
by
simple
proportion.
As
no
above,
99
out
of
100
future
single
measurements
will
fall
within
the
bounds
of
5
2.5670.
For
repeated
measurements,
the
range
decreases
inversely
with
the
square
root
of
the
number
of
repeat
measurements.
Thus,
ninety­
nine
percent
of
the
average
of
future
triplicate
measurements
will
fall
within
the
bounds
off:
1.482
(
5
(
k
2.567/
43
G).
AH
three
metrics
will
be
calculated
in
the
ReMAP
precision
assessments
for
each
measurement
method.

3.2
Estimating
Standard
Deviation
Having
settled
on
metrics
for
describing
measurement
precision,
the
problem
is
reduced
to
determining
standard
deviation
as
a
function
of
measurement
concentration.
From
the
outset,
it
is
critical
to
understand
that
there
is
a
true
value
of
standard
deviation
at
any
given
concentration
but
13
we
will
never
know
its
exact
value.
In
accordance
with
normal
statistical
nomenclature,
the
true
value
of
standard
deviation
is
given
the
symbol
Q
(
si,
gna).
Information
concerning
G
can
be
obtained
from
special
tests
using
two
or
m
ampling
trains
operated
simultaneously
in
the
same
exhaust
stream.
Ideally,
such
tests
extract
sample
from
the
same
nomina
osition(
s)
in
the
stack.

Each
measurement
will
be
subject
to
ran
different
results
from
the
simultaneous
measurements.
Referring
to
the
bell
shaped
distribution
curve
in
Figure
2;
these
two
measurements
represent
two
data
points,
randomly
selected
from
the
total
population
of
potential
data
points.
If
a
larse
number
of
simultaneous
measurements
are
raken,
the
individual
dara
poinrs
should
generate
the
full
distribution.
Typically,
however,
only
two,
three
or
four
sampling
trains
are
operated
simultaneously.
An
estimate
of
the
standard
deviation
for
the
measurement
method
is
obtained
by
calculating
the
standard
deviation
from
dual
o
ad­
train
tests
according
to
equation
1
below.
.

i
Eq.
1
Standard
deviation
calculated
from
experimental
data
is
referred
to
by
the
symbol
S
to
make
a
distinction
between
this
value
and
the
true
standard
deviation
Q.
Clearly,
selecting
two
random
points
from
the
full
population
of
points
that
ma
aped
distribution
provides
a
poor
estimate
of
Q.
Selecting
four
points
provides
a
b
ing
measurement
methods,
the
typi
eated
tests
provide
rep
deviation
under
nearly
s
for
assessing
method
e
method
precision
is
a
d
values
of
the
true
constant
concentration
conditions.

standard
deviation
at
the
characteris
very
strong
function
of
concentrat
standard
deviation
that
are
referred
to
in
this
report
as
Est.
c.

There
are
however,
several
complications
to
the
process
of
estimating
the
standard
deviation
from
dual
and
quad­
train
test
results.
When
standard
deviation
is
calculated
from
smaIl
samples
of
a
large
population,
the
result
is
a
biased
estimate.
The
magnitude
of
the
bias
is
dependant
upon
the
number
of
data
points
used
to
estimate
each
value
of
S.
A
detaifed
presentation
on
the
source
of
this
bias
is
14
beyond
the
scope
of
the
current
discussion.
However,
for
illustrative
purposes,
consider
the
case
where
a
large
number
of
data
pairs
are
randomly
selected
from
a
known
distribution.
Standard
deviation
(
S)
can
be
calculated
for
each
data
pair
according
to
equation
1.
Most
non­
statisticians
will
anticipate
that
the
average
of
the
standard
deviations
(
S)
calculated
from
many
data
pairs
would
closely
approximate
the
true
standard
deviation
(
a)
for
the
overall
distribution.
As
discussion
in
the
Appendix,
that
anticipation
would
not
be
realized.
In
fact,
using
data
pairs,
the
average
standard
deviation
would
be
biased
low
by
a
factor
of
1.253.
If
we
repeated
this
example
using
three
or
four
data
points
for
each
standard
deviation
calculation,
the
average
standard
deviation
will
be
closer
to
the
true
value
but
the
bias
will
still
be
present.
For
triplicate
measurements,
the
bias
factor
is
1.128
while
for
quad­
train
the
bias
factor
is
only
1.085.
In
the
ReMAP
data
analysis,
the
standard
deviation
calculated
from
each
multi­
train
test
must
be
multiplied
by
the
appropriate
small­
sample
bias­
correction
factor.
This
provides
an
unbiased
estimation
of
standard
deviation
at
the
selected
concentration.
This
calculated
parameter
is
referred
to
as
small­
sample,
bias­
corrected
S.
.
­

To
assess
the
impact
of
pollutant
concentration
on
method
precision,
it
is
necessary
to
gather
multi­

train
measurement
data
over
a
broad
range
of
concentration
and
to
fit
the
data
to
an
equation
relating
S
to
average
concentration
(
C).
The
first
step
is
to
check
these
data
for
outliers
and
to
prepare
the
data
for
analysis.
Two
approaches
are
used
by
ReMAP
to
screen
data
for
outliers.
These
procedures
are
defined
in
the
Appendix
and
illustrated
in
the
next
section
of
the
report.
The
first
procedure
is
known
as
the
Dixon's­
r
test.
This
procedure
is,
used
to
examine
a
group
of
data
points
collected
during
a
single,
multi­
train
test
and
to
determine
if
one
or
more
data
points
in
the
group
are
outliers.

It
is
only
applicable
to
tests
with
three
or
more
simultaneous
sampling
trains.
The
second
screening
procedure
is
taken
from
Statistical
Process
Control
(
SPC)
methods
and
is
used
to
identify
outliers
from
multiple
simultaneous
measurements.
The
essence
of
this
procedure
is
to
compare
the
span
between
simultaneous
measurements
against
the
weighted
average
span
for
other
data
in
a
similar
concentration
range.
Special
provisions
are
included
to
account
for
the
fact
that
data
may
exist
as
pair,
triplicates,
or
as
quad­
train
results.

After
outlier
screening,
the
validated
data
are
entered
into
a
spreadsheet;
standard
deviations
are
calculated
and
then
corrected
for
the
above
noted
small
sample
bias.
Figure
3
illustrates
a
hypothetical
set
of
data
showing
small
sample
bias
corrected
standard
deviation
versus
mean
15
.
.
.

c7
LL
T­
O
0
0
0
.­.

0
0
0
?

0
0
P
T
P"

p"
9
­
1
b­
concentration
from
several
multi­
train
tests.
The
objective
is
to
fit
these
data
to
an
equation
relating
standard
deviation
(
Sbias
corrected)
to
average
concentration
(
C).
If
done
properly,
this
curve
fit
wilI
also
approximately
describe
the
relationship
between
G
and
C.
However,
before
fitting
the
data
to
a
functional
form,
it
is
necessary
to
account
for
the
differences
between
data
sets
consisting
of
2,

3,
or
4
simultaneous
measurements.
Equation
1
can
be
applied
to
dual
train
measurements
to
determine
the
standard
deviation
(
S)
with
only
one
degree
of
freedom.
Values
of
S
can
be
determined
from
triplicate
measurements
but
this
S
value
has
two
degrees
of
freedom.
Thus,
a
triplicate
measurement
provides
as
much
information
about
the
precision
of
the
measurement
method
as
two
dual
train
measurements.
Similariy
a
quad
train
provides
as
much
information
a
s
three
paired
trains.
In
curve
fin
g
the
data,
weighting
factors
must
be
applied
to
account
for
the
number
of
degrees
of
freedom
from
each
data
grouping.

­
r
3.3
The
Relationship
Between
S
and
C
i
As
discussed
in
the
Appendix,
a
wide
range
of
functional
forms
is
possible
for
describing
the
relationship
between
standard
deviation
and
concentration.
Based
on
the
characteristics
of
the
availabIe
data,
the
form
selected
and
justified
for
the
ReMAf
program
is
a
simple
power
function
as
6
L
­=
m
described
in
Equation
2,

k
­
4
S
=
k
C
p
Eq.
2
7­

Ld
where
S
is
the
estimated
standard
deviation
for
the
method,
C
is
concentration,
and
k
and
p
are
constants.
For
each
measurement
method,
the
available
data
are
fit
to
this
equation
using
a
least
squares
regression
analysis.
To
facilitate
that
regression,
it
is
convenient
to
first
transform
equation
2
by
taking
logarithms
to
yield,
r
Eq.
3.

Regression
analysis
yields
values
for
Ln(
k)
and
p
.
The
governing
equation
is
obtained
by
taking
inverse
logs.
Unfortunately,
the
transformation
processes
create
yet
another
bias
that
must
be
accounted
for.

17
In
the
database,
an
average
value
of
the
individual
standard
deviations
can
be
calculated
from
the
multi­
train
data
for
a
selected
method.
The
individual
values
of
average
concentration
from
the
database
can
be
entered
into
the
regression
equation
(
Eq.
3)
to
predict
values
of
S
at
each
value
of
For
an
unbiased
model,
the
average
value
of
predicted
S
equals
the
average
value
of
S
With
transformation
of
data
into
the
loplog
plane,
that
value
of
Ln(
S)
{
Predicted]
will
equal
the
av
source
of
this
bias
is
that
Ln(
S)
f
L
n
(
3
This
bias
can
be
accounted
for
by
appropriately
adjusting
the
value
of
k
in
the
model.
Further
explanation
of
this
bias
and
the
procedure
for
bias­
correct
The
above
procedure
provides
a
simple
means
of
using
available
data
to
estimate
the
standard
deviation
as
a
function
of
average
concentration
for
any
given
measurement
method.
At
any
selected
concentration,
the
regression
equation
can
be
determine
an
estimated
value
of
c.

Information
on
Est.
CJ
and
average
concentration
c
the
anticipated
range
for
99
out
of
100
future
ind
as
well
as
the
anticipated
range
for
the
average
o
note,
however,
that
even
after
correcting
for
the
various
biases,
the
regression
line
is
not
a
perfect
indicator
of
true
value
of
Q.
This
evaluation
is
a
best
estimate,
based
on
the
currently
available
data.

Addition
of
new
data
will
undoubtedly
cause
an
adjustment
to­
the
regression
equa
relation
between
Est.
Q
and
C.
stack
concentration)

3.4
Confidence
Intervals
A
critical
question
that
must
be
examined
is
`&
HOW
good
is
the
correlation?"
Based
on
analysis
of
the
available
data,
it
is
possible
to
estimate
the
potential
for
the
regression
line
through
the
S
versus
C
data.
These
potential
bounds
are
referred
t
calculating
confidence
intervals
are
presented
in
the
Ap
he
Appendix
also
includes
several
example
calculations.
Figure
4,
taken
directly
from
the
Appendix,
illustrates
a
hypothetical
set
of
small
sample,
bias­
corrected
S
versus
C
data.
The
heavy
solid
line
through
the
data
represents
the
regression
line
while
the
arched
lines
above
and
below
the
regression
line
illustrate
the
upper
and
­
P
*
*

4,
..
­

cn
­
C
0
m
>
.­
e
.­
8
O
I
I
0
0
0
F
0
0
F
0
0
0
0
­

0
a>
CI,

Q)
2
k
0
0
0
0
P
0
?
rn
Y
a"
0
Q,
Y
P­

I
19
lower
confidence
intervals.
The
regression
line
represents
the
best
estimate
of
the
relationship
between
G
and
average
concentration.
The
analysis
used
to
determine
the
regression
line
also
provides
information
on
the
potential
bound
example,
the
analysis
provides
a
best
estim
analysis
ais0
provides
information
to
de
maximum
slope
of
the
reIation
@).
In
Fi
relation
where
p
is
at
the
minimum
and
confidence
level,
we
know
that
the
slope
Line
A
and
less
than
iliustrated
by
on
the
potential
range
of
the
leading
c
illustrated
in
Figure
4
represent
the
comb
Confidence
intervals
on
a
linear
relation
will
always
ha
the
potential
range
for
the
slope
term.
The
true
be
determined,
but
it
is
possible
to
provide
t
a
given
confidenc
r
the
slope
of
th
ression
equation
@).
The
,
at
a
given
confidence
level,
the
m
,
the
lines
labeled
A
and
B
illustrate
m
values
respectively.
Specifically,
at
the
95%

(
e.
g.,
95
YO),
the
regression
interval.

The
primary
task
for
the
Phase
I
Re
deviation
at
given
values
of
concentr
of
method
precision.
If
95%
confidence
interval
97.5%
confidence
that
the
method's
Similarly,
there
is
97.5%
confidenc
bound.
However,
neither
of
the
precision.
The
currently
available
method
precision.

Plots
such
as
that
provided
in
Figure
4,
frequently
cause
difficulty
for
readers.
Generally,
a
significant
portion
of
the
individual
data
p?
ints
(
circles
on
Figure
4)
fall
outside
the
confidence
limits.
This
is
an
expected
trend
since
the
confidence
intervals
represent
upper
and
lower
bounds
for
the
regression
line
­
not
upper
and
lower
bounds
for
the
data.
A
word
of
caution
is
in
order.
When
the
statistical
analysis
does
not
require
weighting,
it
is
relatively
simple
to
calculate
confidence
intervals
using
software
routines
contained
in
standard,

commercial
spreadsheet
computer
programs.
Recall
that
weighting
of
the
data
is
required
when
the
individual
data
points
have
different
degrees
of
freedom.
For
example,
standard
software
can
easily
be
used
to
calculate
confidence
intervals
in
situations
when
all
of
the
data
consist
of
paired
train
measurements.
When
data
weighting
is
required,
calculation
of
confidence
intervals
becomes
much
more
complex,
requiring
inversion
of
rather
messy
matrices.
Advanced
statistical
analysis
computer
software
generally
includes
routines
for
such
analyses.
Alternately,
special
computer
software
will
need
to
be
written.
For
the
current
report,
detailed
expianation
of
confidence
interval
calculation
has
been
limited
to
those
situations
where
calculations
can
be
performed
using
software
routines
in
standard
spreadsheet
computer
programs
such
as
Excel.

One
additional
subtle
issue
related
to
calculation
of
confidence
intervals
must
be
addressed
before
proceeding
with
the
ReMAP
analysis.
The
appropriate
calculation
process
depends
upon
bow
the
confidence
intervals
are
to
be
used.
For
the
ReMAP
study,
the
intended
use
of
the
various
analyses
is
to
determine
Est.
Q
at
discreet
values
of
average
concentration
and
to
use
Est.
Q
to
calculate
various
precision
metrics
at
those
average
concentrations.
Method
precision
metrics
are
also
calculated
assuming
that
the
true
value
of
Q
is
at
the
upper
and
lower
confidence
intervals
(
at
selected
concentrations).
There
are
alternate
ways
of
using
confidence
intervals
that
require
slightly
different
analysis
procedures.

Reh4AP
statistical
methodology
and
were
deemed
inappropriate
for
the
current
analysis
purposes.
Those
procedures
were
carefully
considered
in
establishing
the
3.5
Summary
of
ReMAP
Analysis
Process
In
summary,
the
ReMAP
analysis
procedure
begins
with
a
database
of
available
multi­
train
data
from
application
of
an
EPA
measurement
method.
These
data
are
screened
for
outiiers
using
procedures
that
purposefully
try
to
include
as
much
data
as
possible.
Data
should
be
discarded
only
if
there
is
an
identified
problem
with
a
measurement
or
if
a
data
pair
(
or
a
single
measurement
from
a
triplicate
or
quad
test)
is
demonstrably
dissimilar
from
the
remainder
of
the
data
in
the
data
set.

For
each
test
run,
the
2,
3,
or
4
simultaneous
measurements
are
entered
into
equation
1
to
determine
21
the
standard
deviation
for
the
run.
Each
of
these
standard
deviation
estimates
is
then
multiplied
by
the
appropriate
correction
factor
to
account
for
small
sample
bias.
The
array
of
bias
corrected
standard
deviation
data
and
average
concentration
data
are
weighted
for
the
number
of
degrees
of
freedom,
transformed
to
the
Log­
Log
plane,
and
subjected
t
linear
regression
analysis.
This
analysis
determines
values
of
k
and
p
in
the
power
fun
used
to
determine
a
predicted
value
of
standard
d
average
value
of
S
from
the
test
data
is
compared
to
the
average
value
of
S
from
determine
an
appropriate
value
for
the
second
bi
correction
factor.
That
factor
is
multiplied
by
the
k
parameter
to
provide
an
unbiased
equation
relating
our
best
estimate
of
standard
deviation
to
concentration.
Next,
the
95%
confidence
intervals
are
calculated
over
the
range
of
available
data.

mote,
the
confidence
intervals
are
actually
calculated
in
the
Log­
Log
plane.
The
second
bias
correction
factor
is
applied
to
the
interval
when
it
is
transformed
back
to
the
Est.
a­
C
plane.]

Data
are
presented
in
four
ways.
First,
the
data
are
presented
in
tabular
and
gaphicat
form
showing
a
scatter
plot
of
calculated
standard
deviation
and
relative
standard
deviation
concentration.
The
second
form
of
data
presentation
is
a
graph
of
the
three
precision
metrics
elorted
against
concentration.
Each
of
these
metrics
is
normalized
by
the
concentration
and
is
based
on
the
best
estimate
of
the
method
standard
deviation.
Third,
data
are
presented
to
illustrate
the
fact
that
the
true
value
of
method
standard
deviation
co
d
be
greater
than
or
less
than
the
best
estimate.

There
are
six
curves
of
interest.
The
first
two
curves,
representing
a
worst
case
scenario,
focus
on
the
situation
that
would
occur
;
f
the
true
method
standard
deviation
(
Q)
were
best
represented
by
the
upper
bound
of
the
95%
confidence
intervaI.
Using
that
upper
limit
of
Est.
o,
the
upper
and
lower
bounds
of
measured
concentration
are
calculated
that
encompasses
99%
of
future
measurements.

These
curves,
plotted
against
stack
concentration,
are
denoted
by
the
symbols
C99u/
S95+
and
C991/
S95+.
Next,
the
data
bands
encompassing
99%
of
future
measurements
are
calculated,

assuming
that
true
standard
deviation
varies
according
to
the
regression
equation.
These
two
lines
are
given
the
notation
C99u/
Sbest
and
C991lSbest.
Finally,
consideration
is
given
to
the
case
where
the
regression
analysis
has
provided
an
over
estimate
of
standard
deviation.
These
curves
are
similar
to
the
first
two
but
are
based
on
the
lower
95%
confidence
interval.
These
two
lines,
given
the
symbols
C99ulS95­
and
C991/
S95­,
can
be
considered
best
case
scenarios.
There
is
97.5%

confidence
that
the
method's
precision
is
worse
than
these
last
two
lines.
i
kr_
r
For
each
of
the
plots
describing
measurement
method
precision,
care
has
been
taken
to
limit
the
range
of
the
presentation
to
the
range
of
the
currently
available
data.
There
has
been
no
extrapolation
beyond
the
range
for
which
experimental
data
was
available.

The
final
data
presentation
is
a
table
quantifying
the
anticipated
range
of
fbture
measurements
at
selected
values
of
average
stack
concentration.
These
tables
list
C99dSbest
and
C99IISbest
over
a
range
of
concentrations
imposed
or
under
consideration
for
current
environmental
regulations.
As
regards
these
tables
as
well
as
all
other
methods
of
describing
method
precision,
it
is
important
to
reiterate
that
various
parameters
are
not
corrected
to
a
constant
excess
air
level.

The
sections
that
follow
examine
each
of
the
EPA
Measurement
Methods
of
interest.
The
first
method
discussed
is
Method
5
for
determining
particulate
matter
concentration.
The
precision
assessment
for
this
method
is
presented
in
great
detail
in
hope
that
the
reader
can
better
understand
the
fuIl
scope
of
the
assessment.

23
This
Page
IntentionaIIy
Left
Blank.
4.0
EPA
Particulate
Matter
Methods
­
Methods
5
and
5i
Sampling
hardware
used
for
the
majority
of
the
EPA
manual
isokinetic
measurement
methods
is
based
upon
the
hardware
used
for
measuring
particulate
matter
(
PM)
concentration
in
stacks.
The
procedure
for
measuring
stack
particulate
concentration
has
been
designated
EPA
Method
5
and
the
associated
hardware
is
referred
to
as
a
Method
5
train.
(
EPA,
1987)
Additional
details
on
Method
5
.

(
and
other
Methods
discussed
in
this
report)
can
be
found
in
40CFR
Part
60
­
Appendix
A
under
the
heading
for
the
Method.
Figure
5
illustrates
the
Method5
hardware.
Describing
the
key
features
of
a
Method
5
train
serves
as
a
convenient
basis
for
fbrther
discussion
of
other
measurement
methods
addressed
in
this
study.

In
general
terms,
application
of
Method
5
involves
inserting
a
probe
into
a
stack
and
extracting
a
composite
sample
that
is
representative
of
average
conditions
across
the
stack.
In
a
typical
sampling
run,
sample
gases
are
extracted
from
the
stack
for
a
period
of
approximately
one­
hour.
The
stack
cross
section
is
divided
into
equal
area
segments.
The
probe
is
traversed
across
the
stack,
e
stack
flow
from
each
segment
for
equal
time
periods.
With
a
round
stack,
traversing
typical
two
ports,
located
perpendicular
to
each
other.
The
rate
of
sample
extraction
is
adjusted
t
the
velocity
of
gases
entering
the
probe
tip
is
essentially
equal
to
the
local
velocity
of
flue
gas
in
the
stack.
This
is
referred
to
as
isokinetic
sampling.
This
feature
of
manual
method
sampling
is
included
to
minimize
the
potential
for
sample
bias
associated
with
preferential
capture
of
solid
phase
material
according
to
particle
size.

The
extracted
sample
is
passed
through
a
heated
line
to
a
heated
filter
assembly
that
captures
solid
phase
particles.
The
mass
of
particulate
captured
during
the
entire
sampling
period
is
determined
gravimetrically.
Additional
features
of
the
method
include
procedures
for
determining
the
volume
of
flue
gas
extracted
from
the
stack
during
the
sampling
period.
Using
standardized
protocols,
the
particulate
concentration
is
determined
as
the
ratio
of
the
mass
of
particulate
collected
divided
by
the
volume
of
flue
gas
extracted.

25
26
ri
L
P
L
Figure
5
illustrates
the
hardware
components
and
their
arrangement
for
Method
5
sampling.
AS
indicated,
sample
gas
is
extracted
through
a
nozzle
and
transported
in
a
heated
glass
probe
to
a
heated
filter
assembly.
The
probe
assembly
consists
of
a
glass
nozzle,
a
heated
glass
probe
liner,
a
s­

type
pitot
probe
and
a
thermocouple
(
TK).
The
T/
C
and
pitot
allow
determination
of
the
local
stack
gas
temperature
and
velocity,
which
provides
a
basis
for
adjusting
the
sample
extraction
rate
to
isokinetic
conditions.
Particulate
matter
in
the
sample
may
be
deposited
on
the
nozzle
and
probe
liner
walls
but
the
majority
of
the
particulate
matter
(
typically
>
go%)
is
collected
on
a
heated
filter.

Heating
of
both
the
probe
and
filter
assembly
is
required
to
prevent
condensation
of
water
and
other
condensable
materials
in
this
portion
of
the
sampIing
train
(
often
referred
to
as
the
front
half
of
the
train).
Located
downstream
of
the
heated
filter
box
is
a
series
of
impingers
in
an
ice
bath
that
remove
moisture
from
the
sample.
An
umbilical
cord
connects
the
impingers
to
the
meter
box.
The
meter
box
contains
a
dry
gas
meter
to
determine
the
volume
of
dry
sample
extracted,
means
for
determining
pitot
probe
AP,
read­
outs
for
key
temperatures,
and
a
vacuum
pump
for
adjusting
sample
extraction
rate.
The
sampling
rate
is
usually
held
between
0.5
and
1.0
cubic
feet
per
minute.

After
completion
of
a
test
run,
the
field
technician
thoroughly
rinses
the
train
components
upstream
of
the
filter
with
the
appropriate
solvent
(
generally
acetone
for
paniculate
samples)
to
recover
any
particulate
that
may
have
been
deposited
on
the
probe
walls
or
nozzle
tip.
The
technician
must
also
record
a
number
of
sampling
system
parameters
necessary
to
determine
the
volume
of
gas
collected
and
the
moisture
content
of
the
flue
gas.
Typically
an
Orsat
analysis
is
performed
on
the
flue
gas
to
determine
the
major
constituents
of
the
flue
gas,
particularly
the
oxygen
concentration.
Back
in
the
laboratory,
the
probe
rinse
and
filter
are
dried
and
the
mass
of
particulate
collected
is
determined
gravimetrically.
To
assure
that
the
final
weig
gain
on
the
filter
represents
dried
particulate,

repeated
measurements
are
performed.
The
Sam
is
considered
dry
and
results
are
reported
when
subsequent
weighings
agree
within
0.5
mg.
Particulate
concentration
is
determined
as
the
ratio
of
the
particulate
mass
colIected
divided
by
the
volume
of
flue
gas
collected.
Usually,
the
sample
volume
is
determined
and
reported
on
a
dry
basis
and
adjusted
to
standard
temperature
and
pressure
conditions.
Standard
temperature
and
pressure
conditions
used
by
the
U
S
 PA
are
20
°
C
and
760
mrn
Hg.
For
regulatory
purposes
dilution
effects
are
accounted
for
by
correcting
the
measured
concentration
to
a
fixed
percent
oxygen
(
or
carbon
dioxide).

27
Some
states
require
special
analysis
pro
ures
to
assess
the
mass
of
material
that
condenses
in
the
impinser
portion
of
the
Method
5
sampling
train.
Those
states
o
require
that
the
mass
of
condensed
phase
material
be
combined
with
the
particulate
catch
in
probe
and
filter
to
yield
a
total
particulate
phase
catch.
These
procedures
were
not
used
for
the
ReMAP
study.
All
particulate
concentration
data
presented
and
anaIyzed
in
the
following
sections
represent
solid
phase
material
collected
in
the
front
half
of
the
train
only.
Moreover,

the
performance
of
particulate
measurement
methods
sh
the
analysis
includes
back
half
catch
from
Method
not
be
applied
to
measurem
4.1
Method
5
Data
and
Precision
Analysis
Multi­
train
data
included
in
the
ReMAP
database
come
from
three
main
reports.
The
first
data
set
includes
a
series
of
EPA­
sponsored
studies
condu
search
Institute
in
the
early
1970s
to
validate
the
pa
date
method
(
Hamil
a
included
a
coal­
fired
PO
plant
and
two
municip
units
were
performed
using
fou
ltaneously
(
quad­
trains).
For
this
study,
each
train
was
operated
b
At
the
power
plant
site,
testi
providing
a
total
of
16
data
poi
For
the
first
MWC
test,
six
test
con
concentrations
ranging
from
runs,
providing
20
individual
these
three
test
series
are
provided
i
(
and
all
subsequent
tables
listing
reference.
Skips
in
run
numb
difficulties
and
suggest
that
t
nt
operating
conditions
thus
ge
from
141
to
240
mg/
dscm.

4
individual
data
points
with
28
­
w
*­.
Table
1.
 PA
Method
5
Data
­
Hamil
and
Cam­
1974
and
I974b.

RunNumber
A
8
C
D
I
1
205
202
204
22
1
ower
Plant
207
240
155
150
141
I
I
1
5
60.4
61.9
63.2
64.6
Mwc
1
,

I
1
J
14
126
123
I34
,
144
15
153
141
161
139
16
103
106
104
103
All
data
expressed
as
mg/
dSm
Data
are
not
corrected
for
oxygen
content
29
The
next
set
of
multi­
train
Method
5
data
is
provided
by
a
second
EPA­
sponsored
study
at
an
MWC
in
Dade
County,
Florida.
The
tests
were
directed
by
Southwest
Research
Institute
(
H
a
d
and
Thomas,
1976).
These
tests
are
unique
among
all
data
collected
for
validation
of
 PA
measurement
methods.
The
stack
test
location
provided
four
sampling
trains
were
used
in
each
port
providing
a
total
of
eight
simultaneous
measurements
for
each
test
condition.
Moreover,
a
total
of
nine
different
samplin
ams
were
used
in
the
collaborative
study.

The
experiments
covered
a
3­
week
period
with
the
test
pian
calling
for
five
runs
per
week.
Seven
different
laboratories
analyzed
the
four
paired
sampling
trains
at
the
train
was
operated
by
a
single
technician
maintain
each
week
(
accounting
for
three
of
the
nine
parti
paired
trains,
a
separate
laboratory
operated
each
t
1
The
test
plan
called
for
fifteen
sampling
runs,
five
per
week
for
th
actually
completed;
three
the
first
week
and
five
each
the
second
and
summary
of
the
measurement
results.
A
total
of
104
data
points
were
collected.
For
run
10,
a
probe
liner
was
broken
on
one
of
the
eight
trains
(
Train
A
operated
by
Laboratory
103).
Accordingly,
that
data
point
was
eliminated
from
the
data
analysis.

The
final
data
source
was
an
ASME­
sponsored
study
by
Rig0
and
Chandler
who
performed
extensive
muiti­
train
experiments
on
a
municipal
w
Chandler,
1997).
A
total
of
I6
Method
5
data
pairs
are
re
tor
in
Piasfield,
Mass
(
Ri
.
The
data
range
for
these
from
14
to
74
mg/
dscm,
which
significantly
gathered
at
Pittsfield
used
essentially
every
nds
the
overall
range
of
the
full
data
set.
Data
method
of
interest
to
the
ReMAP
program.

Particulate
concentration
results
from
the
Rig0
and
Chandler
t
are
provided
in
Table
3.

The
first
step
in
the
ReMAP
analysis
is
to
determine
if
a
approach
is
outlined
in
the
Appendix
and
includes
the
Statistical
Process
Control
(
SPC)
methods.

consisting
of
three
or
more
simultaneous
measurements
and
is
used
to
identify
potential
outliers
f
the
data
groups
are
outliers.
The
n's­
r
test,
a
procedure
taken
from
test
is
applied
to
individual
tests
The
Dixon's
c
I
Pi
3
al
g
31
d
E
e,
E
3
E
.
e,
10
2
0
e
L
B
0
e,
t:
3
0­
l
0
c
8
CJ
eJ
L
4
d
TabIe
3.
EPA
Method
5
Data
­
Pitt
All
dara
expressed
as
mddscm.
Data
are
not
corrected
for
Oy~
gen
content
32
F?
f
within
the
test.
The
SPC
procedure
begins
by
breaking
the
data
into
groups
representing
ranges
of
similar
concentration.
The
span
of
data
is
calculated
for
each
simultaneous
measurement
and
then
weighted
according
to
a
factor
that
is
a
function
of
the
number
of
simultaneous
determinations
(
Le.,

pairs,
quads,
etc.).
Next,
the
average
weighted
span
is
calculated
for
each
concentration
group.
If
the
span
for
a
given
r
exceeds
the
weighted
average
span,
then
data
from
that
run
are
abnormally
large,
relative
to
afa
in
that
concentration
range.
In
SPC
terminology,
the
weighting
factors
are
referred
as
D4.
Table
4
provides
a
listing
of
D4
parameters
as
a
function
of
the
number
of
measurements
in
a
run.
,

Table
4:
SPC
Factors
for
Identification
of
Data
Outliers
Sample
Size,
n
The
choice
of
concentration
ran
were
tested.
There
is
a
strong
Table
5
combines
the
data
prese
procedures
outlined
above.
As
group
representing
power
plant,
at
MWC2
and
at
the
Dade
County
of
these
data
had
average
PM
ions
above
94
mddscm.
The
remaining
data
and
the
Pittsfield
MWC
had
M
concentrations
less
than
68
mgdscm.
The
weighted
average
spread
for
simultaneo
ments
in
the
low
concentration
range
was
13.1
5
mgdscm.

For
measurements
in
the
hig
ion
range,
the
weighted
average
data
spread
was
77.32
mg/
dscm.
Data
points
are
suspect
if
the
actual
measurement
spread
is
greater
than
these
values.

Data
point
number
17
in
the
Rigo
and
Chandler
set
marginally
exceeds
this
limit.
However,
this
data
point
has
the
highest
concentration
in
the
"
low
concentration"
data
group.
When
the
spread
on
this
data
point
is
normalized
by
the
mean
concentration,
the
spread
is
on
the
same
order
as
several
other
data
points
in
the
low
group.
The
ReMAP
program
has
a
bias
for
retaining
all
data
unless
it
is
somewhat
arbitrary.
For
the
ReMAP
analysis,
several
ranges
rence
for
minimizing
the
number
of
data
points
eliminated.

rlier
in
Tables
1,2
and
3
and
assesses
the
data
according
SPC
ut,
the
data
was
separated
into
two
range
groups
with
the
33
Table
5.
Consolidated
Method
5
Data
Set
A11
data
expressed
as
mg/
dscm.
Dam
are
not
corrected
for
0
3
an
obvious
and
significant
outlier.

retained
for
subsequent
anaiysis.
All
data
points
in
the
low
concentration
grouping
have
been
The
high
concentration
range
group
includes
quad
data
and
the
Dade
County
tests
using
octets.
Data
in
this
range
are
suspect
if
the
difference
is
greater
than
77.32
mgldscm.
Only
one
measurement,
run
number
12
from
the
Dade
County
tests,
fails
to
meet
this
criteria.
Data
from
run
number
I
in
the
Dade
County
tests
is
also
quite
large.
The
data
report
provides
no
indication
of
measurement
problems
associated
with
either
of
these
measurements
but
it
is
obvious
from
inspection
that,
for
run
number
i2
the
two
data
points
collected
by
Laboratory
103
(
labeled
A
and
B
in
Table
5)
are
higher
than
the
other
six
determinations.
For
run
number
1,
data
from
Run
C
also
appears
abnormally
high.

Dixon's­
r
procedure
was
applied
to
the
data
from
b
ns
and
results
indicate
that
test
point
C
from
run
number
1
and
test
point
A
from
run
12
are
abn
y
high
and
should
be
considered
as
outliers.

All
other
data
points
in
this
data
set
pass
the
Dixon's­
r
criteria.
After
eliminating
points,
the
remaining
data
in
the
ion
data
group
pass
the
SPA
criteria.

/
the
two
data
The
next
step
in
the
analysis
is
to
calculate
the
average
concentration
and
standard
deviation
for
each
group
of
simultaneous
measure
ts
and
to
correct
the
calculated
sample
standard
deviations
for
the
small
sample
bias.
As
noted
in
ier
discussion,
the
calculated
value
of
standard
deviation
from
the
data,
S,
is
a
biased
estimate
of
the
true
standard
deviation,
CT.
Table
6
presents
the
correction
factors
used
to
caIculate
a
data
points
used
to
calculate
S.

Results
of
these
calculations
are
presented
in
Table
7.
Figures
6a
and
6b
present
scatter
plots
of
the
data
from
Table
7.
Figure
6a
shows
the
scatter
of
bias
corrected
standard
deviation
versus
the
average
particulate
concentration.
Figure
6b
presents
the
same
data,
but
in
a
sIightIy
different
i
35
Facility
RunNo
N
Avg.
Standard
Bias
Esttmared~
Conccnnation
Deviation
Factor
Sisma
All
data
expressed
as
mg/
dscm.
Data
36
37
a
v)
0
ua
N
'
0
0
F1
0
m
r
0
z
0
m
0
d
u
u
L
..
.
.

L.
u
<
format.
Here
the
standard
deviation
has
been
normalized
by
the
concentration
and
presented
in
units
of
percent.
i
The
next
portion
of
the
data
analysis
is
to
evaluate
the
relationship
between
the
estimated
standard
deviation
and
the
average
particulate
concentration.
However,
before
performing
the
regression
analysis,
it
is
necessary
to
weight
the
data
according
to
the
number
of
degrees
of
freedom
for
each
measurement
group.
As
discussed
in
the
previous
section,
statistical
assessment
of
data
containing
differing
degrees
of
freedom
involves
complex
matrix
inversion
procedures.
Details
of
the
caIculation
procedure
are
not
included
here.

It
is
instructive
to
review
the
rationale
for
weighting
the
data.
With
a
quad­
train,
the
four
individual
particulate
measurements
can
be
used
in
a
variety
of
ways.
For
example,
Train
A
can
be
grouped
with
Trains
B,
C,
and
D
to
calcuiate
three
different
standard
deviations
or
the
four
measurements
can
be
combined
in
the
calculation
of
a
single
value
of
S.
Determination
of
S
based
on
data
from
Trains
A
and
B
provides
the
same
level
of
information
achieved
from
dual
train
testing.
Similarly,
S
determinations
using
data
from
Trains
A
and
C
or
from
Trains
A
and
D
convey
the
same
level
of
information
as
dual
train
measurements.
Clearly,
a
calculated
value
of
S
using
ail
four
simultaneous
measurements
conta
more
information
than
a
calculation
based
on
two
measurements.
When
a
data
set
contains
results
from
dual,
triple,
quad,
etc.
measurements
it
is
necessary
to
weight
the
various
data
to
account
fo
e
relative
quantity
of
information
provided
in
each
test.

The
weighted
data
set
is
then
fit
to
a
power
function
relationship,
as
presented
below.

S
=
kCp
Eq.
1
To
assist
in
that
regression,
the
data
is
transformed
into
the
log­
log
plane
such
that
the
governing
equation
becomes:

Ln(
S)
=
Ln(
k)
+
pLn(
C)
Eq.
2
By
performing
the
transformation,
the
regression
analysis
is
linearized.
Results
from
the
analysis
of
data
in
Table
7
are
summarized
in
Table
8
below.
.
.

39
A
regression
analysis
is
a
mathematical
procedure
that
yields
a
best
estimate
for
the
curve
fit
parameters.
One
critical
question
islwhether
the
indicated
values
of
k
and
p
are
statistically
significant.
One
approach
to
answering
this
question
is
the
Student
list
the
t­
statistic
as
a
function
of
the
confidence
lev
g.
95%
confidence)
and
the
nulnber
of
degrees
of
freedom.
The
regression
analysis
also
produces
a
value
of
the
t
parameter.
If
the
calculated
t­
parameter
is
greater
than
the
criticaI
are
statistically
significant.
Conversely,
if
the
statistic,
then
the
regression
analysis
results
co
Table
8,
the
calculated
value
of
the
t
paramet
parameter
for
42
degrees
of
freedom,
at
the
assures
that
there
is
a
relationship
between
S
regression
analysis,
did
not
occur
by
chance.
random
chance.
As
shown
in
The
large
relative
value
o
f
t
Transformation
of
data
from
the
real
plane
to
the
log­
log
plane
greatly
eases
the
regression
analysis
but
it
introduces
a
potentialIy
significant
bias
to
the
results.
One
characteristic
of
a
linear
regression
analysis
is
that
the
average
of
the
predicted
values
for
the
dependent
var
le
should
equal
the
average
val6e
from
the
actual
data.
Since
the
regression
was
performed
in
the
log­
log
plane,
the
weighted
average
value
of
Ln(
S)
will
be
the
same
for
both
the
actual
data
However,
the
average
value
of
the
predicted
values
of
S
will
not
necessarily
be
equal
to
the
average
of
the
small
sample
bias
corrected
S
values.
For
the
current
da
sample
bias
corrected
S
values
is
364.93
while'the
sum
of
the
(
at
the
observed
values
of
concentration)
is
351.013.
Thus,
the
predicted
values
of
S
are
biased
low
40
­
,
and
a
correction
factor
must
be
applied.
For
the
Method
5
data,
the
log
transformation
correction
factor
is
364.93/
35
1
.
O
1
3
=
1.0397.

The
equation
describing
the
estimated
values
of
standard
deviation
versus
concentration
is
the
best
estimate
available,
based
on
available
multi­
train
experimental
data,
but
there
is
uncertainty
associated
with
this
equation.
The
slope
of
the
regression
line
@)
and
the
value
of
the
leading
constant
(
k)
may
be
greater
or
smaller
than
predicted.
Statisrical
data
in
Table
8
can
be
used
to
quantify
uncertainty
in
the
regression
equation.
Specifically,
the
95%
confidence
intervals
on
the
regression
equation
will
be
caiculated.

The
95%
confidence
interval
on
the
slope
term
can
be
expressed
as
I
p95%
=
Ppredicted
5
t95%*[
SE(
coeff)
l
Eq.
3
where
Pg5%
represents
the
upper
and
lower
bounds
of
the
slope
coefficient,
t95%
is
the
critical
t­,
I
statistic
ax
the
95%
confidence
level
and
the
appropriate
number
of
desrees
of
freedom,
and1
SE(
coeff)
is
the
standard
error
of
the
coefficient.

I
,
As
indicated
in
Table
8,
the
predicted
value
of
the
power
term
in
the
regression
equation
@)
is
1.3063
and
the
standard
error
of
that
coefficient
is
0.1477.
The
critical
t
statistic
for
42
degrees
of
freedom,
at
the
95%
confidence
level
is
2.020
(
available
from
standard
statistical
tables).
Thus,
the
best
estimate
for
the
slope
of
the
regression
line
is
the
predicted
value
(
1.3063)
but
with
95%

confidence
it
can
only
be
concluded
that
the
value
of
the
p
coefficient
is
between
1.008
and
1.605:

'
Implications
of
the
potential
range
of
this
slope
term
are
discussed
in
more
detail
later.
r­.

The
weighted
least
squares
numerical
analysis
provided
information
necessary
to
determine
confidence
intervals
on
the
regression
equation.
Results
of
those
calculations
(
at
the
95%

confidence
level)
are
presented
in
Figure
7.
When
plotted
on
log­
log
scale,
the
regression
equation
is
a
straight
line
and
the
confidence
intervals
appear
as
horn
shaped
curves
on
either
side
of
the
prediction.
AI1
three
lines
in
this
figure
have
been
adjusted
to
include
the
log­
log
transformation
41
0
0
s2
E
e
E
rq
i
bias
correction
factor.
Superimposed
on
Figure
7
is
the
small
sample
bias
corrected
data
from
Table
7.

The
meaning
of
confidence
intervals
often
confuses
those
with
limited
background
in
statistical
analysis.
The
straight
line
through
the
data
represents
the
best
estimate
of
the
relationship
between
standard
deviation
G
and
mean
concentration,
p.
The
confidence
intervals
define
potential
bounds
for
the
regressi
the
straight
line.
Confidence
intervals
do
not
represent
boundaries
for
the
actual
data.
It
is
le
to
calculate
potential
bounds
for
data,
but
those
bounds
are
referred
to
as
tolerance
intervals.
Thus,
it
is
fully
anticipated
that
a
portion
of
the
experimental
data
(
individual
determinations
of
S)
will
fall
outside
the
confidence
intervals.

Before
proceeding
with
additional
assessment
of
the
Method
5
results,
it
is
necessary
to
examine
the
implications
of
the
regression
analysis.
The
regression
equation
itself
was
found
to
be
'

s
=
0.021
Eq.
4
If
both
sides
of
the
equation
are
divided
by
the
mean
concentration,
the
left­
hand
term
becomes
S/
C,

which
is
the
r
tandard
deviation
(
RSD).
After
performing
this
operation,
the
regression
equation
becomes
RSD
=
0.02
1
lC0.306
~
100%.
Eq.
5
This
implies
that
the
RSD
increases
with
increasing
concentration,
which
is
a
difficult
result
to
rationalize.
Typical
random
errors
that
might
be
attributed
to
the
sample
collection
process,
such
as
failure
to
adequateIy
rinse
particulate
matter
from
the
probe
liner,
should
produce
errors
that
are
roughly
proportionaI
to
the
PM
loading.
Another,
often
observed
error
in
sample
collection
is
for
a
small
portion
of
the
filer
to
stick
to
the
filter
housing.
This
type
of
error
causes
an
underestimation
of
the
mass
of
particulate
collected
but
the
magnitude
of
the
error
will
not
be
a
function
of
concentration.
Random
error
in
the
weighing
process
should
also
be
relatively
independent
of
PM
concentration.
It
can
even
be
argued
that
the
relative
magnitude
of
analytical
error
might
decrease
with
increasing
concentration.
These
considerations
suggest
that
the
value
of
the
slope
term
(
for
any
43
Method)
should
be
expected
to
fall
between
ze
slope
of
the
regression
line
in
Figure
7
and
in
d
1.0.
More
significa
ons
4
and
5
is
too
high.

The
forzoing
statistical
analysis
is
obvio
characteristics
of
those
data.
Two
facto
large
value
for
the
Standard
Error
of
th
1.008
to
1.605.
This
lower
limit
on
the
anticipated
bounds
on
the
regression
equ
by
the
confidence
interval
of
the
statistic
A
separate
argument
has
been
forwarded,
suggesting
that
it
may
not
be
valid
to
group
the
various
Method
5
data
sets
into
a
single
analysis.
The
mathematical
procedures
of
regression
analysis
predict
a
high
value
for
the
slo
excessively
high
S
or
if
the
data
at
lower
concentrations
have
uncharacteristically
low
values
of
S.

In
the
outlier
analysis
presented
earlier,
the
available
data
were
divided
into
two
concentration
groups.
The
high
concentration
group
contained
quad
train
and
octet
data
with
all
tests
reporting
data
at
high
concentra
average
PM
concentration
above
94
rngldscm.
These
data
were
collected
in
the
early
to
mid
1970s.

The
low
concentration
data
included
six
quad
t
aired
train
runs
from
the
tests
at
Pittsfield.
The
Pittsfield
data
was
collected
in
the
mid­
1990s.
The
regression
analysis
is
heavily
weighted
by
the
Dade
County
octet
data
that
is
also
high
concentration
data.
If
the
Dade
County
data
exhibited
uncharacteristically
high
standard
deviation,
the
slope
term
from
the
regression
analysis
would
be
uncharacteristically
high.
It
has
been
suggested
that
the
high
concentration
data
were
collected
shortly
after
Method
5
was
first
developed
and
that
the
field
testing
crews
were
still
learning
how
to
properly
apply
the
Method
was
collected
more
than
a
decade
later,
allowing
the
test
contrast,
the
Pittsfieid
data
sampling
procedures.

A
second
consideration
involves
the
stack
sampling
ti
exception
of
the
Rig0
and
Chandler
data
However,
for
the
tests
at
Pittsfield,
stack
gases
we
difference
in
sampfing
time
could
possibly
result
i
particulate
concentration.
the
data
include
in
Tabfe
5.
With
the
es
were
nominally
r
approximately
4
hours.
This
es
for
data
coIlected
at
lower
44
There
is
certainly
merit
to
an
argument
that
the
skill
level
of
sampling
teams
directly
impact
the
standard
deviation
of
measurement
results.
However,
there
is
no
direct
information
available
to
quantify
the
capability
of
testing
teams
or
to
provide
relative
weighting
of
data
quality.
Similarly,
it
is
reasonable
to
speculate
that
sampling
time
might
impact
measurement
precision
but
there
is
nothing
within
Method
5
that
precludes
extended
sample
collection
times.
For
these
reason,
the
analysis
of
the
Method
5
data
will
continue
based
on
the
entirety
of
the
available
data
but
with
a
strong
caution
that
slope
of
the
true
S
versus
C
relation
is
probably
very
close
to
1.0.

Not
withstanding
the
forgoing
comments,
the
regression
line
in
Figure
7
provides
the
best
estimate
available
for
the
standard
deviation
of
data
collected
using
Method
5.
As
discussed
in
Section
3,
this
estimate
of
standard
deviation
also
defines
the
anticipated
distribution
of
future
measurements
collected
with
that
method.
For
example,
based
on
currently
available
data,
it
is
anticipated
that
repeated
Method
5
measurements
of
a
stack
gas
containing
100
mg/
dscm
of
particulate
matter
would
exhibit
a
standard
deviation
of
8.639
mg/
dscm
or
8.64
%
RSD.
This
is
a
hypothetical
source,
where
the
stack
PM
concentration
is
not
varying
with
time.
Sixty
eight
percent
of
future
measurements
taken
on
this
stack
should
1
within
1.0
cr
(
28.639
mgldscm)
and
ninety­
nine
percent
of
those
measurements
should
fall
w
n
the
range
of
2
2.57*
0.
Thus,
in
the
example
of
a
stack
with
a
PM
loading
of
100
mgldscm,
99
ut
of
100
Method
5
measurements
are
expected
to
fall
within
&
22.20
mg/
dscm
of
the
true
conce
ration.
For
the
average
of
triplicate
measurements,
99
out
of
100
measurements
would
fall
within
the
range
o
f
f
2.57*
0/.\/
3.
Thus,
the
average
of
triplicate
Method
5
measurements
from
this
hypbthetical
stack
is
ex2ected
to
fall
within
5
12.82
mg/
dscm
af
the
true
I
I
concentration.
,

Figure
8
presents
the
predicted
relative
standard
deviation
and
the
99%
bounds
for
future
single
measurements
as
a
function
of
stack
PM
concentration.
Data
in
this
figure
are
based
on
currently
available
data
and
do
not
include
the
effect
of
time
variation
in
source
characteristics.
The
X­
axis
of
Figure
8
represents
the
true
concentration
of
PM
in
the
hypothetical
stack.
Values
indicated
on
the
Y­
axis
represent
the
precision
of
Method
5
at
the
selected
values
of
sack
concentration.
The
99%

bounds
are
also
normalized
by
the
stack
concentration
and
represent
the
anticipated
range
of
individual
measurements.
Compliance
with
regulatory
limits
is
typically
based
on
the
average
of.

45
m
.
I
c
M
I
.
I
;
0
0
N
0
46
c
triplicate
measurements.
The
predicted
range
for
99
out
of
100
triplicate
measurements
is
also
included
in
Figure
8.
When
Method
5
is
applied
to
a
real
stack,
a
wider
range
of
experimental
results
can
be
anticipated
due
to
time
variations
in
source
characteristics.
Data
presented
in
Figure
8
should
not
be
extrapolated
beyond
the
indicated
limits.
Further,
based
on
physical
considerations,
it
is
anticipated
that
the
true
variation
of
these
precision
metrics
with
concentration
are
expected
to
be
a
flat
line
or
even
to
decrease
slightly
(
whereas
the
curves
increase)
with
increasing
concentration.

Data
in
Figure
8
were
generated
using
the
predicted
values
of
standard
deviation,
Recall,
however,

that
there
is
uncertainty
in
those
estimates.
It
is
know
with
95%
confidence
that
the
relationship
between
standard
deviation
and
concentration
falls
between
the
upper
and
lower
confidence
limits
illustrated
in
Figure
7.
If
the
actual
relationship
between
a
versus
C
for
Method
5
conforms
to
the
upper
Confidence
limits,
the
anticipated
range
of
future
Method
5
data
will
be
greater
than
suggested
by
the
data
in
Figure
8.
Conversely,
a
tighter
ranse
of
concentrations
are
anticipated
if
the
variation
in
standard
deviation
conforms
to
the
lower
confidence
limit.
Figure
9
illustrates
the
ranges
of
anticipated
concentrati
data
under
three
scenarios:
(
1)
when
standard
deviation
conforms
to
theL
upper
confidence
limit
)
when
Est.
CT
conforms
to
the
predicted
reIationship;
and
(
3)
when
Est.
CT
conforms
to
the
lower
confidence
limit.
The
X­
axis
in
Figure
9
represents
the
true
concentration
of
PM
in
a
hypothetical
stack
that
does
not
vary
with
time.
The
Y­
axis
represents
the
anticipated
range
of
measured
concentra
using
Method
5.
The
upper
and
lower
curves
in
the
figure
represent
the
upper
and
lower
bo
99
out
of
100
future
measurements,
assuming
that
the
standard
deviation1
equals
the
upper
95%
confidence
limit.
There
is
97.5%
confidence3
that
99
out
of
100
future
measurements
would
fall
below
the
upper
curve
and
97.5%
confidence
that
the
future
measurements
will
fall
above
the
lower
curve.
Similar
curves
are
provided
for
the
cases
where
Est.
Q
conforms
to
the
regression
curve
fit
and
where
Est.
cs
is
equal
to
the
lower
confidence
limit.

Based
on
the
above
anaIysis,
and
concerns
over
the
slope
of
the
regression
equation,
it
is
difficult
to
draw
firm
conclusion
about
the
actual
precision
of
Method
5.
However,
certain
trends
do
appear
obvious.
Within
the
confidence
bounds
of
the
analysis
and
based
on
the
available
data,
it
appears
that
Method
5
standard
deviation
varies
approximately
linearly
with
concentration
and
that
the
395%
confidence
implies
that
there
is
a
2.5%
chance
that
the
a
relationship
falls
above
the
upper
confidence
limit
and
a
2.5%
chance
that
the
relationship
falls
below
the
Iower
confidence
limit.

47
m
m
n
­
U
M
L
.­
I
F1
i
l
C)

P
t
0
P­

,
I
h,

relative
standard
deviation
for
the
method
is
approximately
constant.
For
PM
concentrations
­
3
\
between
15
and
217
mg/
dscm,
the
best
estimate
of
the
relative
standard
deviation
for
Method
5
is
4'
between
about
4.8%
to
12.2%.

(

49
4.2
Method
5i
Data
In
the
middle
1990s
the
US.
 PA
began
develop
ate
measurement
method,

specifically
desizned
to
improve
measurement
precision
at
low
loadings.
The
method
itself
was
published
in
1999
as
part
of
the
new
MACT
regulation
verning
hazardous
waste
incinerators
(
62
FR
52828,
Sept.
30,
1999)
and
has
been
giv
designation
Method
5i.
The
hardware
configuration
for
Method
5i
is
illustrated
in
Figure
10.
Methods
5
and
5i
are
similar
in
many
respects,
but
there
are
two
important
hardware
differences
and
several
operational
differences.
The
primary
hardware
differences
are
in
the
filter
assembly
for
the
two
methods.
Method
5
uses
a
large
diameter
filter
that
must
be
carefully
removed
from
its
holder
as
part
of
the
sample
recovery
process.

Often
a
small
quantity
of
the
collected
particulate
can
be
lost
or
a
small
portion
of
the
filter
itself
can
adhere
to
the
holder
walls.
This
results
in
measurement
imprecision
that
can
potentially
become
critical
when
the
total
particulate
catch
is
small.
Method
5i
uses
a
much
smaller
diameter
filter
and
filter
holder.
The
recovery
and
analysis
procedures
call
for
the
filter
to
remain
in
its
holder
through
the
entire
weishing
process.
This
eliminates
certain
sources
of
random
error
but
it
creates
another
potential
problem.
Since
the
weight
of
the
glass
filter
holder
is
much
larger
than
the
weight
of
the
collected
particulate,
the
analysis
process
must
determine
a
small
weight
gain
in
a
relatively
large
mass.
Because
of
the
small
filter
diameter,
Method
5i
is
intended
for
use
only
under
situations
where
the
particulate
concentration
is
expected
to
be
below
50
mg/
dscm.
The
second
key
feature
implemented
with
Method
5i
is
the
reauirement
that
tests
be
conducted
using
dual
trains.
Moreover,

measurement
precision
requirements
are
defined
as
part
of
the
method.
~

I
Data
on
the
precision
of
Method
5i
comes
from
two
studies
directed
primarily
at
evaluation
of
particulate
matter
continuous
emission
monitors.
The
first
of
these
studies,
conducted
under
EPA
sponsorship,
was
executed
on
a
hazardous
waste
incinerator
owned
by
Dupont
and
located
in
WiImington,
Delaware
(
62
FR
67788).
The
second
study,
sponsored
by
an
industry
consortium,
was
conducted
at
a
hazardous
waste
incinerator
owned
by
the
Eli
Lilly
Company
(
Eli
Lilly,
1999).

Results
from
these
two
studies
provide
a
large
database
for
assessment
of
Method
5i
precision.
Note
that
there
are
numerous
experimental
programs
that
were
recently
completed
(
or
still
underway)

using
Method
5i
for
calibration
of
PM
continuous
emission
monitoring
systems.
Since
Method
5i
50
c
I
51
requires
use
of
dual
trains,
the
available
database
ssessment
of
this
method's
precision
is
expected
to
greatly
expand
over
time.

As
noted
above,
Method
5i
is
a
relatively
new
meas
issues
associated
with
execution
of
the
method
that
si
Both
the
 PA
test
report
and
the
Eli
Liliy
associated
with
obtaining
acceptab
were
performed
but
have
not
been
used
by
either
g
program,
the
only
data
used
are
Tables
9a
and
9b
provide
a
sum
actual
data
pairs,
the
average
concentration
pair,
and
the
small
sample
bias­
corrected
st
there
are
a
variety
of
subtle
ct
the
precision
significant
learning
curve
er
of
paired
train
tests
ysis.
For
the
ReMAP
the
original
study
authors.

ncluded
in
the
tables
are
the
ted
standard
deviation
for
each
Figures
1
la
and
1
1
b
present
deviation
data
versus
averag
corrected
standard
deviation.
Fig
11
b
presents
relative
standard
d
almost
50
mg/
dscm.
Also
note
the
general
char
concentration
range,
the
individual
estimates
of
Stan
discernable
trend
to
either
ethod
5i
standard
small
sample
bias­

gjdscm
while
Figure
om
less
than
10
to
Over
the
entire
distributed
with
no
I
~

1
The
data
in
Tables
9a
and
9b
we
concentration
range
grouping
were
examined
atte
particulate
concentrations.

runs
53,64,66
and
71
fro
sts.
Examination
of
these
data
points
suggests
that
runs
64,
66,
and
71
from
the
Eli
Lilly
tests
are
only
marginally
ng
criteria.
Several
I
r
b
f­

b:

above
the
SPC
screening
criteria.

anaiysis.
The
spreads
for
data
point
53
(
Eli
Lilly)
and
60
(
EPA
D
they
have
been
deleted
from
the
following
analysis.
Accordingly,
those
data
poin
re
retained
for
subsequent
were
sufficiently
large
th
­

il
I
'
L'
Table
9a.
Method
5i
Data
and
Standard
Deviation
­
Eli
LiUy
Data
53
4
TabIe
9a
(
Continued).
Method
5i
Data
and
Stan
54
\
RIM
Number
Avg
Conccnmtion
Standard
S
­
Bias
RSD
*
Bias
mddscm
Deliation
RSD
Concctcd
Conected
Train
A
Train
B
P
1'
9
0
=

8
m
9
0
v
8
m
8
N
8
­

8
1
k,

c
L
a
++

+

++

111
I
B
a
11
I
t
P­

i
L
57
i
k
all
Method
5i
data
were
obtained
using
dual
trains,
no
weighting
of
the
data
is
required.
Results
from
the
regression
analysis
are
presented
in
Table
I
O
below.

Table
10.
Results
of
Regression
Analysis
for
Method
5i
Data
Residuals
T
I
1.32
The
regression
analysis
indicates
that
the
estimated
standard
deviation
varies
with
according
to
the
relationship
concentration
P
=
0.243
5
0.366
or
from
­
0.123
to
0.6094
4
The
predicted
value
ofp
(
0.243)
is
taken
directly
from
the
regression
analysis.
The
2
0.3659
term
is
the
product
of
the
t­
statistic
for
1
14
degrees
of
freedom
(
1.980)
and
the
s
error
forp
(
0.1
848).
This
finding
is
consistent
with
the
earlier
observation
(
see
Figure
1
la)
that
the
standard
deviation
data
appears
to
be
broadiy
distributed
in
a
box
covering
the
full
range
of
concentration
and
standard
deviation
between
zero
and
about
6
mgfdscm.

It
is
mathematically
possible
to
construct
a
range
of
method
precision
metric
for
Method
5i
as
a
function
of
concentration
but
the
indicated
relations
would
have
little
statistical
significance.
In
such
situations,
the
analysis
approach
is
to
calculate
a
pooled
standard
deviation
for
the
data.
The
analysis
procedure
is
described
in
the
Appendix
but
essentially
involves
calculation
of
the
weighted
average
of
the
variance
for
the
available
data.
Variance
is
equal
to
the
square
of
the
standard
deviation
and
the
weighting
factor
for
each
data
point
is
the
number
of
degrees
of
freedom
for
the
data
point.
Since
all
available
Method
5i
data
are
from
paired
train
tests
(
DF=
I)
all
weighting
factors
are
1.0
and
thus
the
pooled
standard
deviation
is
simply
the
square
root
of
the
sum
of
the
squares
for
the
Si
values.
As
expIained
in
the
Appendix,
the
appropriate
values
of
Si
to
calculate
the
pooled
standard
deviation
are
taken
directly
from
the
raw
data
without
adjustment
for
small
sample
bias.

The
above
described
pooling
procedures
were
applied
to
the
data
in
Table
9a
and
b.
There
are
114
individual
data
pairs
and
the
sum
of
the
individual
variances
is
234.13.
Accordingly
the
pooled
variance
is
2.054
(
234.13/
114)
and
the
pooled
standard
deviation
is
1.433
mg/
dscm.
This
single
value
is
the
best
estimate
available
for
the
Estimated
o
for
Method
5.

Table
1
in
the
Appendices
provides
a
list
of
factors
to
calculate
the
confidence
intervaI
(
at
the
95%

confidence
level)
for
a
pooIed
value
of
Est.
cr.
Using
linear
interpolation,
the
values
of
P0.025
and
P0.975
are
0.883
and
1.155
respectively.
Accordingly,
the
upper
and
Iower
95%
confidence
intervals
on
Estimated
c
are
1.265
and
1.655
mg/
dscm
respectively.
The
confidence
intervals
are
afso
constant
values
­
not
a
function
of
concentration.
Figure
12
presents
a
scatter
plot
of
the
Method
Si
data
along
with
the
estimated
values
of
standard
deviation
and
the
confidence
intervals.

Since
Est.
cr
and
the
confidence
intervals
are
constants,
they
are
illustrated
as
straight
lines
in
Figure
12.

59
.
.
I
'
1
­
0
8
I
!
The
estimate
of
standard
deviation
provides
information
on
the
anticipated
range
of
future
measurements
using
Method
5i.
Figure
13
presents
three
precision.
metrics
for
Method
5i.
Included
are
the
relative
standard
deviation,
the
expected
bounds
for
99
out
of
100
future
individual
measurements
as
well
as
the
anticipated
bounds
for
the
average
of
triplicate
measurements.
These
precision
metrics
have
been
normalized
by
the
concentration.
Thus,
even
though
Est.
G
is
a
constant,
normalized
precision
metrics
are
strong
functions
of
concentration.

The
general
presentation
approach
adopted
for
the
current
report
is
to
present
a
figure
defining
the
anticipated
range
of
concentrations
for
99
out
of
100
future
measurements,
under
three
different
scenarios
for
an
assumed
variation
of
standard
deviation.
Such
a
figure
provides
little
information
under
conditions
where
the
standard
deviation
is
evaluated
to
be
essentially
a
constant.
It
is
much
cleaner
to
simply
state
the
anticipated
variation
in
future
measurements.

If
the
true
standard
deviation
is
essentiaily
equal
to
the
pooled
standard
deviation,
then
99
out
of
100
future
Method
Si
measurements
are
anticipated
to
faif
with
2
3.68
mg/
dscm
of
the
true
concentration.
This
assumes
that
there
is
no
bias
in
the
measurements
and
that
the
m
e
concentration
is
between
about
4
and
50
mg/
dscm.

If
the
m
e
standard
deviation
for
Method
5i
is
essentially
equal
to
the
lower
95%

confidence
interval,
then
99
out
of
100
future
measurements
are
anticipated
to
fall
with
k
3.25
mg/
dscrn
of
the
true
concentration.

If
the
true
standard
deviation
for
Method
5i
is
essentially
equal
to
the
upper
95%

confidence
interval,
then
99
out
of
100
future
measurements
are
anticipated
to
fall
with
t
4.25
mg/
dscm
of
the
true
concentration.

4.3
Discussion
of
Particulate
Matter
Measurement
Results
The
forgoing
discussion
provides
strikingly
different
conclusions
relative
to
the
precision
of
Methods
5
and
5i.
Specifically,
the
regression
analysis
indicates
that
the
standard
deviation
of
Method
5
is
a
strong
function
of
concentration.
In
fact,
it
is
suggested
that
a
reasonable
interpretation
of
the
data
is
that
Method
5
has
a
constant
relative
standard
deviation.
In
contrast,

61
c,
u
E
Q)
L
3
M
tz
0
0
v)

0
w
0
c1
0
62
!
LA
I
`
Ld
analysis
of
Method
5i
data
could
detect
no
relationship
between
standard
deviation
and
concentration
at
the
95%
confidence
level.

Prior
discussion
has
suggested
that
random
error
associated
with
the
sample
collection
process
tends
to
drive
the
power
function
term
@)
in
the
regression
equation
toward
1.0.
Similarly,
random
error
in
the
analytical
process
tends
to
drive
p
toward
zero.
These
are
only
anticipated
trends
but
they
do
suggest
that
different
types
of
random
error
have
driven
the
assessment
of
these
two
particulate
measurement
methods.

w
'

When
Method
5
is
applied
at
high
particulate
concentration,
it
is
reasonable
to
anticipate
that
the
fiIter
weighing
process
is
sufficiently
precise
that
it
contributes
negligibly
to
the
overall
precision
of
the
method.
A
large
portion
of
the
multi­
train
Method
5
data
was
collected
from
high
concentration
stacks
(>
90
mgidscm).
Further,
the
high
concentration
data
were
collected
during
a
time
frame
when
many
sampling
teams
were
gaining
experience
with
application
of
the
method.
Thus,
results
from
the
statistical
analysis
of
Method
5
data
can
ea
y
be
rationalized.
1
:
/
B_
u
h
I
The
Method
5i
data
were
all
collected
under
low
particulate
concentration
conditions
(­
GO
mg/
dscm
with
the
majority
of
the
data
at
much
lower
concentration).
Under
these
conditions,
it
is
anticipated
Ld
I
that
imprecision
of
the
weighing
process
may
.
contribute
significantly
to
the
overall
Method's
precision.
As
described
earlier,
collected
samples
must
be
dried
before
recording
the
final
particulate
weight
gain.
Collected
samples
are
placed
in
a
dessicator
and
repeatedly
weighed
untii
the
tare
weight
is
stabiIized.
The
sample
is
considered
to
have
reached
its
final
weight
if
the
repeated
weighing5
agree
within
k0.5
mg
or
21.0%
of
the
tare
weight,
whichever
is
greater.
For
a
typical
Method
5
or
5i
particulate
measurement,
a
sample
is
collected
from
the
stack
for
approximately
one
hour
during
which
time
approximately
1
cubic
meter
of
flue
gas
is
extracted.

Thus
the
process
of
determining
particulate
loading
on
the
filter
is
no
more
precise
than
the
concentration
measurement
is
no
more
precise
than
20.5
mg/
dscm.
That
c
measurement
imprecision
is
insignificant
when
the
stack
concentration
is
on
the
order
of
100
mg/
dscm.
However,
for
measurements
in
stacks
with
PM
concentrations
on
the
order
of
10
mg/
dscm,
this
represents
a
significant
relative
contribution
to
overall
measurement
precision.

5
Samples
must
remain
in
a
dessicator
for
a
minimum
of
6
hours
between
weighings.
i.

1
L
L
P
,
L
.
L
A
r
Based
on
the
above
considerations
it
is
reasonable
to
anticipate
that
the
analytical
portion
of
Method
5i
measurements
will
contribute
significantly
to
the
overall
precision
of
the
method
and
that
random
error
in
the
weighing
p
also
subject
to
random
method
precision
should
vary
with
concentratio
available
Method
5i
data
have
been
collected
measurement
teams
expended
significant
effo
data
from
numerous
tests
were
discarded
as
a
result
of
personnel
climbing
the
learning
curve.

Finally,
all
data
in
the
Method
5i
data
set
above
about
15%.
All
of
these
factors
c
the
sampling
process
has
a
small
contribution
to
s
will
not
vary
significantly
with
particulate
concentration.
Method
5i
is
associated
with
The
above
considerations
are
provided
as
one
possible
rationalization
for
the
observed
differences
in
the
precision
characteristics
of
the
two
methods.
the
characteristics
of
the
measurement
methods
and
the
c
used
to
assess
the
methods.

As
regards
Method
5,
it
appears
like
mpling
teams
collecting
data
in
the
low
and
high
concentration
ran
ed
to
assess
the
method.
od
5
standard
deviation
on
concentration
is
less
than
indicated
by
the
current
data
set.
Further
it
is
likely
that
As
regards
Method
ji,
recall
that
regression
analy
CT
is
a
function
of
particulate
concentrati
can
be
confirmed
at
the
95%
confiden
performed.
Consid
for
Methods
5
and
5,
it
is
likely
that
stan
with
increasing
stack
particulate
conc
ncludes
that
no
relationship
It
is
important
to
place
the
above
considerations
into
practical
perspective.
When
Method
Si
is
used
to
measure
PM
loading
in
low
particulat
data
suggests
that
99
O
u
t
of
100
future
true
concentration.
The
original
data
set
(
before
outlier
screening)
contained
1
16
pairs
of
dual
train
­
f
L
n
t
results.
Assuming
that
the
true
concentration
for
each
test
is
the
average
of
the
test
pair,
dividing
the
spread
in
each
pair
by
2
provides
a
crude
way
to
assess
this
prediction.
For
the
entire
data
set
(
Tables
10a
and
10b)
the
maximum
spread
between
any
data
pair
occurred
in
run
number
53
from
the
Eli
Lilly
data
set.
The
reported
concentrations
for
that
data
pair
were
30.3
and
37.7
with
an
average
concentration
of
34.0
mg/
dscm.
Thus,
for
I
I6
paired
measurements
(
232
applications
of
the
Method)
the
maximum
difference
between
the
measured
concentration
and
the
estimated
true
concentration
was
3.7
mg/
dscm.
Interestingly,
that
measurement
was
determined
to
be
an
outlier
and
was
eliminated
from
the
overall
analysis.

It
is
certainly
possible
(
even
likely)
that
the
precision
of
Method
5i
has
some
dependence
on
concentration.
However,
the
forgoing
analysis
suggests
that
the
constant
si,
oma
assumption
provides
a
reasonable
and
practical
estimate
of
the
Method's
precision.

It
is
unlikely
that
the
imprecision
of
Method
5
increases
as
rapidly
with
concentration
as
suggested
by
the
data
in
Figures
7,8
and
9.
It
is
expected
that
increased
experience
of
field
sampling
teams,

including
the
lessons
learned
from
application
of
Method
5,
have
already
reduced
the
range
of
random
errors
impacting
Method
5
results.
It
is
anticipated
that
the
inherent
precision
of
Method
5
should
be
similar
to
that
for
Method
5i
but
CJ
for
the
method
almost
certainly
does
increase
with
concentration.
Note
that
the
Method
5
data
from
the
Pittsfield
tests
were
collected
in
the
mid­
1990s
and
should
reflect
increased
experience
for
the
testing
team.
Data
from
this
test
series
(
16
valid
data
pairs
)
were
examined
to
determine
the
range
of
the
data
pairs
relative
to
the
pair
average.
For
runs
15
and
17,
the
spread
minus
the
mean
were
4.4
and
6.8
mg/
dscm
respectively
while
the
spreads
for
the
remainder
of
the
data
were
less
than
3.5
mg/
dscm.
This
suggests
that
Method
5
might
provide
'
slightly
less
precise
results
than
Method
5i
but
not
dramatically
less.
Even
this
observation
must
be
tempered
by
the
fact
that
the
standard
deviation
for
the
method
increases
with
increasing
concentration.
Based
on
these
qualitative
considerations,
it
is
suggested
that
the
data
in
Figures
7,8,

and
9
should
be
taken
a5
an
upper
limit
on
the
imprecision
of
Method
5.
To
fully
assess
Method
5
precision
at
higher
concentrations
(>
1
OOmg/
dscm)
additional
multi
train
data
is
required
in
that
concentration
range.

65
This
page
Intentionally
Left
Blank
r
t
5.0
EPA
Method
23
For
Measuring
Dioxin
and
Furan
Emissions
The
EPA
method
for
measurement
of
dioxin
and
furan
stack
emissions
is
denoted
as
Method
23
(
56
FR
67788
and
40
CFR
Part
60
­
Appendix
A).
The
hardware
for
the
method
is
illustrated
in
Figure
14
and
has
several
similarities
to
the
hardware
discussed
previously
for
Method
5.
The
major
difference
is
addition
of
a
module
filled
with
an
absorbent
material
known
as
XAD.
A
small
circulating
pump
maintains
the
temperature
of
the
XAD
module
at
approximately
60"
F.
The
XAD
module
is
spiked
with
known
quantities
of
labeled
compounds
that
are
used
for
both
system
calibration
and
to
experimentally
determine
the
recovery
of
the
overall
sampling
and
analysis
.

process.

The
quantity
of
dioxin
and
furan
collected
and
analyzed
by
the
method
is
extremely
small.
Typical
stack
concentrations
are
on
the
order
of
a
few
ng/
dscm.
To
collect
sufficient
material
for
analysis
by
high
resolution
GC/
MS,
each
sampling
run
extends
for
at
least'
three
hours
and
may
last
for
more
than
6
hours.
There
are
eight
possible
homologues
of
both
polychIorinated
dibenzo(
p)
dioxin
and
dibenzofuran.
Only
those
homolo,
oues
with
four
to
eight
chlorine
atoms
are
adverse
health
effects.
Acco
ngly,
some
environmental
regulations
@
e.,
the
rules
ipal
waste
combustors)
limit
the
release
of
all
tetra
through
octa­
chlorinated
dioxins
nt
for
the
fact
that
different
dioxin
and
furan
congeners
and
ikrans.
Other
regulations
take
ac
have
vastly
different
toxici
Most
of
the
world
has
adopted
a
listing
of
relative
conge
that
was
developed
under
the
auspices
of
NATO.
These
relative
toxicity
factors
are
m
the
concentration
of
each
congener
to
yield
an
emission
concentration
that
is
equiv
toxicity
that
would
occur
if
all
of
the
indicated
mass
was
found
as
the
most
toxi
2,3,7,8
tetrachloro
dibenzo@)
dioxin).
Emissions
expressed
in
this
manner
are
International
Toxic
Equivalent,
or
ITEQ.
Regardless
of
whether
an
emission
stan
as
total
mass
of
tetra
through:
octa
or
as
ITEQ,
the
sampling
and
analysis
proce
Method
23
is
the
same.
The
only
difference
is
that
the
ITEQ
process
provides
significant
weighting
factors
to
a
select
group
of
individual
congeners.
As
will
be
shown
in
material
that
follows,

application
of
these
weighting
factors
does
impact
the
indicated
precision
of
the
measurement
method.

67
5.1
Available
Mufti­
Train
Data
for
Method
23
as
Total
PCDDPCDF
Extensive
effort
has
been
expended
in
development
of
sampling
and
analytical
methodology
for
determination
of
dioxin
and
furan
emission
concentrations.
Separate
procedures
have
evolved
in
Europe,
Canada
and
the
US
which
are
similar
in
many
respects.
There
are
however,
small
differences
in
the
analytical
procedures
that
may
have
significant
impact
on
the
precision
of
measurement
results.
Accordingly,
the
current
study
focuses
onIy
on
US
EPA
Method
23
since
that
is
the
method
which
must
be
used
to
determine
compliance
with
US
emission
standards.
Before
presenting
the
available
multi­
train
data
for
Method
23,
it
is
important
to
note
that
the
procedures
used
by
EPA
to
validate
Method
23
are
different
from
those
used
to
validate
other
methods.

Specifically,
in
lieu
of
gathering
multi­
train
data
from
one
or
more
source
categories,
the
Agency
I
developed
hardware
and
a
procedure
for
dynamically
spiking
a
sampling
train
with
known
quantities
of
isotopically
la
eled
dioxin
and
furan
congeners.
Validation
of
the
method
focused
on
experiments
determining
the
fractional
recovery
of
the
dynamically
spiked
compounds.

There
are
a
variety
of
approaches
that
may
be
used
to
validate
performance
of
a
method.

Dynamically
spiking
a
sampling
train
with
a
known
quantity
of
a
tracer
compound
is
a
potentially
valid
approach.
In
fact
many
of
the
EPA
method
validation
efforts
have
used
dynamic
spiking
in
quad
train
tests
to
gain
information
on
both
precision
and
bias
of
an
emerging
method.
However,
use
of
dynamic
spiking
experiments
as
the
sole
approach
for
method
validation
is
valid
only
under
conditions
where
there
is
no
possibility
for
formation
of
the
pollutant
of
interest
in
the
sampling
train
itself
(
e.
g.,
for
methods
measuring
the
total
emission
of
an
element
such
as
a
heavy
metal).
As
regards
dioxin
and
furan
measurement,
there
is
a
significant
potential
for
formation
of
these
compounds
under
thermal
conditions
that
may
occur
within
a
sampling
probe
or
within
the
hot
filter
box
of
the
Method.
The
potential
for
formation
of
the
target
analytes
within
the
sampling
train
raises
serious
concern
about
the
completeness
of
EPA
studies
validating
Method
23.

The
report
describing
the
Method
23
validation
effort
indicates
that
a
quad­
train
was
dynamically
spiked
with
isotopicaily
labeled
dioxin
and
furan
congeners
(
MRI,
1991).
The
report
indicates
that
the
collected
samples
were
analyzed
for
both
the
native
congeners
as
well
as
the
dynamically
spiked
congeners.
In
fact,
the
report
includes
tables
listing
the
collected
mass
of
native
dioxin
and
furan
in
69
5.2
Analysis
of
Method
23
Data
for
Total
Dioxin
and
Furan.
I
r
k'
Table
1
1.
Method
23
Data
as
Total
Mass
of
Tetra
through
Octa
Dioxi
t
L
71
vi
rl
c)
L
W
a
tk
.
I
f
u
d
111
73
.
The
SPS
data
outlier
procedures
were
applied
to
the
data
in
Table
11.
Several
different
range
groupings
were
evaluated
and
each
grouping
identified
Run
number
7
from
the
Rigo,
and
Chandler
tests
as
an
outlier.
The
basis
for
this
identification
is
easily
seen
in
Figure
15.
However,
when
presented
as
relative
standard
deviatio
remainder
of
the
data.
The
SPC
outlie
data
appears
to
be
abnormally
large.
,
In
decision
was
made
to
retain
the
data
for
the
n
number
7
is
only
slightly
identify
data
points
where
the
span
of
data
point
has
been
examined
and
a
Data
from
Table
1
I
were
submitted
to
regression
analysis
to
de
weighting
were
required
since
all
available
results
are
from
indicate
that
the
estimated
standard
deviation
varies
as
a
concentration
according
to
the
equation
S
(
for
Method
23
as
total
PCDD/
PCDF)
=
0.2722
*
Co.
56.

p
=
0.56
k
0.48
orp
lies
between
0.08
and
1.04.

Figure
17
presents
the
regression
results
including
the
small
sample
bias­
corrected
data,
the
regression
line
and
the
upper
and
lower
95%
confiden
precision
metrics
for
Method
23.
Data
between
Est.
Q
and
C.
If
that
relation
is
ng/
dscm
(
excluding
temporal
variation),
99
out
of
should
fall
within
f
30%
of
the
true
concentration.
Source
variation
will
increase
those
bounds.
ents
using
Method
23
r­

w
k
E
L
J
i
0
s
c
0
0
75
E­
L,
r
a
L:

76
It
is
critical
to
recall
that
there
is
considerable
uncertainty
in
the
value
of
the
slope
term
in
the
regression
equation.
Figure
19
illustrates
the
anticipated
bounds
on
99
out
of
100
individual
measurements
for
three
different
scenarios
on
the
S
versus
C
relationship.
I
f
the
regression
relation
is
the
proper
description
of
how
standard
deviation
varies
with
concentration,
the
anticipated
spread
of
future
data
is
relatively
tight.
For
example,
in
that
situation,
samplins
a
stack
that
actually
contains
20
ng/
dscm
of
total
dioxin
plus
furan
should
result
in
99
out
of
100
measurements
falling
in
the
range
of
16.3
to
23.7
ng/
dscm.
Conversely,
if
the
standard
deviation
of
the
method
is
more
closely
described
by
the
upper
confidence
interval,
a
much
broader
range
of
data
can
be
anticipated.

In
this
case,
sampling
the
etical
stack
containing
20
ngldscm
dioxin
and
furan
using
Method
23
should
yield
99
out
of
1
surements
falling
in
the
range
of
9.13
to
30.87
ng/
dscm.
LL*
*

F
a
&
h
Y
L
r
P*

L
F""

b
t
I
Table
12
presents
a
tabular
summary
of
the
anticipated
range
of
measured
PCDDPCDF
concentration.
This
table
i
ased
on
the
assumption
that
the
regression
equation
properly
describes
the
variation
of
standard
deviation
with
concentration
for
the
best
estimate
of
standard
deviation.

This
is
the
best
estimate
available
for
method
precision
based
on
the
available
data.
It
is
critically
t
4
­
1
YLU"

important
to
reiterate
that
concentration
information
presented
in
this
table
(
as,
well
as
the
concentration
data
in
all
the
tables
and
figure
in
this
report)
are
not
corrected
to
constant
excess
air
level.
An
exam
s
in
order.
Assume
that
a
facility
operates
at
11%
0
2
in
the
stack
and
must
comply
with
a
Adjusting
the
emission
standard
from
7
0
2
shows
that
the
facility
must
maintain
PCDDRCDF
stack
concentration
below
24.9
ng/
dscm.
If
the
true
stack
concentration
was
exactly
24.9
ng/
dscm,
imprecision
from
repeated
application
of
Method
2
ouid
produce
99
out
of
100
measurement
results
ranging
from
20.7
to
29.2
ng/
dscm.
When
co
d
back
to
the
basis
of
the
standard,
the
anticipated
data
range
is
*
from
29.1
to
40.9
ng/
dscm
@
7%
02.
At
the
95%
confidence
level
for
this
hypothetical
facili
single
measurement
below
20.7ng/
dscm
is
below
the
standard
while
a
measurement
above
29.2
ngldscm
is
above
the
standard.
At
the
95%
confidence
level,
resuIts
between
20.7
and
29.2
could
be
E
PCDF
emission
limit
of
35
ng/
dscm
I@

7%
02.

I
&
LA
P
m
E
L
i
L­

I
either
in
or
out
of
actual
compliance.
CY
c""
The
above
analysis
clearly
points
to
the
fact
that
there
is
an
insufficient
body
of
data
available
to
adequately
assess
the
precision
of
EPA
Method
23.
The
limited
quantity
of
available
data
suggests
that
the
precision
of
Method
23
conforms
to
the
predictions
presented
in
Table
12.
However,
there
is
t
'
Table
12.

Concentration
ng/
dscm
&

Anticipated
Range
of
Measured
PCDDRCDF
Concentration
Based
on
Best
Estimate
of
Method
23
Standard
Deviation
Measurements
Measurements
Lower
Limit
lupper
Limit
Lower
Limit1
Upper
Limj
I
I
0.5
0.97
0.03
0.77
0.23
2.0
4.0
6.0
8.0
0.97
2.60
I
1.40
3.03
5.52
2.4%
4.88
3.12
7.91
4.09
7.10
4.90
10.2
5.76
9.29
6.71
I
12.5
10.0
12.0
7.46
11.5
8.53
14.8
9.19
17.1
10.9
14.0
16.0
79
13.6
10.4
15.8
12.2
19.3
12.7
17.9
I
14.1
21.5
1
14.5
18.0
20.0
22.0
23.7
16.3
25.9
18.1
20.0
16.0
22.2
17.8
24.3
19.7
28.1
19.9
26.4
24.0
21.6
30.3
26.0
21.7
28.5
23.5
32.5
23.5
28.0
30.6
25.4
significant
uncertainty
associated
with
this
analysis.
if
the
actual
method
precision
conforms
to
the
upper
confidence
interval
in
the
analysis,
a
can
only
be
resolved
by
g
particular
importance
wo
included
in
the
current
data
set.
can
be
anticipated.
The
issue
of
concentrations.
Of
ions
above
the
levels
80
5.3
Available
Multi­
Train
Data
for
Method
23
as
ITEQ.

Data
for
Method
23,
with
results
expressed
as
ITEQ,
are
the
same
as
those
for
Method
23
with
results
expressed
as
total
m
a
s
of
tetra
through
octa
dioxin
plus
furan.
Table
13
presents
the
ITEQ
results
including
the
results
of
each
run,
the
average
concentration
and
the
calcuiated
standard
deviation
from
the
run.
Also
included
are
data
following
application
of
the
srnall­

sample,
bias
correction
factor.
These
data
are
illustrated
in
Figures
20
and
21
as
scatter
plots
of
standard
deviation
and
relative
standard
deviation
versus
the
average
concentration
calculated
fiom
the
data
pair.
The
results
are
generally
similar
to
those
for
the
Method
as
total
PCDDPCDE
except
that
the
scales
are
greatly
reduced.
The
range
of
the
concentration
data
is
i
The
above
Method
23
data
were
submitted
to
regression
analysis
and
results
indicate
that
S
is
related
to
C
according
to
the
equation,

S
=
0.4795C0.345.

Unfortunately
the
t­
statistic
on
the
power
term
is
only
1.02
which
is
well
below
the
critical
value
lies
that
the
regression
equation
could
have
occurred
by
chance
and
that,
at
e
level,
no
statistically
meaningful
relationship
between
S
and
C
was
detected.

result
is
easily
observable
in
the
data
presented
in
Figure
20.
Note
that
the
appear
as
a
scattering
of
points
at
concentrations
below
0.4
ng
ITEQ/
dscm
onlbelow
0.04
ng
ITEQ/
dscm.
There
are
four
data
points
with
standard
054
dg
ITEQ/
dscm.
These
data
might
suggest
that
S
increases
with
increasing
t
e
f
UT
points
are
discounted,
one
can
easily
envision
an
opposite
slope
to
a
rkgression
,
analysis
allows
the
potential
range
of
the
power
term
to
be
/
confidence
level,
thep
parameter
could
be
as
large
as
1.051
and
as
small
as
­
0.36.
The
magnidde
of
the
'
uncertainty
concerning
the
precision
of
Method
23
for
dioxin
and
furan
as
ITEQ
is
further
ilhstrated
in
Figure
22.
This
figure
shows
the
small
sample
bias­

corrected
data,
the
regression
equation
and
the
upper
and
lower
confidence
intervals.
It
is
I
,

?

%
I
u
s
0
f
r4
1
00
k
.
I
+

+

r­
co
m
w
m
cv
8
8
8
8
8
8
83
0
I
­­.
I
d
0
0
9
­
0
0
­
0
2
8
I
85
Method.

Since
the
above
analysis
failed
to
determine
a
relationship
between
CT
and
C,
the
alternative
approach
is
to
reevaluate
the
data
assuming
that
CT
is
a
constant.
The
pooled
analysis
procedure
is
to
first
determine
the
pooled
variance.
The
22
individual
values
of
S
from
Table
13
are
squared,
summed,
and
then
divided
by
22
to
determine
the
pooled
variance.
The
pooled
variance
=
0.000712.
The
square
root
of
this
paramet
s
taken
to
determine
the
pooled
standard
deviation;
pooled
S
=
0.0267
with
22
degrees
o
provide
factors
for
determining
the
95%
confidence
bounds
on
0.
Those
bounds
are
0.0207
and
I
0.0374.

Figure
23
presents
the
pooled
standard
deviation
and
the
95%
confidence
intervals
overlaid
with
the
experimental
data.
Since
the
estimated
standard
deviation
and
the
confidence
intervals
are
constants,
they
are
illustrated
as
straight
lines
in
the
Figure.
The
various
precision
metrics
are
presented
in
Figure
24.
e
are
normalized
by
the
average
concentration
and
thus
show
The
data
shown
in
this
inverse
relationship
If
the
characteristic
standard
deviation
of
Method
deviation,
then
measurement
imprecision
should
cause
99
out
of
100
future
measurements
I
to
deviate
f?
om
the
true
concentration
no
more
than
20.068
ng
ITEQ/
dscm.
If
the
Method's
characteristic
standard
deviation
is
more
appropriately
approximated
by
the
upper
95%

confidence
bound,
then
method
imprecision
should
cause
99
out
of
10
deviate
from
the
true
concentration
by
no
more
than
59.095
ng
ITEQIdscm.

It
is
critically
important
that
the
above
estimates
for
Method
23
imprecision
be
placed
in
perspective.
Recent
EPA
regulations
governing
hazardous
waste
co
stion
SY
stems
and
fossil
fbeI
fired
cement
plants
have
set
dioxin
and
furan
emission
limits
of
0.2
ng
ITEQ/
dscm
@
7%
\

86
Y
L,

0
0
­
0
87
cu
a2
m
I
I
.
.
,
*
I
.
.

I
.

88
c1
I
L
0,
The
potential
range
for
future
measurements
fkom
measurement
imprecision
is
large
relative
to
the
standard.
At
the
upper
95
%
confidence
limit,
the
possible
range
of
a
single
measurement
(
minus
0.095
to
plus
0.095
=
0.19)
is
essentially
equal
the
standard
itself
EIC
i"""
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kd
i
i
f
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Page
Intentionally
Left
Blank
90
r
i
6.0
EPA
Me
od
26
for
Hydrochloric
Acid
The
method
for
measurement
of
hydrochloric
acid
and
chlorine
gas
is
designated
EPA
Method
26
and
is
fully
described
in
4OCFR
Part
60
­
Appendix
A
under
the
heading
for
the
Method.
The
hardware
arrangement
for
Method
26
is
illustrated
in
Figure
25.
Impingers
in
the
back
half
of
the
train
are
filled
with
sulfuric
acid
to
collect
HCl
while
the
sodium
hydroxide
impingers
collect
chlorine
gas.

ata
for
Method
26
are
available
from
three
sources,
summarized
in
Table
14.
As
indicated
in
the
table,
relatively
high
HCl
concentration
data
(
about
80
to
220
mgdscm)
are
provided
by
the
tests
of
Rig0
and
Chandler
at
an
MWC
facility
in
Pittsfield,
MA
Chandler,
1997).
These
data
were
collected
using
a
quad
train.
Entropy
Corp
collec
CI
concentration
(
4
to
74
mg/
dscm),
as
part
of
the
EPNOAQPS
effort
and
Margeson,
1989).
Two
ofthe
EPA/
OAQPS
tests
(
run
Method
26
(
Steinberg
and
12)
were
perfo
midget
impingers
in
what
is
now
considered
the
standard
Method
26
procedure.
The
other
trains
used
fidl
size
impingers
typically
associated
with
Method
5
trains.
A
significant
bias
detected
in
the
results
from
run
number
12
and
those
results
are
not
included
in
the
ReMAP
analysis.
The
remainder
of
the
EPNOAQPS
test
was
conducted
using
dual
trains
with
midget
impingers.
Finally,
very
low
HC1
concentration
data
(
0.3
to
2.0
mg/
dscm
HCI)
were
collected
by
EER
as
part
of
an
effort
for
EPNOSW
(
EER,
1997).
These
EPNOSW
tests
were
executed
using
quad­
trains.
Data
outlier
analysis
was
performed
on
these
data
and
alI
data
points
passed
the
outlier
criteria
set
by
the
SPC
procedures.

Figures
26
and
27
provide
scatter
plots
of
the
available
HCI
data
illustrating
the
standard
deviation
as
a
fimction
of
average
HC1
concentration.
Figure
26
presents
all
of
the
available
data
while
Figure
27
includes
only
data
from
the
EPNOAQPS
and
EPNOSW
tests
(
low
HCl
concentration
data).
Figure
28­
presents
these
data
as
relative
standard
deviation.
Data
presented
in
all
three
of
these
figures
have
been
corrected
for
smali
sample
bias.
As
shown,
when
the
91
L
P
I
T
(""

LA­.%

Table
14.
Method
26
Multi­
Train
Data
and
Standard
Deviation
for
HCI
Fq
L
E
l
i3
=
E
I
a
M
Lrc
.
I
Q
w
n
t;
(
v
95
0
(
0
0
w
0
m
0
w
0
F
0
.
,
_
I.._..
­
.._
­..
..
,_,
"...
average
HCI
concentration
is
above
about
10
mg/
dscm,
relative
standard
deviation
(
RSD)
for
the
various
runs
is
consistently
below
10%.
Below
IO
mg/
dscm,
the
RSD
data
tend
to
increase
sharply.
Figures
26
and
27
show
that
the
sharp
increase
in
RSD
is
caused
by
the
rapidly
decreasing
value
of
the
Concentration
rather
than
a
sharp
increase
in
standard
deviation.
f
After
applying
appropriate
weighting
factors,
the
data
in
Table
14
were
submitted
to
a
weighted
regression
analysis
and
results
indicate
that
the
estimated
standard
deviation
for
the
Method
varies
with
HC1
concentration
according
to
the
relation:

S
(
Method
26
for
HCI)
=
0.15259
*
C0.803.

This
equation
includes
both
the
small
sample
bias
correction
and
the
bias
correction
associated
with
the
log­
log
transfornation.
The
concentration
term
in
this
equation
is
in
units
of
mg/
dscm.

The
t­
statistic
for
the
regression
is
17.22,
which
is
well
above
the
critical
t­
statistic
for
95%

confidence
and
29
degrees
of
freedom
(
2.042).
At
the
95%
confidence
level,
the
value
of
the
power
coefficient
is
P
=
0.803
k
0.095
or
between
the
limits
of
0.707
and
0.898.

Figure
29
presents
a
plot
of
the
data,
along
with
the
regression
line
and
the
upper
and
lower
confidence
limits.
Note
that
the
confidence
inte
Is
do
not
deviate
sigificantIy
from
the
regression
line.
Using
the
regression
equation
to
describe
the
variation
of
Est.
G
with
concentration,
estimates
can
be
developed
for
the
probable
variation
in
measurements
associated
with
imprecision
in
the
Method
itself
Figure
30
presents
resuIts
of
those
calculations
including
the
variation
in
relative
standard
deviation,
the
estimated
spread
for
99
out
of
100
single
measurements,
and
the
estimated
spread
for
99
out
of
100
triplicate
measurements.
The
anticipated
spread
for
measurements
is
projected
to
be
relatively
close
to
the
true
stack
concentration.
For
example,
if
Method
26
is
applied
to
a
stack
containing
40
mg/
dscm
HCl,

results
from
99
out
of
100
triplicate
measurements
are
expected
fall
within
10.9
'
YO
of
the
true
concentration.
At
Iower
concentrations,
the
range
of
future
measurements
is
predicted
to
97
*
4
0
0
0
4
0
0
0
H
98
t
4
E
w
v1
0
.
I
L
Y
S
0
m
0
Q)
.­.
.
I
L
s
0
0
*
m
s
99
0
VI
(
u
0
0
(
u
0
VI
I
ul
I
0
G
ti
0
~
~~
i~~
~
~
~~
~~~
~

increase
(
as
a
percentage
of
the
true
concentration)

conditions,
the
actual
spread
in
data
&
om
method
imprecision
is
predicted
to
be
relatively
small.

For
example,
99
out
of
100
triplicate
measurements
in
a
stack
containing
1.0
mgldscm
HCI
are
expected
to
fa11
within
the
bounds
of
0.80
and
1.20
mgldscm.

The
data
in
Figure
30
assumed
that
the
standard
deviation
for
Method
26
varied
according
to
the
regression
equation.
Figure
29
presented
the
95%
confidence
bounds
for
the
regression
equation.

Those
data
have
been
used
to
estimate
the
anticipated
range
for
99
out
of
100
future
measurements
assuming
confidence
interval,
the
Results
for
those
calcul
The
best
estimate
of
the
precision
of
Method
26
is
provided
by
the
data
were
presented
graphically
in
Fi
these
data
in
tabular
form.
!
The
first
corrected
for
excess
oxygen).
The
second
out
of
100
future
single
measurements
(
at
the
fifth
columns
provide
the
i
IO1
I
i
I
i
I
I
I
1
i
1
E
Table
15.
Range
of
Anticipated
Future
HC
102
PY
E
l
b
r
i
L
,­

I
­­
I
i?
t
i
s
,

.
.
.
7.0
EPA
Methods
29,
lOla
and
lOlb
for
Mercury
Considerable
effort
has
been
expended
developing
methods
for
determination
of
mercury
emissions
from
combustion
sources.
For
details
on
the
Methods,
refer
to
40
CFR
Part
60
­
Appendix
A
under
the
headings
Method
29
and
Method
101.
Mercury
is
emitted
from
combustion
sources
as
either
the
base
metal
or
in
the
+
2
vaience­
state.
It
may
be
in
the
vapor­

state
or
it
may
be
associated
with
solid
phase
material.
At
least
three
EPA
Methods
have
been
published
or
proposed
and
one
additional
method
is
under
active
development.
Figure
32
illustrates
the
hardware
used
for
Method
101%
which
is
the
simplest
of
the
mercury
procedures.

The
sample
gas
is
passed
through
a
heated
filter
and
then
goes
to
impingers
filed
with
a
KMn04­

10?
40H,
S0,
(
permanganate)
solution.
After
the
sampling
event
the
filter
and
permanganate
solutions
are
digested
and
a
single
combined
measurement
of
total
mercury
concentration
is
generated.
Method
29
was
developed
as
a
multi­
metal
measurement
method,
including
mercury.

The
hardware
configuration
for
Method
29,
illustrated
in
Figure
33,
includes
a
pair
of
nitric
acid
impingers
foHowed
by
permanganate
irnpingers.
The
various
fractions
are
analyzed
separately
for
a
wide
range
of
metals
and
results
summed
to
develop
a
reported
stack
concentration.

Finally,
Method
10
1
b,
iIlustrated
in
Figure
34
is
a
simple
variant
on
Method
29.
Method
10
1
b
replaces
one
of
the
nitric
acid
impingers
in
Method
29
with
two
water
impingers.
The
various
fractions
are
analyzed
separately
in
an
attempt
to
determine
the
split
between
Wgo
and
Hg'
2.
The
total
mercury
concentration
is
determined
by
adding
the
catch
fiom
the
various
fiactions.

An
extensive
array
of
mdti­
train
data
is
available
describing
the
precision
of
these
three
mercury
measurement
methods.
The
first
set
of
results
was
developed
by
EPNOAQPS
as
part
of
the
validation
of
Method
29
(
Radian,
1992).
Those
tests,
conducted
by
Radian
C
o
p
,
were
performed
at
a
municipal
waste
combustor
operated
by
American
Ref­
Fuel
in
New
Jersey.
That
data
set
includes
8
quad­
train
runs
with
stack
mercury
concentration
ranging
from
130
to
575
pg/
dscm.
The
next
set
of
data
comes
from
the
EPA
efforts
to
validate
Method
IOlb
(
EER,

1997).
Extensive
testing
was
conducted
at
a
hazardous
waste
burning
cement
kiln.
Testing
consisted
of
triplicate
train
runs
using
both
Methods
101
b
and
Method
29
(
test
series
1)
and
quad
­
_
l
­
"

103
Pi
m
m
r
,
pan
1
'
I
1
L
k
.

I
.....
..,.,
,

2
"
CI
+
Q=
a
P­
I
4­.

.
..
.
.".
I._
.
_
.
­
...
I
..
.

I
i,
I
106
c
c
train
runs
using
only
Method
101
b
(
test
series
2.).
The
tripiicate
train
tests
consisted
of
a
Method
1Olb
train
located
in
the
breaching
to
the
stack
(
downstream
of
all
air
pollution
controls)
as
well
as
Methods
10
1
b
and
29
trains
located
at
the
same
plane
of
the
stack.
These
three
measurements
all
treated
as
simultaneous
but
it
is
distinctly
possible
that
the
diverse
locations
could
contribute
to
an
increased
apparent
method
imprecision
for
this
data
set.
For
the
quad
train
tests
two
of
the
lines
were
dynamically
spiked
with
Hgo
and
HgC12.
For
the
ReMAP
analysis,
only
the
unspiked
data
fiom
the
quad
trains
have
been
used.

A
third
set
of
multi­
train
data
was
provided
by
the
Rig0
and
Chandler
tests
on
the
MWC
facility
in
Pittsfield,
MA.
These
tests
provide
dual­
train
measurements
using
EPA
Method
29.
A
fourth
set
of
multi­
train
data
is
provided
in
EPA
tests
at
the
Stanislaus
County
MWC
(
Radian,
1992).

In
those
tests,
two
Method
29
measurements
were
made
simultaneously
in
the
stack.
From
these
tests,
the
only
dual­
train
metal
data
available
from
the
EPA
were
for
mercury.

A
fifth
set
of
data
is
provided
by
tests
performed
at
EPA's
research
facilities
in
RTP,
NC
(
EPA,

1998).
There
are
several
key
features
to
the
data
fiom
these
tests
that
should
be
pointed
out
as
part
of
the
R
e
m
data
analysis.
First,
numerous
Method
29
tests
were
conducted
as
part
of
an
effort
to
assess
performance
of
multi­
metal
continuous
emission
monitors.
The
EPA
combustion
facility
at
RTP
is
a
pilot­
scale
rotary
kiln
incinerator
with
a
full
RCRA
permit.
As
part
of
the
CEMS
assessment,
the
metal
content
of
the
waste
feed
was
varied
to
adjust
the
range
of
metal
concentration
in
the
stack.
The
physical
arrangement
of
the
stack
causes
the
flow
to
travel
from
a
mezzanine
level,
down
m
e
floor,
and
then
horizontally
to
a
final
clean
up
baghouse.
A
series
of
multi­
metals
CEMS
were
installed
in
the
vertical
portion
of
this
duct.
Method
29
trains
were
located
in
the
horizontal
duct
runs
at
the
meuanine
level
(
before
the
CEMS)
and
at
the
floor
Because
of
the
wide
concentration
range
of
these
paired
data,
these
results
are
extremely
important
to
the
overall
ReMAP
effort.
A
carefui
assessment
of
the
data
indicates
that
there
is
a
distinct
bias
in
the
results.
That
bi
only
detectable
because
of
the
large
number
of
metals
being
measured.

[
Material
presen
the
Appendix
discusses
the
data
trends
in
some
detail.]
The
essence
of
imprecision
is
that
simultaneous
measurements
of
the
same
stack
gas
yield
different
anual
method
data
were
collected
simultaneously.

107
measurement
results.
What
is
unusual
about
the
EPA
pilot­
scale
tests
is
that
the
reported
concentrations
for
all
of
the
metals
tend
to
move
in
concert.
If
the
mezzanine
trai
higher
concentration
for
one
metal
(
relative
t
1
sampling
train),
it
will
also
indicate
a
higher
concentration
for
the
other
metals
as
SME
ReMAP
team
conducted
a
thorough
assessment
to
determine
the
se
of
this
bias.
Unfortunately
no
firm
conclusions
were
forth
co
e
problem
can
be
traced
to
the
sample
collection
process
or
the
h
pIe
as
opposed
to
the
laboratory
analytical
procedures.
Other
re
also
investigated.

Though
there
is
a
distinct
bias,
the
data
from
these
tests
have
been
used
as
provided
by
the
EPA
researchers.
The
effect
may
be
to
slightly
increase
indicated
standard
deviation
of
individual
method
29
data
points,
but
the
wide
range
of
d
atly
improves
the
overall
quality
of
the
method
precision
estimates.

Tables
16a
and
16b
provide
a
summary
of
all
the
merc
step
in
the
analysis
is
to
perform
an
outlier
analysis
outlined
previously.
The
data
were
grouped
into
sets
wi
lOOpg/
dscm.
The
analysis
identified
four
data
points
as
having
abnormally
large
spans.
Those
runs
included
Run
Number
9
from
the
EPA/
and
Runs
5­
2,8­
3
and
9­
1
from
the
Stanislaus
County
tests.
The
span
clearly
out
of
line
with
the
remainder
o
data
with
concentrations
below
100
pg/

suspect
Runs
6­
3,
8­
1,
and
9­
2
as
pote
program
and
generally
accepted
statistical
analysis
procedure
all
data
udess
there
is
a
clear
rationale
for
data
elimination.
Accordingly,
only
the
four
measurements
identified
as
having
abnormally
large
data
spans
have
been
eliminated
f?
om
further
analysis.
Figures
35
and
36
present
the
data
from
Tables
16a
and
16b
showing
s
plots
of
mndarcl
deviation
and
relative
standard
deviation
as
a
function
ng.
It
seems
appare
*
sion
data
noted
above.
The
first
that
test
series
as
well
as
with
values
of
RSD
there
is
also
reason
to
Table
16a.
Methods
29
and
101
Data
for
Mercury
109
c
0
0
c\

0
3
0
0
r­

0
0
W
0
0
rn
0
0
­
3
0
0
cc)

0
0
N
0
0,

0
I12
I
=:
3
n
.­
.
L
e
w
E
I
0
0
0
P
confidence
intervals
as
well
as
the
small
sample
bias
corrected
data.
The
t­
statistic
for
the
regression
is
7.45,
which
is
well
above
the
critical
value
for
67
degrees
of
freedom
and
95%
confidence.
After
applying
a
bias
correction
factor
for
the
log­
log
transformation
the
regression
relation
is
found
to
be:

S
(
Hg
total,
Methods
29
and
101)
=
0.208
*
Co.
877.

The
vaIue
of
the
power
coefficient,
at
th
fidence
level
is:

P
=
0.877
5
0.234
or
between
0.

Figure
38
presents
three
different
forms
of
the
p
total
mercury.
The
relative
standard
deviat
between
about
10
and
15%

above
10
pg/
dscrn.
Tripli
relatively
narrow
range
of
the
true
stack
concent
pg/
dscm,
Method
imprecision
is
anticipated
to
deviating
by
less
than
f
23.3%
from
the
actual
concentration
is
above
10
pgldscm,
99
out
of
100
single
m
licate
measurements
5
40.4%
of
the
true
stack
concentration.

Data
presented
in
Figure
36
are
based
on
the
assumption
that
standa
concentration
according
to
the
regression
relation
shown
in
Figure
it
is
possible
that
standard
deviation
could
be
as
high
as
the
upper
c
the
lower
confidence
interval.
The
potential
range
for
99
out
of
1
imprecision
in
the
measurement
method,
has
been
calculated
of
true
'
stack
concentration.
Results
from
those
calculations
are
presented
in
Figure
39.
If
the
precision
of
the
mercury
measurement
methods
is
as
large
as
the
upper
confidence
interval,
a
significant
variation
in
measurement
results
may
be
anticipated.
For
example,
if
the
method
standard
deviation
varies
according
to
the
upper
confidence
limit,
measurement
of
a
stack
containing
500
pg/
dscm
of
mercury
could
result
in
a
spread
for
99
out
of
100
data
points
ranging
from
275
to
725
pgldscm.
If
the
Method
precision
is
best
described
by
the
lower
confidence
interval,
Yo
confidence
level,

,
t)
3
u
.
e
t
I
Y
115
I16
measurement
of
that
same
stack
containing
500
pg/
dscm
mercury
should
result
in
a
99
out
of
100
future
data
points
falling
between
428
and
572
pg/
dscm.
It
is
noteworthy
that
the
RSD
data
listed
in
Tables
16a
and
16b
for
individual
mercury
measurements
occasionally
exceeded
50%
arid
that
the
firms
conducting
the
tests
were
highly
qualified
stack
festers
and
laboratory
anafysts.
This
serves
to
underline
the
critical
importance
of
precision
in
stack
testing.
From
an
owner's
perspective,
it
is
ow
the
precision
of
the
data
being
gathered
to
determine
compliance.
From
a
regulatory
development
perspective,
it
is
critically
important
to
know
the
precision
of
data
being
used
to
establish
regulations.

The
best
estimate
of
the
precision
of
Method
29/
101iV101B
is
provided
by
the
regression
analysis.

Those
data
were
presented
graphically
in
Figures
38
and
39.
To
assist
the
reader,
Table
17
presents
these
data
in
tabular
form,
focusing
on
the
range
of
concentrations
anticipated
to
be
of
primary
interest
to
facilities
being
regulated
under
the
new
and
emerging
US
EPA
emission
rules.
The
first
column
lists
the
true
concentration
of
total
mercury
in
the
stack
(
not
corrected
for
excess
oxygen).

The
second
and
third
columns
present
the
anticipated
range
for
99
out
of
100
future
single
measurements
(
at
the
given
true
stack
concentration).
The
fourth
and
fifth
columns
provide
the
anticipated
range
for
99
out
of
IO0
future
triplicate
measurements.

117
ij
L
Q,
v,
c
d
C
C
r
118
8.0
EPA
Method
29
for
Multi­
Metals
The
essential
elements
of
 PA
Method
29
were
presented
in
the
previous
section.
As
noted,
the
various
components
of
the
train
are
analyzed
to
determine
the
concentration
of
various
metals.
The
method
is
used
to
determine
compliance
with
a
wide
range
of
metals
but
there
are
very
limited
multi­
train
data
available
to
assess
the
precision
of
the
method
for
those
pollutants.
For
three
of
the
key
metals,
cadmium,
chromium,
and
Iead,
the
Agency
did
perform
multi­
train,
Method
validation
from
those
tests
suggest
that
additional
data
may
have
been
gathered
on
ocumentation
of
the
results
(
i
any)
were
not
available.
Note
that
lead
and
ed
pollutants
under
the
municipal
waste
combustor
MACT
rules.
Other
metals
rsenic,
and
beryllium.
Other
sources
of
multi­

d
by
Rig0
and
ChandIer
as
well
as
the
EPA
EM
demonstration
program.

ta
for
Antimony,
Arsenic,
Beryllium,
Cadmium,
Chromium,
and
Lead
Tables
18
through
23
summarize
the
available
Method
29
data
for
antimony,
arsenic,
beryllium,

,
and
lead
respectively.
In
these
tables,
some
difficulty
may
be
experienced
umber
designations
for
data
from
the
EPA
pilot­
scale
tests
and
for
the
EPA­

able
22).
Tables
18
through
23
utilize
the
run
number
designations
provided
in
ce.
The
difficulty
is1
that
the
same
run
numbers
are
repeated.
Separate
runs
early
come
from
different
testing
series
but
insufficient
information
ly
describe
the
differences
between
run
series
or
why
run
designations
were
8.1.
I
Antimony
taFor
antimony,
data
is
available
from
the
Rig0
and
Chandler
tests
and
from
the
EPA
pilot­
scale
tests.
The
Rigo
and
Chandler
tests
provide
dual
train
data
in
the
30
to
80
pgldscm
concentration
range.
The
EPA
pilot
scale
tests
were
also
dual
train.
They
provide
data
in
two
different
concentration
ranges;
a
lower
range
of
approximately
20
to
30
pg/
dscm
and
an
upper
range
of
approximately
60
to
90
pgldscm.
The
outlier
analysis
indicates
that
run
number
2
from
the
119
Table
18.
Method
29
Multi­
Trai
eviation
For
t
Table
19.
Method
29
Multi­
Train
Data
and
Standard
Deviation
For
Arsenic
121
Table
20.
Method
29
Multi­
Train
Data
and
S
dard
Deviation
For
Beryllium
I
I
I
I
I
I
/
Table
21.
Method
29
Multi­
Train
Data
and
Standard
Deviation
For
Cadmium
I23
Table
22.
Method
29
Multi­
Train
Data
and
Standard
Deviation
For
Chromium
124
Table
23.
Method
29
Multi­
Train
Data
and
Standard
Deviation
For
Lead
125
EPA
pilot
scale
tests
(
first
of
EPA
pilot­
tests
designated
as
run
2)
has
an
abnormally
lar,
we
data
range.
After
examining
several
data
grouping,
it
was
concluded
that
this
run
represents
a
data
outlier
and
accordingly,
it
was
ehinated
from
the
precision
analysis.
Figures
40
and
41
prdsent
the
antimony
data
in
graphical
form.
Figure
40
is
a
scatter
plot
of
the
small­
sample
standard
deviation
data
while
Figure
41
deviation.
As
sh
s
to
approximately
'

30%.

8.1.2
Arsenic
Dora
Multi­
train
data
sour
standard
deviation
dat
relative
standard
d
on
the
Pittsfieid
M
limit
for
the
laborat
­
scale
tests.
Those
have
been
jnclwd
Iow
levels
to
h
DataMulti­
train
data
for
cadmium
emissions
u
three
sources.
Tests
by
Rigo
and
Chandler
provide
data
pg/
dscrn.
The
EPA
pilot
scale
tests
provide
data
in
two
ranges;
a
low
range
centered
at
about
20
ge
of
about
20
to
50
/­
,­

I
i
i
j
­

m
N
+

+

+

­­
I
.+
I
*
I
b
m
I
I
'

I
I
I
7
m
0
127
t
0
128
v,
cu
.
.
a
m
0
N
­
7­
El
1
..
1
I
­
t
I29
0
0
0
­

0
o\

0
00
0
­

0
\
3
0
v)

0
u­

0
m
0
N
0,

0
I
I
0
M
CJ
L
0
z
i­
cy,
131
a
2
a
CD
Li
+
I
132
r:
ti
F
t
u
pg/
dscm
and
an
upper
range
that
spans
40
to
80
pg/
dscm.
The
EPA
method
validation
tests
provide
data
at
a
very
low
concentration
range
of
about
1.5
to
2.5
pg/
dscm.
AI1
data
in
this
data
set
pass
the
SPC
outlier
criteria
and
have
been
included
in
the
precision
analysis.
Figures
46
and
47
present
scatter
plots
of
the
data
including
the
small
sample
bias
corrected
standard
deviation
and
relative
standard
deviation
as­
a
function
of
mn
average
concentration.
Figure
47
shows
that,
for
concentrations
above
about
20
pgldscrn,
the
RSD
covers
approximately
the
same
span
as
the
other
Method
29
metals
presented
above.
However,
the
low
concentration
data
from
the
Method
validation
tests
indicate
significantly
higher
RSD.
Data
in
Figure
46
show
that
the
actual
standard
deviation
tends
to
increase
with
increasing
concentration,
even
at
the
very
low
concentrations
of
the
validation
tests.
This
shows
that
the
significant
rise
in
RSD
is
a
result
of
the
denominator
in
the
RSD
calculation
tending
toward
zero
rather
than
rapid
expansion
of
the
standard
deviation.

8.1.5
Chromium
Data
Three
sets
of
multi­
train
data
are
available
for
assessment
of
the
precision
of
Method
29
for
chromium.
The
Rig0
and
Chandler
tests
provide
data
with
concentration
in
the
range
of
about
4
to
10
pgidscm.
The
EPA
pilot
scale
tests
again
provide
data
in
two
ranges.

The
low
range
results
are
centered
at
about
20
pg/
dscm
while
the
high
concentration
results
cover
the
range
of
about
60
to
70
pgldscm.
Finally,
the
EPA
Method
validation
tests
are
at
very
low
cadmium
concentration
­
ranging
from
about
1
to
3
pddscm.
Outlier
analysis
for
this
data
set
indicates
that
two
data
points
have
abnormally
large
data
spreads.
Specifically,
run
number
7
from
the
Rigo
and
Chandler
tests
and
run
number
8
for
the
EPA
method
validation
tests.
Both
of
these
runs
are
specially
marked
in
the
run
number
column
of
Table
22.
The
Rigo
and
Chandler
run
was
eliminated
from
further
analysis,
while
only
the
data
from
train
C
of
the
EPA
tests
were
eliminated.

Note
that
there
were
several
other
data
points
indicating
very
large
spreads
but
they
have
all
been
included
in
the
analysis.
Figures
48
and
49
present
scatter
plots
of
the
small
sample
bias
corrected
data
for
standard
deviation
and
relative
standard
deviation
as
a
function
of
run
average
concentration.

8.1.6
Lead
Data
Three
sets
of
multi­
train
data
are
also
available
for
Method
29
measurement
of
lead.
The
Rig0
and
Chandler
tests
at
the
Pittsfield
MWC
provide
data
at
lead
concentrations
ranging
from
about
400
to
1500
pgldscm.
The
EPA
piiot
scale
tests
provide
data
in
two
concentration
ranges.
The
low
range
data
cover
the
span
of
about
20
to
30
pg/
dscm
.
~
^
?
>

133
JL
;
si
m
3
f
m
I
+

+
+
+
+

+
+
+

I
134
n
u
bl,
e.

.
f""

I,.
E
w
I
I
i
I
I
B
E
0
VI
0
w
0
m
0
v)
0
J
`
136
P
r­
F
L
r­
t
11
...
F""

L
r
t.

IFLc"
4
I
h.
2
137
whiIe
the
higher
concentration
results
were
obtained
in
the
range
of
about
50
to
95
pddscrn.
Finally
the
EPA
Method
validation
test
result
ere
obtained
at
concentfations
in
*
e
range
of20
to
4o
pg/
dscm.
AI1
data
in
the
lead
data
set
pass
the
plots
ofthe
small
sampl
ias
corrected
stand
average
concentration.
Note
that
the
high
co
exhibit
RSD
values
less
than
13%,
while
th
data
exhibit
a
broader
range
of
RSD
values.
from
the
Rig0
and
Chandler
8.2
EPA
Method
29
Regression
Analyses
After
elimination
of
outliers,
the
Method
29
multi­
train
data
for
antimony,
arsenic,
beryllium,

cadmium,
chromium,
and
lead
were
analyzed
with
weighted
regression
analysis.
Results
from
those
analyses
are
summarized
in
Table
24
below.

Table
24.
Results
of
Method
29
Regression
Analysis
for
Various
Metals
There
are
clearly
differences
between
the
regression
equations
for
the
six
metals
listed
above
but
there
are
also
significant
similarities.
The
variation
of
ndard
deviation
for
versus
concentration
appears
to
be
significantly
different
from
the
other
metals.
For
cadmium,
the
maximum
potential
value
for
the
p
term
in
the
p
0.61
1.
For
any
of
the
other
five
metals,
within
t
coefficient
could
fall
between
0.692
and
0.929.
Five
of
the
six
regression
analyses
produced
t­
ction7
at
the
95%
con
confidence
bounds,
t
158
I39
c
c
statistics
that
are
above
the
critical
value
of
that
statistic.
For
antimony
the
t­
statistics
(
at
the
95%

confidence
level)
is
slightly
below
the
critical
value
and
the
t­
statistic
for
beryllium
is
only
marginally
above
the
critical
vaiues.
This
results
in
wide
ranges
for
the
potential
values
of
the
power
function
p
coefficient
for
both
antimony
and
beryllium.

Recall
that,
with
Method
29,
each
data
pair
provides
data
on
the
full
range
of
metals.
With
the
exception
of
the
EPA
Method
validation
tests,
every
data
point,
for
each
metal,
has
a
companion
data
point
for
the
other
five
metals.
This
is
important
since
random
error
enters
the
measurement
process
through
both
the
sampling
process
and
the
chemical
analysis
processes.
In
a
multi­
metal
procedure
such
as
Method
29,
random
errors
in
the
sampling
process
should
be
reflected
in
every
metal
being
monitored.
Moreover,
when
the
value
of
the
power
coefficient
is
close
to
1.0,
random
error
in
the
sample
collection
process
is
a
significant
contributor
to
the
overall
Method
precision.

For
these
reasons,
there
is
increased
reason
to
anticipate
similarity
in
the
various
relationships
between
standard
deviation
and
concentration.

Figures
52
through
57
illustrate
the
regression
equations
and
the
95%
confidence
intervals
for
measurement
of
each
of
the
six
metals
using
Methud
29.
Figures
58
through
63
present
data
on
the
various
precision
metrics,
assuming
that
the
standard
deviation
varies
according
to
the
regression
equation.
It
is
instructive
to
compare
the
general
level
for
the
predicted
relative
standard
deviation
and
the
variation
of
RSD
for
each
of
the
six
metals.
Figure
58
indicates
that
the
RSD
for
antimony
measurement
using
Method
29
is
basically
a
flat
function
of
concentration
over
the
entire
range
of
available
data.
At
a
true
concentration
of
20
pddscm
the
predicted
RSD
is
11.8%
while
the
predicted
RSD
is
9.3%
at
90pg/
dscm.
In
the
concentration
range
between
about
20
to
100p~
ldscm,

a
relatively
flat
RSD
versus
concentration
trend
is
also
observed
for
arsenic,
beryllium,
and
chromium.
In
that
range,
the
RSD
for
arsenic
varies
between
about
15
and
16.3%
(
see
Figure
59).

For
beryllium,
RSD
only
varies
between
17.0%
and
17.8%
(
see
Figure
60).
SlightIy
greater
variation
is
predicted
for
chromium
but,
as
shown
in
Figure
62,
the
anticipated
variation
in
RSD
is
only
from
21.3%
at
20
pg/
dscm
to
18.2%
at
71
pddscm.

141
142
1
143
.
.
d
.­
E
.­
­
I
L
9
3
=
.
n
t
1
0
144
I45
a
0
0
0
c
r:
I
'
l.
a.
&
0
cr
0
3
.­

I47
I
0
E
.
I
0
o\

0
00
0
P
5
VJ
9
a
M
I
1
v3
L
i
0
QI
0
01
0
b
0
W
0
Wl
0
d
0
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0
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0
I
0
I
149
0
v)

c
J
.
,
I
s
0,
0
151
s
0
3
3
z
0
rc
0
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3
0
In
0
Q­

0
m
0
r
4
2
0
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0
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=
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a
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u
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k
F;;;
1
0
i­

k:.
l
s
s
0
0
d
m
(
u
s
0
0
0
rn
­.

0
0
d
1
0
0
c\
1
­

0
0
0
­.
1
0
0
W
0
0
Q
0
0
d
0
0
c\
1
0
_.
t
anticipated
when
concentration
drops
below
20
p,
a/
dscm.

As
noted
earlier,
the
data
in
Figures
58
through
63
are
based
on
the
assumption
that
standard
deviation
varies
according
to
the
re
ssion
equations.
However,
within
g5%
confidence
bounds,
it
is
distinctly
possible
that
standard
ation
be
greater
Or
lines.
Figures
64
through
69
present
the
anticipated
ranges
for
99
out
of
100
future
a
function
of
the
true
stack
concentration,
assu
the
upper
95%
confidence
limit,
according
to
95%
confidence
limit.
These
figures
illustrate
the
critical
importance
overall
precision
assessment.
As
indicated
by
results
presented
in
Fisures
5
deviation
of
Method
29
antimony
measurements
varies
according
to
the
out
of
100
future
measurements
(
at
a
stack
concentration
within
23%
ofthe
true
stack
that
future
data
might
have
a
spread
as
large
as
+­
5
1.9%
a
ng
that
that
standard
deviation
varies
according
to
e
regression
The
significance
of
the
unce
more
dramatic
for
Method
29
measurements
of
be
Method
29
beryllium
measurements
are
made
at
true
stack
concentrations
of
80
pg/
dscm,
available
data
indicate
that
99
out
of
100
future
measurements
Wil
concentration
(
45
to
115
pg/
dscm).
Also,
99
out
of
100
triplicate
measurements
are
expected
to
fall
within
k
25.3%
of
the
true
stack
concentration
(
when
true
concentration
equals
80
pddscm).

However,
at
the
95%
confidence
level,
it
is
only
possible
to
conclude
that
the
future
single
measurements
will
fall
within
f:
97.5%
of
the
true
concentration.
This
large
spread
between
our
best
estimate
and
the
95%
confidence
limits
is
a
direct
result
of
the
limited
amount
of
multi­
train
data
for
beryllium
using
Method
29.
The
potential
range
for
fu
er
metals
is
standard
deviation
concentration
is
even
As
indicated
in
Figures
6o
and
66y
when
within
43­
8%
Of
the
true
illustrated
on
the
respective
figures.
W
E
.
I
5
155
0
0
­

0
o\

0
00
0
b
0
\
3
0
v,

0
d
0
m
0
P
4
0
i
i""
PP
f
.­).
5
157
M
E
3
a
f
0
U
rn
.
A
ki­

p\
1
L,

E
L,
.1
0
m
0
ri
0
I
159
160
i_

Earlier
discussion
of
the
results
presented
in
Table
24
noted
a
similarity
in
the
regression
analysis
for
five
of
the
six
metals,
including
antimony,
arsenic,
beryllium,
chromium.
and
lead.
It
was
pointed
out
that
Method
29
collects
a
sample
that
is
subsequently
analyzed
for
all
of
the
target
metals.

Random
errors
in
the
sample
collection
and
sample
recovery
operations
are
likely
to
contribute
similar
random
error
to
each
of
the
measured
metal
concentrations.
Finally,
it
was
noted
that
random
error
in
the
sample
collection
and
recovery
process
tend
to
drive
the
value
of
the
power
function
coefficient
toward
1.0
while
random
error
in
the
analytical
analysis
are
more
typically
characterized
by
constant
standard
deviation
(
p
equals
zero
in
the
regression
equation).
In
Table
24,

note
that
with
the
exception
of
cadmium,
the
regression
analysis
for
five
metals
indicates
that
the
p
.

coefficient
is
between
0.703
and
1.039
sugsesting
that
random
error
in
sampling
and
recovery
are
major
contributors
to
overall
megsurement
imprecision.

The
general
similarity
in
these
resression
results
further
suggests
that
for
these
five
metaIs,
it
may
be
appropriate
to
assess
a
composite
precision
estimate
for
Method
29.
To
perform
that
assessment,
the
multi­
train
data
presenred
in
Tables
18,
19,
20,
22,
and
23
were
combined
into
a
single
data
set.

With
the
exception
of
the
multi­
train
data
for
tead,
the
majority
of
the
individual
data
sets
were
from
tests
where
the
metal
concentrations
ranged
from
single
digit
to
less
than
100
pg/
dscm.
Further
the
majority
of
the
lead
data
are
from
this
same
concentration
range.
To
form
a
composite
data
set
for
regression
analysis,
the
Rig0
and
Chandler
data
were
eliminated
from
the
lead
data
yielding
data
for
all
five
metals
in
the
same
concentration
range.
The
data
were
appropriately
weighted
for
the
number
of
degrees
of
freedom
and
then
subjected
to
a
regression
analysis.
The
resuItant
regression
equation
has
158
degrees
of
freedom
and
produced
a
t­
statistic
equal
to
10.66
­
well
above
the
critical
t­
statistic.
The
analysis
suggests
that
the
'
relationship
between
S
and
concentration
is
described
by
the
equation:

The
value
of
the
p
coefficient
(
0.821)
is
easily
within
the
95%
confidence
ranges
forp
determined
by
regression
analysis
for
each
of
the
five
individual
metals
(
see
Tabte
24).
Figure
70
is
a
plot
of
the
regression
equations
for
the
composite
data
set
including
the
95%
confidence
intervals
on
that
161
regression.
Figure
71
presents
a
comparison
of
the
re,
oression
equation
for
each
of
the
five
individual
metals
and
the
regression
equation
from
the
composite
analysis,

It
is
important
to
reiterate
that
only
a
limited
body
of
data
is
available
to
assess
the
precision
of
Method
29.
Moreover,
one
of
the
critically
important
data
sets,
the
EPA
pilot
scale
tests,
contains
a
known
bias,
Inchdins
these
biased
results
in
the
analysis
clearly
results
in
a
slight
over
estimate
of
the
standard
deviation
at
any
given
stack
concentration
(
partico
However,
if
those
data
were
eliminated
from
the
assessment,
the
result
would
be
an
even
larger
aver
estimate
of
the
Method's
imprecision.
As
a
result
of
the
limited
quantity
of
data
and
the
known
biases
in
some
of
those
data,
the
precision
of
Method
29
for
metals
can
only
be
generally
estimated.

The
analysis
of
the
composite
data
set
provides
a
basis
for
the
overall
assessment
of
the
method's
precision.
Figure
72
presents
various
precision
metrics
determined
from
the
regression
analysis
of
the
composite
d
t.
Based
on
the
available
data,
it
appears
that
Method
29
provides
an
RSD
between
13
and
when
the
metal
loading
is
between
20
arid
about
IOOug/
dscin.
At
ineta1
concentrations
b
about
10
pg/
dscm,
the
imprecision
of
the
method
appears
to
increase
asymptotically.
Relative
to
future
measurements,
if
the
precision
of
Method
29
conforms
to
the
composite
analysis
and
if
the
metals
concentration
is
greater
than
20
pg/
dscrn,
99
out
of
100
single
measurements
should
deviate
from
the
true
concentration
by
no
more
than
45%.
Similarly,
in
the
same
rage,
99
out
of
IO0
triplicate
measurements
should
deviate
from
the
true
concentration
by
less
than
26%.
Unfortunately,
the
available
data
do
not
support
a
more
definite
assessment.

Tabie
25
provides
a
summary
of
the
anticipated
range
of
measurement
results
for
application
of
Method
29
for
determination
of
the
concentration
of
antimony,
arsenic,
beryllium,
chromium,
and
lead.
Data
in
this
table
are
derived
from
analysis
of
the
composite
data
set
and
cover
the
concentration
range
of
4
to
100
pg/
dscm.
Note
that
the
data
in
the
table
do
not
include
correction
for
oxygen
content
in
the
stack.

163
,
6
l
e
0'

rl
P
2
E
f
ED
0
0
c
r
­
5:

a
3
+
M
c
164
i;­

P
I65
I
Table
25.
Range
of
Anticipated
Future
Metals
Data
Antimony,
Arsenic,
Beryllium,
Chromium,
or
L
I
I66
9.0
Other
Measurement
Methods.

1
An
attempt
was
made
to
gather
multi­
train
data
for
a
variety
of
additional
EPA
measurement
methods.
No
multi­
train
data
or
method
validation
test
repons
were
uncovered
for
EPA
methods
0030
or
001
1
for
volatile
and
semi­
volatile
organic
emissions.
The
same
can
be
said
for
EPA
Method
23a,
which
is
a
special
procedure
for
measuring
dioxin
and
furan
emissions.
In
the
absence
of
multi­
train
measurement
data,
it
is
not
possible
to
fully
assess
the
precision
of
these
methods.

167
This
page
Intentionally
left
blank.

168
"~

10.
Conclusions
The
ReMAP
study
has
assembled
a
database
containins
all
known
multi­
train
data
sets
using
various
EPA
measurement
Methods.
Data
in
that
database
have
been
subjected
to
a
detailed
analysis
to
assess
the
precision
of
the
Methods
as
a
function
of
stack
concentration.
The
scope
of
the
available
data
is
Cxtremely
limited,
especially
considering
the
importance
of
results
from
application
of
the
Methods.
Certain
of
the
Methods,
especia
Methods
5
and
5i
have
significant
databases
and
the
precision
of
those
methods
is
relatively
well
established.
Using
relative
standard
deviation
as
the
precision
metric,
the
precision
of
Method
5
is
between
5
and
1
I%
when
applied
to
stacks
with
a
broad
range
of
concentrations.
If
applied
with
attention
to
detail,
this
method
is
capable
of
providing
reasonably
precise
resuits,
even
at
stack
particulate
concentrations
as
low
as
15
mg/
dscrn.
Whether
an
RSD
of
5
to
1
I%
is
sufficiently
precise
is
likely
to
be
application
specific.

Methqd
5i
was
specifically
developed
to
provide
precise
measurement
resuIts
for
particulate
matter
concentrations
below
50
mgdscrn.
Based
on
available
data,
this
precision
of
this
Method
has
no
statistically
significant
variation
with
stack
concentration.
Pooled
anaiysis
of
the
data
indicates
that
the
Method
(
when
applied
at
concentrations
between
about
5
and
50
mg/
dscm)
has
a
characteristic
standard
deviation
of
1.43
mg/
dscm.

Method
23
for
dioxin
and
furan
emissions
is
a
critically
important
method
for
current
EPA
emission
regulations
and
for
public
perception
of
risk
associated
with
emissions
from
combustion
facilities.

There
is
only
a
very
small
database
for
assessment
of
the
precision
of
this
Method.
Based
on
available
data,
the
anticipated
RSD
for
measurements
of
the
total
mass
of
tetra
through
octa
chlorinated
dioxin
and,
furan
is
estimated
to
be
between
6.3
%
and
20%
for
stack
concentrations
in
the
range
of
2
to
27
ng/
dscm
(
higher
RSD
at
lower
concentration).
Recall
that
the
stated
range
of
stack
concentrations
are
given
on
an
"
as­
measured
basis"
and
therefore
do
not
include
excess
air
diIution
correction
factors
(
e.
g.,
correction
to
7%
02).
The
anticipated
range
for
99%
of
future
individual
measurements
is
t
2.57
times
the
standard
deviation.

Method
23
is
also
used
to
determine
dioxin
and
furan
emissions
calculated
as
ITEQ.
Analysis
of
available
data
for
emissions
expressed
in
this
manner
did
not
yield
an
accep~
able
regression
169
expression.
That
is,
the
t­
statistic
for
the
regression
was
less
than
the
critical
t­
statistic
at
the
95%

confidence
kvel.
This
implies
that
stron
sociated
with
application
of
Toxic
Equivalence
Factors
may
be
masking
k
weighting
factors,
variation
between
simultaneous
significantly
amplified
relative
to
differe
data
and
when
used
to
dete
variation
of
Method
performed
to
determine
a
characteristic
Stan
the
pooled
standard
concentration
range
0.02
to
0.9
ng
ITE
confidence
limit,
the
possible
range
of
Method
23
data
point
indicates
stack
concentration
that
data
point
(
at
the
95%
confidence
level)
could
be
as
low
­
Moreover,
using
the
limited
quantity
of
currently
available
data
and
at
the
95%
confidence
level,
it
is
not
possible
to
determine
compliance
with
a
PCDDPCDF
emission
limit
below
0.095
ng
ITEQ/
dscrn.
on
the
avaiIabie
ote
that,
at
the
95%

Method
26
for
hydrochloric
acid
measurements
was
found
to
be
as
precise
as
any
of
the
manual
measurement
methods.
Typically,
the
RSD
for
this
and
lo%­
RSD
does
increase
at
very
low
HCI
concentrations
but
the
regression
analysis
suggests
that
RSD
should
only
increase
to
15.9%
at
concentrations
as
low
as
1
mg/
dscrn.

Mercury
emission
measurements
are
also
regulations.
A
relatively
large
array
of
mult
analysis.
The
analysis
of
results
found
that
the
and
101
had
minimal
variation
with
ppldscm
the
measurement
method
RSD
varied
from
9.6
to
12.4
percent.
A
significant
portion
of
the
overall
database
is
for
measurements
at
relatively
low
mercury
concentrations.
Forty
out
of
73
mercury
data
points
had
average
concentrations
below
were
at
average
stack
concentration
less
than
30
pgld
data
was
available
for
the
ReMAP
ercury
measurements
by
Methods
29
As
concentration
drops
from
SO
to
5
pg/
dscm,
the
ReMAP
analysis
shows
that
RSD
is
anticipated
to
increase
from
12.4
to
I
5.4%.

170
­
­
­
Method
29
is
also
used
for
measurement
of
other
metals­­
Precision
analysis
was
completed
for
six
other
metals
including
antimony,
arsenic,
beryllium,
cadmium,
chromium,
and
lead.
The
analysis
shows
that
five
of
the
six
metals
all
behave
similarly
with
respect
to
measurement
method
precision.

Data
for
all
metals
except
cadmium
exhibit
a
standard
deviation
versus
concentration
relation
where
the
power
function
coefficient
(
p)
has
a
value
of
approximately
0.82.
Composite
analysis
of
data
for
this
group
of
metals
suggests
that
Method
29
provides
an
RSD
on
the
order
of
I3
to
18%
\
vhen
the
metal
loading
is
between
20
and
about
IOOpg/
dscm.
Data
for
lead
is
available
at
much
higher
concentration
and
the
method
RSD
for
lead
appears
to
asymptote
between
5
and
10%.
At
metal
concentrations
below
about
20
pg/
dscm,
the
imprecision
of
the
Method
appears
to
increase
asymptotically.
For
cadmium,
based
on
the
available
data
standard
deviation
of
the
Method
has
a
different
relation
with
concentration.
The
indicated
value
of
the
p
coeflicient
is
approximately
0.45
suggesting
that
for
the
available
cadmium
data,
random
error
(
or
differences)
in
the
chemical
analysis
was
a
significant
contributor
to
the
overall
imprecision
of
the
Method.

One
additional
conclusion
from
the
ReMAP
Phase
1
project
is
that
there
is
a
pressing
need
for
additional
multi­
train
data
to
refine
the
precision
estimates
of
the
 PA
Reference
Methods.
If
such
experimental
programs
are
to
be
conducted,
significant
attention
should
be
given
to
the
appropriate
range
of
stack
concentrations.
Results
presented
in
this
report
can
help
to
guide
the
test
planning
efforts.
1.
nn
A
C
9.
EPA
Reference
Method
23
­
Determination
of
Polychlorinated
Dibenzo­
p­
Dioxins
and
Polychlorinated
Dibenzofurans
from
Stationary
Sources.
56
FR
5758,
February
13,
1991
(
with
several
revisions).

10.
Validation
of
Emission
Test
Method
for
PCDDs
and
PCDfs.
Prepared
by
Midwest
Research
Institute,
EPA
Contract
No.
68­
02­
4395,
Work
Assignment
23
for
 PA
EMSL.
February
24,
1989.

Rig0
&
Rig0
Associates
and
A.
J.
Chandler
and
Associates
under
the
Direction
of
ASME.
June
1
1.
Retrofit
of
Waste
to
Energy
Facilities
Equipped
with
Electrostatic
Precipitators.
Prepared
by
1997.

Aggregate
Kiln.
Prepared
by
Energy
and
Environmental
Research
Corporation,
Contract
No.
68­
D2­
0164
for
the
 PA
Office
of
Solid
Waste.
October
10,
1997.
12.
Dioxins/
Furans,
HC1,
C12
and
Related
Testing
at
a
Hazardous
Waste
Bumin,
(
J
Light­
Weight
v
13.
EPA
Reference
Method
23
­
Determination
of
Polychlorinated
Dibenzo­
p­
Dioxins
and
Polychlorinated
Dibenzofurans
from
Stationary
Sources.
56
FR
5758,
February
13,
199
I
.

14.
OMSS
Field
Test
Report
on
Carbon
Injection
for
Mercury
Control
Completed
at
the
Ogden
Martin
of
Stanislaus,
Inc.
Prepared
by
Radian
Corporation,
Conrract
No.
68­
D
i
00
IO
for
the
EPA
Office
of
Research
and
Development.
September
1992.

15.
EPA
Reference
Method
29
­
Determination
of
Metals
Emissions
from
Stationary
Sources.
61
FRl8262,
April
25,
1996.

16.
 PA
Reference
Method
1
0
1
a
­
Determination
of
Mercury
Emissions
from
Sewage
Sludge
Incinerators.
47
FR
24703,
June
8,
1982.

17.
Proposed
Draft
EPA
Method
10
1
b
­
Determination
of
Mercury
Species
from
Stationary
Sources.

18.
Validation
of
Draft
Method
29
at
a
Municipal
Waste
Combustor.
Prepared
by
Radian
Corporation,
Contract
No.
68­
D9­
0054
for
the
 PA
Emission
Measurements
Branch.
September
30,
1992.

19.
Mercury
CEMS
Demonstration
at
the
HoInam,
Inc.
Hazardous
Waste
Burning
Cement
Kiln
in
Holly
Hill,
SC.
Energy
and
Environmental
Research
Corporation
for
EPA
Ofice
of
Solid
Waste
and
Emergency
Response.
October
1997.
(
also
see
62
FR
67788).

20.
Internal
EPA
Study
at
the
Pilot
Scale
Rotary
Kiln
Incinerator
Located
in
Research
Triangle
Park,
NC.
SarnpIing
and
Analysis
performed
by
 PA.

21.
Emissions
of
Metals
and
Organics
from
Municipal
Wastewater
Sludge
Incinerators.
Prepared
by
Entropy
and
DEECO,
Contract
No.
68­
CO­
0027,
for
EPA
Risk
Reduction
Engineering
Laboratory.

\
I
y
c
,

c
­
i
Appendix
Statistical
Analysis
Procedures
for
the
ReMAP
Program
Prepared
by:

Charlie
Hendrix
Statis
tical
Consult
ant
r
I,"
u
Procedures
for
Analyzing
Simuitaneousfy
Sampled
Concentration
Data
to
Determine
Measurement
Precision
(
Random
Error)

This
appendix
is
concerned
with
the
statistical
methods
used
in
the
...­
b
1
analysis
of
simultaneousiy
sampled
data.

Confidence
Interval
on
a
Mean
­
#
¶
W
i
­
ab+
Suppose
w
e
have
collected
the
following
replicate
data
from
a
process
operating
under
fixed
conditions.

103.2
107.9
101.6
109.1
105.3
The
average
of
these
is
105.42;
the
standard
deviation
is
3.132
with
4
degrees
of
freedom
(
df).
If
these
are
representative
data
from
this
process,
then
the
95%
confidence
interval
on
the
true
mean
p
is
105.42
of
freedom
(
df).
t
=
2.776.
The
95%
interval
on
p
is
105.42
3.89
or
101.53
to
109.31.
"
95%
of
the
intervals
calculated
in
this
manner
will
encompass
the
true
mean,
p"
From
this
we
infer
that
"
the
probability
is
95%
that
the
interval
101.53
to
109.31
has
captured
the
true
mean,
p"
t*
3.132/&
where
t
is
the
reference
value
of
t
with
4
degrees
cerns
about
whether
the
data
came
from
a
non­
normal
little
bearing
on
this
calculation
under
most
Confidence
Interval
on
a
S
tandard
Deviation
The
following
replicate
data
also
came
from
a
process
operating
under
a
fixed
set
of
conditions.

1.03
1.24
0.91
1.36
0.97
1.22
The
standard
deviation
of
these
data
is
S
=
0.177
with
5
degrees
of
freedom
(
df).
If
these
are
representative
data
from
this
process,
then
the
95%
confidence
interval
on
the
true
standard
deviation
a
is
calculated
in
the
following
manner.
Go
to
Tabie
1;
ent
with
df
=
5;
find
the
factors
0.624
and
2.453
under
the
heading
"
For
95%
onf.
Int."
Multiply
0.177
by
each
of
these
factors
to
obtain
0.110
and
0.434.
df
1
2
3
4
5
6
7
8
.
9
10
12
15
20
25
30
50
100
200
500
paae
2
For
95%
Conf.
I
n
t
.

PF
il`

0.566
3.727
0.599
2.875
0.624
2.453
0
.644
2.202
0
661
0.675
I.
826
1.755
0.717
1.651
0.73
1.548
0.765
1.444
0.785
1.380
1.337
1.243
0
*
942
1.066
"
95%
of
the
intervals
calculated
in
this
ma
standard
deviation
0.''
that
the
interval
0.110
to
0.434
has
captured
the
true
standard
deviation
sigma
(
o)".
This
assumes
that
the
data
c
underlying
"
true
standard
deviation
o"
wh
accuracy
of
confidence
intervals
on
CT
is
affe
original
data.
er
encompass
the
true
e
from
a
process
with
an
From
this
we
infer
that
"
the
pro
biiity
'
is
95y0
Table
1
is
derived
from
the
Confidence
Interval
on
Siama
­
M
u
l
t
i
d
e
Measures
of
Variation
Suppose
we
have
data
from
six
tests.
Each
pair
of
data
was
obtained
by
drawing
simultaneous
samples
and
analyzing
those
samples
for
the
concentration
of
a
pollutant.
­
Time
Data
S
t
a
n
d
a
r
d
Deviation.
S
df
1
1
1
1
1
1
2:
30
PM
27.2
30.0
1.980
5:
50
PM
20.9
27.2
4.455
6:
25
PM
28.7
33.1
'
3.111
7:
15
PM
25.5
24.2
0.919
4:
15
PM
19.1
23.7
3.253
5:
05
PM
28.3
26.8
1.061
*"^
.
.
.).
,
.
,
.
s
I
/­.
<
_
paae
3
We
are
concerned
with
the
inherent
variation
due
to
the
sampling
and
analysis
procedures
(
measurement
precision),
measured
as
the
variation
within
tests.
The
standard
deviation
of
each
pair
of
samples
is
shown.

Our
objectives
are
to
(
1)
estimate
the
standard
deviation
a
due
to
sampling
and
asurement
precision)
and
(
2)
to
calculate
a
95%
confidence
int
estimate
of
0.

cal
to
average
the
standard
deviations
and
report
that
as
t
h
e
estimate
of
0.
Unfortunately
that
average
will
be
a
of
ci.
This
bias
can
be
substantial.
A
more
accurate
estimate
of
CT
is
found
by
sed
estimate
iations.
Pooling
requires
squaring
the
individual
to
obtain
variances;
weight­
averaging
the
variances
to
obtain
the
pooled
variance;
then
take
the
square
root
to
find
the
pooled
standard
devia
ance
is
weighted
by
the
number
of
degrees
of
freedom
assoc
variance.
The
number
of
degrees
of
freedom
andard
deviati
is
the
sum
of
the
degrees
of
ndard
deviati
Pooled
Variance
=
(
Sum
of
df*
Variance)/(
Surn
of
df)

80)
z
+
1"(
3.253)*
+
...
+
1*(
0.919)*]/[
1
+
1
+
1
+
1
+
1
+
11
=
45.99816
=
7.666
Pooled
S
=
67.666
=
2.77
with
6
df.

Pooled
S
is
an
estimate
of
G.
We
can
calculate
the
95%
confidence
interval
on
(
r
by
entering
Table
1
with
6
df
to
find
the
factors
0.644
and
2.202,
Multipl
2.77
by
each
of
these
factors
to
find
1.78
and
6.10.
The
probability
is
95%
th'at
this
interval
has
captured
the
true
value
of
0.

Can
we
calculate
a
confidence
interval
on
CJ
by
treating
the
individual
,
3.253,
...
a
0.919)
as
"
data";
calculate
those
"
data"
and
then
calculate
confidence
limits
data"
as
if
we
were
calculating
the
confidence
The
answer
is
a
qualified
"
yes",
but
only
after
taking
that
have
not
been
addressed
at
this
point.
d
for
the
analysis
of
the
R
MAP
data.
Although
the
involves
fitting
the
data
to
a
mode
by
least
squares
and
nderlying
principle
is
founded
on
weighted
~

­­­
~­
­­­­­
­­­
­­­
­
­_
­­
111­

­
­­­
__­
­
_

paae
4
The
ReMAP
Procedu
re
The
structure
of
the
ReMAP
data
precludes
direct
pooling
to
estimate
CJ
h
e
primary
data
is
re
was
designed
t
of
deviations
in
e
fact
that
G
varies
nonlinear
least­
square
method.
ition
to
obtaining
Tens
of
thousands
of
synthetic
d
were
examined.
The
sirnutat
scale
of
C
;
sometimes
Monte
Carlo
simulation
estimates
of
G
and
also
show
that
the
con
approximately
as
stated.
in
this
manner.
Cases
of
N
=
12
pairs
of
data;
N
=
24
airs
of
data;
and
other
cases
r
t
vals
on
(
sigma)
are
This
will
be
discussed
later.

d
PI
i
i
,
­
­­
n
1,
The
ReMAP
Model
S
=
kCP
Out
of
all
the
possible
models
that
could
be
used
to
associate
S
with
Cy
why
was
S
=
kCp
chosen?
Is
this
mogel
adequate
for
all
of
the
pollutants?
These
questions
...
and
others
concerning
this
model
form,..
are
discussed
in
more
detail
in
Fittina
Sta
ndard
De
viation
vs.
Concentration
Data
to
Alternative
Models.

In
choosing
a
model
form,
one
of
the
first
requirements
is
that
the
variation
in
the
residuals
(
residual
=
difference
between
observed
and
e
constant
along
the
scale
of
concentration.
This
is
s
variance".
Simple
graphics
depicting
S
as
a
function
requirement
is
not
met
in
the
ReMAP
data
...
at
least
in
which
those
data
span
realistic
ranges
on
the
scale
of
C.
Before
fitting
the
data
to
a
model
we
need
to
stabilize
the
variance.

.
When
the
data
are
presented
in
Ln­
tn
coordinates,
statistical
tests
confirm
that
the
variance
is
has
been
done
by
linearizing
S
=
kCP
to
mogeneous
along
the
scale
of
concentration.

Typical
values
of
p
range
from
0
5
to
0.9.
The
exceptions
were
pollutants
in
which
the
concentration
spanned
narrow
ra
ges
and
the
confidence
intervals
on
p
were
wide.
Since
values
of
p
have
been
associated
with
sampiing
variation
as
opposed
to
variation
due
to
chemical
analysis,
the
power­
law
model
has
merit
aside
from
its
statistical
properties.

A
fundamental
difficulty
with
the
ReMAP
data
lies
in
the
fact
that
these
data
are
poorly
arranged
along
the
scale
of
concentration.
Rather
than
being
concentrated
at
two
.
or
three
positions
on
that
scale,
the
data
are
often
ttered;
sometimes
concentrated
near
the
centroid
and
sparse
at
the
seldom
focused
near
t
h
e
ends
of
the
concentration
scale.
Furthermore,
data
collected
from
one
source
are
sometimes
positioned
near
one
level
of
concentration
and
data
from
other
sources
are
positioned
at
other
levels.
in
order
to
obtain
precise
estimates
of
p,
we
need
data
that
spans
decades
(
factors
of
10)
on
the
scale
of
concentration;
in
reality
there
are
instances
in
which
the
data
bareiy
spans
one
decade.
These
factors
virtually
preclude
building
models
more
complex
than
the
form
S
=
kCp.
Where
there
were
questions
about
this,
the
adequacy
of
this
model
form
was
testing
by
t
h
e
usual
stati
tical
procedures;
in
every
instance
it
was
found
that
a
more
complex
mode
could
not­
be
justified.
,

This
is
not
to
claim
that
a
power­
law
model
will
be
adequate
for
ail
The
choice
of
model
form
is
presently
limited
by
the
factors
future
data.
noted
above.
paae
6
7
The
Relationshi
­
mi
n
r
d
D
v
i
i
n
A
standard
de
sigma.
Sigma
is
the
When
we
estimate
(
3
truth"
(
accuracy,
unbia
truth"
(
precise;
small
If
we
calculate
S
from
a
using
other
data
fro
e
interval
arou
If
we
collect
two
simultaneous
samples,
the
standard
deviation
of
that
sample
must
be
rnuitipli
1.253
to
make
it
an
unbiased
estimate
of
u.
With
larger
amounts
o
in
the
sample,
the
bias
is
s
is
a
brief
table
of
bias
cur
w
2
3
4
5
10
Bias
Correction
Factor
1.253
1.128
1.085
1
Remember
each
value
of
S
estimate
of
a.
r
estimate
of
6;
Averaging
values
this
average
will
be
rn
will
still
not
be
accur
r"

r
k
c
If
we
intend
must
multiply
each
before
averaging.
The
bias
relafed
to
the
number
of
sample
standard
deviation
standard
deviation;
it
is
rela
individual
sa
mpie
s
ta
nda
i
d
de
via
tio
n
s
tirnate
of
G,
the
as
correction
factor
t
the
average
sed
to
to
get
the
~~
An
Examole
Table
2
shows
data
in
which
the
standard
deviation
varies
with
t
h
e
average.
Our
purpose
is
to
find
an
empirical
relationship
between
S
and
the
sample
averages.'
For
N
=
2,
unbiased
S
=
1.253'
s.
3%

­"
w,

'
F
&
I­

klrd
1
I
Lr*
r
Table
2
Samo
le
Data
Ava.
c
1
893.7
1080.2
986.95
2
2240.4
2127.0
2183.70
3
2070.3
2219.7
2145.00
4
529.4
553.3
541.35
5
2351.1
2652.2
2501.65
6
358.9
342.7
350.80
1316.20
2434.95
2479.60
1434.80
743.6
655.9
699.75
1
3
960.3
1099.1
1030.00
1
5
247.2
297.6
272.40
16
1866.4
2247.1
2056.75
12
1356.8
1392.8
1374.
ao
1
4
1949.0
1803.1
1876.05
S
a
n
b
­
iS5­
d
S
131.88
565.25
a
o
.
19
Z30.48
105.64
122.37
16.90
51.18
212.91
255.78
1
1
.
4
6
14
­
3
6
2
0
7
.
6
1
250.14
161.43
202.27
13.15
16.48
26.87
33.67
62.01
7
7
.
7
0
25.46
3
1
.
9
0
98.57
123.55.
103.17
129.27
35.64
4
4
.
6
6
269.20
337.31
Fig.
1
shows
the
relationship
between
S
and
Avg.
C.
Fig.
2
presents
the
same
data
in
Log­
Log
coordinates.
The
nature
of
this
relationship
is
more
visible
in
Fig.
2
than
in
Fig.
1.
These
data
will
be
fit
to
the
rnqdel
p
after
linearizing
to
Ln(
S)
=
Ln(
k)
+
p*
tn(
C).
This
is
equivalent
to
working
in
Log­
Log
coordinates
as
in
Fig.
2.

By
fitting
the
data
in
Table
2
to
Ln(
S)
=
Ln(
k)
+
p*
Ln(
C)
we
not
only
obtain
estimates
of
k
and
p
but
also
certain
statistics
that
tell
us
how
accurateiy
this
model
will
predict
G.
A
least
squares
analysis
of
these
data
is
shown
in
Table
3.
.
.
.
.
.

i
a
2
.
i
i
3
E
paae
8
0
0
0
0
0
0
rn
(
u
O
0
m
0
0
0
0
0
0
m
0
0
cu
rn
0
m
(
v
P
7
0
0
0
rc)
c3
0
w
B
L
c
[
,

r
l
El
!
j
iJ
P
L
i
'
c5
Y
p"

cn
P
2
9
LY
LJ
w
Table
3
RIT
0.05
&
0.01
=
2.17
&
2.98
VARIABLES
SH
OF
COEFF
T­

0
Intercept
1
P
o
w
e
r
C
o
e
f
f
i
c
i
e
n
t
p
=
0
0.34030
2.15
RESSUMSQ
STDDEV
OF
RES
DF
12.16245
..
­

ics
I
n
Ln
U
n
i
t
s
In
O
r
i
a
i
n
a
l
Metr
OBSVD
PRED
RESID
STD
RES
O
b
s
e
r
v
e
d
P
r
e
d
i
c
t
e
d
D
i
f
f
.
68.69
96.56
1
5.107
4.230
0.878
0.94
165
­
2
5
2
4.610
4.810
­
0.200
­
0
.
2
1
100.48
122.73
­
22.25
3
4.886
4.797
0.089
0.10
132.37
121.14
11.23
4
3.053
3
.
7
9
1
­
0.738
­
0.79
21.18
44.29
­
23.11
5
5.586
4.909
0.677
0
.
7
3
266.78
135.55
131.23
6
2.664
3.474
­
0,809
­
0.87
14.36
32.25
­
17.89
7
5.561
4.440
1.121
1.20
8
5.310
4.890
0.420
0
.
4
5
9
2.802
4.903
­
2.101
­
2.25""
16.48
134.67
­
118.19
10
3.517
4.503
­
0.986
­
1.06
33.67
90.29
­
56.62
11
4.353
3.978
0.375
0.40
77.70
1
2
3.463
4.472
­
1.009
­
1.08
3
1
*
90
13
4.816
4
.
2
6
1
0.556
1
2
3
.
5
1
1
4
4.862
4.699
0.163
129.27
1
0
9
.
8
4
19.43
1
6
5.821
4,766
1.055
1.13
337.31
117.47
219.84
15
3.799
3.289
0.510
0
.
5
5
44.66
26.81
17.
as
RES
SUMSQ
FROM
REGRESSION
=
12.16245
RES
SUMSQ
DIRECT
=
12.16245
A
v
e
r
a
g
e
Observed
=
122.3331
A
v
e
r
a
g
e
P
r
e
d
i
c
t
e
d
=
89.5749
B
i
a
s
C
o
r
r
e
c
t
i
o
n
Factor
=
122.333
89.5749
=
1.3657
Ln(
S)
=
­
0.8093
+
0.731*
Ln(
C)

0.731
s
=
0.445.
c
ln
Table
3
the
observed
and
predicted
values
of
S
and
their
residuals
(
differences
between
observed
and
predicted)
are
shown
in
Ln
units,
then
in
their
original
metrics.
Sample
calculation:

From
Table
2,
first
row:
C
=
986.95
Spred
=
E~
p(­
U.
8093)*
C*­~
3~
=
0.445'
Co­
737
=
68.69
(
Table
3)

The
average
of
the
observed
values
is
122.3331;
t
h
e
average
of
the
predicted
values
is
89.5749.
The
ratio
of
the
average
observed
to
average
predicted
is
122.3331/
89.5749
=
1.3657.
This
offset
or
bias
was
caused
by
linearizing
d
fitting
in
terms
of
Ln(
S)
followed
by
conversion
back
to
the
original
u
The
unbiased
model
for
predicting
CJ
from
C
is:

0.731
0.731
Est
G
=
1.3657*
0.445*
6
Or
Est
0
=
0.608.
C
where
Est
CY
is
an
unbiased
c
1
10
100
1000
BY
compare
for
other
estimate
of
sigma.

Fst
(
r
0.608
60.8%*
F(
sD
3
.
2
7
3
2
.
7
0
*
17.6%
9.5%
17.62
94
­
8
2
k
*
extrapolation
fitting
all
of
the
pollutant
data
to
consistent
models
we
can
model
coefficients
for
one
pollutant
against
model
coefficients
pollutants.
paae
12
vow
Good
is
This
Model?

The
answer
to
t
with
the
model.
Let`
model­
building
process.
on
what
we
intend
to
do
T­
CRIT
0.05
&
0.01
=
2.17
&
2
.
9
8
VARIABLES
F
COEFF
T
0
Intercept
1
Power
Coefficient
.
p
=
0.73084
.
0.34030
2.15
.
.

RESSUMSQ
STDDEV
OF
RES
DF
R­
SQ
1
2
.
I6245
0.93207
1
4
0.2478
The
model
coefficients
are
­
0.8093
and
0.731.
SE
OF
COEFF
is
a
measure
of
how
well
we
have
estimated
the
coefficient,
p.
t
=
0.73087/
0.34031
=
2.15.
A
t­
ratio
larger
abou
2­
0
implies
we
have
detected
a
relationship
between
0;
and
C.
A
t­
ratio
2
(
approx­)
means
that
CT
is
not
a
constant,
but
is
associated
with
C.
substantially
larger
than
2.0
are
ecessary
to
a
coefficient.
The
reference
value
t
at
the
w
~
5
is
actually
2.1
5
.
See
the
line:
T­
CRIT
0.05
&
0
.
­
1
7
Ed
2
­
9
8
.
So
our
observed
value
of
t
(
2.15
as
compared
to
the
reference
value
2.17)
is
"
right
on
the
edge".
However,
t­
ratios
tely
estimate
a
model
5%
probability
level)

The
95%
confidence
interval
on
the
coefficient
p
is:

0.731
2.17*
0.340
or
from
0.00
to
1.47
which
suggests
that
the
true
coefficient
eo
d
be
as
small
as
"
zero"
(
implying
no
association
between
C
and
0)
r
as
large
as
1.47.
It
would
be
misleading
to
report
p
=
0.731
without
the
uncertainty
in
this
estimate.
If
we
compare
a
power
coefficie
r
one
pollutant
to
that
of
another,
we
must
recognize
that
when
t
or
P
is
modest,
th
confidence
interval
on
that
value
of
p
m
R­
SQ
(
R­
squared)
=
0.2478
means
this
model
explains
4778%
of
the
variation
in
t
h
e
data.
STDDEV
OF`
RES
is
t
h
e
standard
deviations
of
residuals.
This
is
t
h
e
standard
deviation
of
the
differences
between
observed
and
predicted
values
in
Ln(
S)
units.
This
is
not
an
estimate
of
0,
STDDEV
OF
RES
is
a
measure
of
variation
among
values
of
Ln(
S).
It
is
also
an
estimate
of
the
standard
deviation
that
we
would
find
if
we
could
run
replicate
tests
under
a
fixed
set
of
conditions
and
report
the
variation
among
values
of
Ln(
S).
In
this
context
"
the
data"
is
in
terms
of
Ln(
S).
paae
13
A
logical
extension
to
this
would
be
to
inquire
"
how
good
is
a
prediction
made
from
this
model?"
This
suggests
we
will
calcuiate
the
unbiased
estimate
of
C
(
Est
0)
for
a
fixed
value
of
C....
then
calculate
a
confidence
interval
on
that
predicted
value.
Before
doing
this,
here
are
two
values
that
we
will
need.
One
of
these
is
the
average
of
Ln(
C)
and
the
other
is
average
of
the
L
(
s).
Avg(
LnC)
7,1116.
Avg(
LnS)
=
4,3881.

The
confidence
interval
on
Est
CT
is
best
found
by
re­
stating
the
model
in
a
different
format:

Original
Format:
Ln(
Est
CT)
=
­
0.8093
+
0.731*
Ln(
C)

New
Format:
Ln(
Est
0)
=
Avg(
LnS)
+
0.731*[
Ln(
C)
­
Avg(
LnC)]
New
Format:
Ln(
Est
o)
=
4.3881
+
0.731*[
Ln(
C)
­
7.11161
The
variance
of
a
prediction
of
Ln(
o)
is:

Var(
Lno)
=
[
StdDev
of
Res12/
N
+
[
SE(
Coeff)
12*[
Ln(
C)
­
7.1
11
6j2
Eq.
1
Table
vslue
of
t
I
T­
CRIT
0.05
&
0.01
=
2.17
I
&
2.98
VARIIBLES
COEFFICIENTS
SE
OF
COEFF
T­
RATIO
I
0
Intercept
­
0,80
932
RESSUMSQ
STDDEV
OF
RES
DF
R­
SQ
12.16245
0.93207
14
0.2478
1
Power
Coefficient
p
=
0.73084
0.34030
2.15
I
I
I­

t­
ratio
calculated
r
N
=
1
6
f
r
o
m
data
L*
i
Var(
Lno)
=
[
0.9321
]*/
I6
+
[
0.3403]**[
Ln(
C)
­
7.1
1
16J2
Var(
Lncr)
=
0.0543
+
O.
l158*[
Ln(
C)
­
7.111612
P
LA
SE(
Lno)
=
dVar(
Lno)
predicted
value
of
Lno,
also
called
the
standard
error
of
This
is
the
standard
deviation
of
the
prediction.
See
note
at
the
bottom
of
page
14.
_.
"~
paae
14
Here
is
t
h
e
sequence
for
calculating
a
95%
confidence
interval
on
CT:

Step
1:
Calculate
the
predicted
valu
either
of:

Ln(
Est
CT)
=
­
0.

Ln(
Est
a)
=
4.3881
+.
0.731*[
Ln(
C)
­
7.1
1161
SE(
Est
0)
=
dVar(
Est
0)
See
footnote.

Step
3:
The
95%
confidence
interval
on
Ln(
Est
0)
is
then
Ln(
Est
G)
t*
SE(
Est
)
where
t
is
the
table
or
reference
value
of
t
at
the
0.05
level
of
significance.
t
=
2.17
in
this
instance.
r
L'

Step
4:
Revert
to
the
orig
I
units
and
the
unbiased
estimates:

Take
antiin
of
Est
CT
Take
antiLn
of
the
lower
bound
Take
antiLn
of
the
upper
bound
Multiply
Est
0,
the
lower
bound,
and
the
upper
bound
by
the
bias
correction
factor
1.3657
Est
G
and
t
h
e
95%
confide
e
On
are
shown
in
4­

The
expression
Standard
Error
(
Symbol:
SE)
means
the
Standard
deviation
Of
a
StatiStiC.

Literally,
the
standard
deviation
of
a
value
calculated
from
data.
This
is
Stan
designed
to
keep
issues
about
"
t
~
e
standard
deviation"
(
calculated
from
"
the
from
issues
about
the
standard
deviation
of
other
quantities
calculated
from
data.
4
LOWlS
U?
p?
Z
A
V
P
T
;
I
~
~
C
LiFir
t
s
t
CT
Limbic
10
0
.
c93
3.254
118.073
20
0.249
5
.
4
2
5
118.174
50
0.946
10.600
118.756
100
2.583
17.594
119.830
500
24.797
57.058
131.283
1000
55.878
94.704
160.5C9
zoao
84.433
151.189
292.637
200
6.979
29.203
122.537
5000
96.804
307.125
974.353
A
graphical
analysis
of
this
table
is
presented
in
Fig.
3.

Minimiz,
ina
t
h
e
Width
of
the
Confidence
Interval
Equation
1
(
repeated
here)
determines
the
width
of
the
confidence
interval
'
on
the
estimated
value
of
sigma,
Est
G.

Var(
Est
a>
=
[
StdDev
of
ResI2/
N
+
[
SE(
Coeff)]**[
Ln(
C)
­
AvgLn(
C)]'
Eq.
1
Whereas
Est
CT
is
a
measure
of
variation
due
to
sampling
and
analyzing,
the
StdDev
of
Res
(
standard
deviation
of
residuals)
is
a
measure
of
the
variation
among
individual
values
of
LnfS).
Reducing
the
variation
in
sampling
and
analysis
methods
would
reduce
t
h
e
magnitude
of
probably
reduce
StdDev
of
Res
as
well.
A
reduction
in
StdOev
reduce
the
width
of
the
confidence
intervals.

N
is
the
"
number
of
tests"
(
number
of
duplicates,
triplicates,
quads,
etc.);
literally
t
h
e
number
of
rows
in
the
data
table
from
which
we
fit
S
vs
C.
Increasing
N
will
decrease
[
StdDev
of
Res]*/
N
and
will
therefore
decrease
the
width
of
the
confidence
interval.

SE(
Coeff)
is
strongly
influenced
by
the
span
of
t
h
e
data
along
the
scale
of
C,
the
concentration
of
a
pollutant.
Varying
C
over
a
wide
range
will
decrease
SE(
Coeff)
and
will
therefore
decrease
the
width
of
the
confidence
interval.
concentrated
at
a
"
low
value
of
C"
and
one­
half
of
the
data
are
concentrated
at
a
"
high
value
of
C",
then
SEfCoeff)
will
be
minimized.
SE(
Coeff)
is
also
reduced
by
increasing
N
and
by
reducing
StdDev
of
Res.
Furthermore,
if
about
one­
haif
of
the
data
are
[
Ln(
C)
­
AvgLn(
C)
J2
is
a
function
of
where
the
prediction
is
being
g
the
scale
of
C.
When
a
prediction
is
made
at
the
centroid
of
tn(
C)
=
AvgLn(
C)
and
this
term
goes
to
zero.
When
this
is
so,
then
Var(
Est
0)
=
[
StdOev
of
Res]*/
N.
This
means
that
the
width
of
the
confidence
interval
will
be
minimized
when
predictions
are
made
at
the
centroid
of
Ln(
C).
.

The
best
way
to
visualize
this
is
with
an
example
in
which
data
are
concentrated
at
two
points
on
the
scale
of
C.
The
data
in
Table
5
are
simulated
data
from
the
same
source
as
the
foregoing
example.

Data
Sample
1
243.3
2
5
3
.
6
2
237.3
233.7
3
151.1
143.5
4
2p0.4
216.6
5
1
7
3
.
1
207.6
6
141.8
159.0
7
233.2
208.4
8
139.9
153.6
9
1733.4
1828.4
10
2022.6
1754.9
11
2127.9
2014.9
12
2064.0
2047.6
13
2016.6
1934.1
1
4
1s
1
6
2003.9
1808.6
Ava.
C
s
147.36
5.37
248.45
7.28
235.50
2.55
233.50
23.90
190.35
24.40
150.40
12.16
220.80
17.54
146.75
9.69
67.18
1780.90
1888.75
189.29
2071.40
79.90
2055.80
11.60
1975.35
58.34
1822
.)
2
0
77.78
2326.75
233.98
1906.25
138.10
gzbiased
s
9.12
3.20
6.73
29.95
30.57
15.24
21.98
12.14
84.18
237.18
100.11
14.53
73.10
97.46
293.18
173.04
I
is,
Table
6
is
t
h
e
feast
squares
analysis
of
the
data
in
Table
5.
The
relationship
between
S
and
C
is
shown
in
Figures
4
and
5.

i­
x
I
I
L
Se
are
equivalent
to
the
lower
and
upper
95%
confidence
!­­­
inten/
af
on
the
slope
in
Ln­
Ln
coordinates;
i.
e.,
on
the
model
coefficient
p.
Recall
that
the
,
L
lower
limit
on
p
was
0.00;
hence
"
A"
is
horizontal.
This
may
aid
in
seeing
how
the
imprecision
in
estimating
the
slope
impacts
the
confidence
interval
on
predicted
values
of
sigma.
This
imprecision
in
estimating
the
slope
is
reported
as
SE
of
Coeff.
pz"*
i
paae
18
.
.
.
.
i­

f­?
­~
i
~
­
~

~.
­~
­~
­
__­

paae
20
T
a
b
l
e
6
T
a
b
l
e
=­
slue
of
t
I
T­
CRIT
0.05
&
0.01
=
2.17
&
2.98
VAR
IA9
LES
COEFFICIENTS
SE
OF
COE?
F
T­
RATIO
0
Intercep
I
1
Power
Co
0
­
18436
4.73
RESSUMsQ
STDDEV
OF
RES
I
.
"
10.51455
I
fficient
p
=

.
.

I
t
­
r
a
t
i
o
calculated
StdDev
of
Res
N
=
16
from
data
I
n
Ln
U
n
i
t
s
I
n
Oriainal
Metrics
OBSVD
PRSD
RESID
STD
RES
O
b
s
e
r
v
e
d
Predicted
D
i
f
f
.

1
2.210
2.791
­
0.580
­
0.67
9.1
16.29
­
7.17
2
1.163
2.744
­
1.581
­
1.82
3.20
15.55
­
12.35
3
1.907
2.335
­
0.429
­
0.49
6.73
10.33
­
3.60
15.43
14
­
52
4
3.400
2.737
0.663
0.76
29.95
5
3.420
2.559
0.861
0.99
30.57
12.92
1
7
.
6
5
6
2.724
2.353
0.371
0.4
15.24
io.
52
4
­
72
7
3.090
2.688
0.402
0
­
4
21.98
'
14.70
7.28
8
2.497
2.332
0.164
0.19
12.14
10.30
1.84
9
4.433
4.506
­
0.0t3
­
0.08
84.18
90.60
­
6.42
10
5.469
4.558
0.911
1.05
237.18
95.36
141.82
If
4.606
4.638
­
0.032
­
0.04
100.11
103.34
­
3.23
12
2.676
4.631
­
1.955
­
2.26**
14.53
102.66
­
88.13
73.10
99.16
­
26.06
13
4.292
4.597
­
0.305
­
0.35
14
4.579
4.526
0.053
0.06
92.42
5.04
15
5.681
4.739
0.941
1.09
114.36
178.82
16
5.154
4.566
0.588
­
68
173.04
96.13
76.91
RES
SUMSQ
FROM
REGXESSION
=
10.51455
RES
SUMSQ
DIRECT
=
10.51456
Average
O
b
s
e
r
v
e
d
=
75.1069
A
v
e
r
a
g
e
P
r
e
d
i
c
t
e
d
=
56.2545
B
i
a
s
Correction
Factor
=
75.1069/
56.2545
=
1.3351
0.871
Est
c
=
1.3351'
0.1335*
C
t
r
t
0.871
Est
CJi
=
0.178'
C
The
95%
confidence
interval
on
p
is:

an
improvement
over
0.00
to
1.47
in
the
previous
example,

New
Format:
Ln(
Est
G)
=
Savg
+
0.8712*[
Ln(
C)
­
Cavg]
New
Format:
Ln(
Est
0)
=
3.58126
+
0.8712+[
Ln(
C)
­
6.422821
The
variance
of
a
prediction
is
(
Eq.
1
is
repeated
here):

Var(
Est
0)
=
[
StdDev
of
Res]'/
N
+
[
SE(
Coeff)
J2"[
Ln(
C)
­
Avg
of
Ln(
C)
l2
Eq.
1
t
0)
=
[
0.86S63J2/
16
+
[
0.18436j2'[
Ln(
C)
­
6.422821'

Var(
Est
0
)
=
0.04694
+
0.0344*[
Ln(
C)
­
6.42282J2
Note
that
lSE(
Coeff)]*
=
0.0344
compared
to
0.1158
in
the
previous
exampfe.
By
concentrating
data
at
the
extremes
of
the
experimental
space
~

the
width
of
the
confidence
interval
has
been
reduced
significantly.
Est
oand
the
95%
con
ence
on
are
shown
in
Tab,
e
7.

Table
7
Lower
Averace
c
.
L
i
m
i
t
10
0.236
20
0.564
50
1.765
100
4.125
500
24.812
1000
43.978
5000
113.262
200
9.375
2000
68.641
­­
1:
324
2.422
5.381
9.843
18.004
40.000
73.
1
6
7
133.836
297.342
Upper
Limit
7.421
10.400
16.402
23.484
34.577
64.235
121.723
260.95:
780.600
A
graphical
analysis
of
Table
7
is
presented
in
Figure
6
.
..

e
.
I
v3
O
I
I
I
0
0
paae
22
The
simulated
data
used
in
these
examples
(
Tables
2
and
5)
came
from
this
model:
0
=
0.28*
C0*
8.
The
value
of
C
was
varied
randomly
in
Table
2
and
varie
domly
around
two
points
on
the
scale
of
C
in
Table
5.
calculated
from
C;
from
a
Source
with
mean
C
and
n
0,
two
random
normal
numbers
were
generated;
those
numbers
are
the
data.
This
process
was
repeated
16
times.
When
C
=
100
the
true
RSD
=
11
.
WO;
when
C
=
1000
the
true
RSD
=
7.0%.
These
levels
of
ical
of
those
encountered
in
the
analysis
of
t
h
e
actual
The
model
derived
from
data
in
the
first
simulation
(
Tabfe
2)
is
Est
a
=
0.608*
C0*
73'
The
95%
confidence
interval
on
p
is
0.00
to
1.47.

The
model
derived
from
data
in
the
second
simulation
(
Table
5)
is
Est
0
=
0.178*
C0­
871
The
95%
confidence
interval
on
p
is
0.47
to
1.27.

With
this
in
mind,
here
are
some
important
conclusions.

Even
when
simultaneously
sampled
data
come
from
a
"
perfect"
situ
ation
such
that:

e>
the
underlying
model
is
exact
and
the
data
are
contaminated
only
by
random
variation
C>
there
are
no
concerns
about
sample
contamination,
selective
or
biased
sampling
of
particles,
or
other
"
special
causesy'

finding
a
relationship
between
Est
CT
and
the
average
concentration
C
yields
model
coefficients
and
predictions
that
are
subject
to
statist
ica
1
u
nc
e
rt
ai
n
t
y
.
­

The
evidence
of
this
uncertainly
is
illustrated
by
the
fact
that
two
sets
of
data
from
a
"
perfect
situation"
produce
models
that
have
different
coefficients
and
therefore
different
estimates
of
Est
CF
as
a
function
of
the
average
concentration
C.

.
SE(
Coeff)
is
a
major
contributor
to
wide
confidence
intervals
Although
not
discussed
in
detail
here,
SE(
Coeff)
is
on
Est
0.
strongly
influenced
by
(
1)
the
allocation
of
experimental
points
along
the
scale
of
C;
(
2)
the
amount
of
data:
and
(
3)
the
inherent
variation
in
t
h
e
data.
Weiqhted
Rearession
Although
the
majorit
samples
with
octets.
Reca
When
those
values
are
derived
fro
should
be
weighted
in
acc
information
in
each
value
As
a
rule,
t
h
e
qua
21
there
were
insta
is
Q
=
Sum
of
W,
t(
S,
­
pred
Si)
2
where
Si
is
an
observed
standard
deviation;
pred
Si
is
the
predicted
is
the
weight
assigned
to
the
i­
th
inversely
proportional
to
the
varia
approximation,
Minimize
Q
=
Sum
of
(
1/
Var
Si)'(
Si
­
pred
Si)
2
The
variance
of
Si
is
(
an
approximation)
proportional
to
O
be
assigned
to
each
servations
used
to
a
as
The
eight
assigned
to
each
of
that
standard
deviation;
and
Wi
weights
should
be
1/[
2(
N
­
I)].
Thus
the
re1
is
2(
N
­
1)
where
N
is
th
given
value
of
S.
This
is
observed
valu
freedom
associated
with
that
value
of
S.
If
N
=
2
the
weight
is
1.
If
N
=
3
the
weight
is
2,
etc.

unweighted
regre
)
­
But
the
for
weighted
regression
are
s
the
confidence
intervals
requires
For
these
reasons
we
reco
regression
be
used
for
this
Of
to
just
the
number
of
degrees
of
The
calculations
for
weighted
regression
to
those
for
In
particular,
calculating
matrix
Operations­
e
designed
for
weighted
Errors.
Outliers,
and
Mavericks
paae
25
Questionable
data
is
given
a
diversity
of
names,
such
as
mavericks
fliers,
outliers,
sports,
and
blunders.
These
aberrations
can
be
caused
by
contamination
of
samples,
switched
or
mislabeled
samplss,
faulty
equipment
or
reagents,
key
entry
errors,
and
a
host
of
other
events.
Such
data
is
a
source
of
frustration,
and
often
causes
pointless
discussions
and
wasted
effort.
Some
statistical
criteria
are
available
to
assist
in
learning
whether
or
not
the
largest
or
smallest
observation
is
significantly
far
removed
from
the
main
body
of
the
data.
1
In
this
section
we
will
address
this
matter
from
two
perspectives.
The
first
of
these
is
an
omnibus
examination
of
all
of
the
data
in
one
pass.
The
other
is
more
focused,
and
addresses
only
one
triplicate
or
quad.

Table
8
was
derived
from
Table
5.
The
data
were
broken
into
two
categories...
low
C
and
high
C...
with
the
expectation
that
variation
will
be
constant
(
or
virtually
constant)
at
low
C
and
that
variation
will
be
constant
at
high
C.
Of
course
we
expect
that
variation
will
change
between
low
C
and
high
C,
which
was
the
point
to
breaking
the
table
into
these
two
categories.

Ranae
Ava,
C
248.45
10.3
1
243.3
253.6
3.6
2
237.3
233.7
235.50
147.30
7.6
3
151.1
143.5
233.50
33.8
4
250.4
216.6
5
173.1
207.6
150.40
17.2
6
141.8.
159.0
220.80
24.8
7
233.2
208.4
146.75
13.7
8
139.9
153.6
Data
SamDle
190.35
34.5
Avg
Range
=
18.19
9
1733.4
1828.4
1780.90
95.0
10
2022.6
1754.9
1888.75
267.7
11
2127.9
2014.9
2071.40
113.0
12
2064.0
2047.6
2055.80
16.4
13
2016.6.
1934.1
1975.35
82.
i
15
2161.3
2492.2
2326.75
330.9
16
2003.9
1808.6
1906.25
195.3
14
1877.2
1757.2
1822.20
110.0
Avg
3an'ge
=
151.35
The
range
is
shown
for
each
simultaneous
sample.
The
average
range
is
reported
for
each
of
the
two
groups.

In
Statistical
Process
Co
whether
any
of
these
ranges
a
quads
we
only
test
for
abnor
small
ranges
is
not
meaningful.
determine
whether
any
of
the
ra
s
customary
to
test
.
.
.
.
.
.
.
,
.
.
.
.

SamDle
Size,
n
2
4
­

2
3
.
2
6
7
3
2
.
5
7
5
4
2
­
2
8
2
5
2
.
1
1
5
Step
1:
The
data
used
to
calculate
ranges
were
duplicates.
The
sample
size
is
n
=
2.

Step
2:
Multiply
the
average
range
by
0,
for
each
category.
3.267
x
18.19
=
59.4
3.
151.35
=
494*
5
Step
3:
Compare
t
dividual
ranges
ag
these
limits.
When
C
is
ranges
larger
than
are
suspect.
When
C
is
questionable.
t
ges
larger
than
494.4
are
­
All
of
the
ranges
passed
the
test.
re
is
no
evidence
for
any
of
the
data.

WC
t
t
Now
let's
consider
how
t
data
was
not
concentrated
at
t
derived
from
Table
2.
Table
10
is
ran
ed
to
a
in
ca'e
Of
c.
Ta
and
then
broken
into
three
cat
ego
ries
.
r
t
­
*
F
k
Fm­
­
247.2
297.6
358.9
342.7
743.6
655.9
893.7
1080.2
529.4
553.3
960.3
1099.7
7
1
4
6
3
.
0
1169.4
12
1356.8
1392.8
10
1415.8
1453.8
1
4
1949.0
1803.1
!
1
6
1865.4
2247.1
3
2070.3
2219.7
r
2
2240.4
2127.0
Lw
8
2
5
4
9
.
1
2320.8
9
2488.9
2470.3
5
2
3
5
1
.
1
2652.2
L
,

The
rules
are
applied
as
before.
i
I
L
c
t
9vrJ.
c
3.
a
?.?
a
350.80
15.2
272.40
5
­
3
.
4
541.35
23.9
699.75
87.7
985.95
185.5
72.94
=
k
v
g
Range
1030.00
1316.20
1374.80
1434.80
1
8
7
5
.
0
5
130
139.4
293.6
35.3
3
8
.
0
145.9
58
=
&­..
g
R
a
n
g
e
2056.75
380.7
2145.00
149.4
2183.70
113.4
2434.95
228.3
2479.50
18.6
2501.65
301.1
238.22
=
Avg
R
a
n
g
e
Step
1:
The
data
used
to
calculate
ranges
were
duplicates.
The
sample
size
is
n
=
2.
D,
=
3.267
Step
2:
Multiply
the
average
range
by
0,
for
each
category.
3.267
x
72.94
=
238.3
3.267
x
130.58
=
426.6
3.267
x
238.22
=
778.3
Step
3:
Compare
the
individual
ranges
against
these
limits
category­
by­
category
as
before.

F
n
i
any
of
the
data.
.
AI1
of
the
ranges
passed
the
test.
There
is
no
evidence
for
excluding
L
as
an
exam
n
using
this
If
there
are
gaps
in
the
ranke
categories
at
those
points.
There
i
of
data
will
be
in
each
category.
ctice
we
should
average
C,
then
break
the
data
into
ement
that
t
h
e
same
amount
.

The
extension
of
this
t
quads
only
requires
using
.
.
other
values
of
D4.
n
If
we
examine
only
one
set
or
triplicates
or
quads,
then
Dixon's­
r
procedure
is
appropriate.'

Consider
the
following
sirnultaneo
ly
data:

22.3
29.4
49.1
28.2
Step
1:
Rank
the
data
from
smallest
to
largest:

=
(
49­
1
­
29­
4M49.1
­
23­
8)
23.8
28.2
29.4
49.1
Step
2:
Calculat
r
=
0.779
Table
11
P
o
95­
P
o
.
99­
n
3
0.941
0.988
4
0.765
0.889
5
0
I
642
0.780
Step
3:
The
sample
size
n
=
4.

Step
4:
The
calculated
value
r
than
Po.
95
(
POag5
=
0.765).
The
evidence
suggests
that
the
remainder
Of
Ihe
data*

If
the
calculated
value
of
r
exceeds
the
table
value
at
Po.
99
then
the
evidence
is
even
stronger.

­­_.­­­

'
Dixon,
W.
J.
and
Massey,
F.
J.;
Introduction
to
StatisticaI
Analysis,
3rd
Ed.;
McGraw­
Hill;
1969.
pages
328
­
330.
­
p
t
h
F
1
f
L
.

Dixon's­
r
is
of
the
form:
r
=
(
Distance
between
the
largest
and
its
nearest
neighbor)/(
Full
Range
of
the
data.)
This
can
be
arranged
to
inquire
about
the
status
of
a
number
that
is
unusually
low
when
compared
to
the
remainder
of
the
data.

Examole:
121
179
185
193
r
=
(
179
­
121)/(
193
­
121)
=
0.805
This
is
farger
than
the
table
value
of
r
(
0.765)
with
n
=
4.
So
the
121
is
inconsistent
with
the
remainder
of
the
data.

Dixon's­
r
cannot
be
used
with
n
=
2
data.
It
assumes
the
data
came
from
a
normal
distribution.
This
is
a
reasonable
assumption
with
simultaneously
sampled
concentration
data.

See
Table
2
test
9
and
Fig.
2.
S
=
16/
48
seems
to
be
unusually
low.
This
is
also
appears
as
a
I
small
samples
(
espe
standard
deviation
to
of
duplicates
s
may
even
be
"
zero"
occasionally.
So
even
though
these
may
seem
unusual,
they
are
not.
/
Iy
duplicates
and
triads)
is
is
very
low.
In
the
for
the
paae
30
A
power­
law
model
was
used
throughout
this
report
because
the
data
will
not
support
more
than
two
There
may
be
instances
in
which
we
will
need
to
entertain
other
model
forms.
For
example,
please
draw
curve
to
expr
relationship
between
S
and
C
in
Fig.
7.
efore
proceedi
The
relationship
between
S
and
coordinates.
It
is
reasonable
to
con
model,
perhaps
S
=
a
i
kCP.
In
S
wifl
approach
a
when
C
=
0.
This
suggests
the
does
not
seem
to
be
linear
in
LkLn
Before
we
begin
setting
up
the
tools
to
estimat
a,
k,
and
p
in
this
extended
model,
we
should
work
through
the
1.
Test
the
data
to
deter
ther
the
appearance
of
curvature
(
in
Ln­
Ln
coordinates)
is
"
real"
o
hance
variation
data.
If
the
perceived
curvatu
to
random
va
the
data
...
and
not
a
syst
then
attempting
to
fit
thes
will
be
misleading
and
disapp
transforming
to
t
n
­
L
n
coordinates,
of
course.
he
test
for
curvature
after
2.
The
most
direct
way
to
test
for
curvature
is
to
fit
the
data
to
the
usual
power­
faw
model
...
Ln(
S)
=
Ln(
k)
­
i­
pLn(
C)
...
then
ask
whether
there
is
evidence
of
"
lack­
of­
fit".
This
is
easily
done
by
testing
to
see
whether
the
data
will
support
adding
associated
with
b
is
larger
than
the
appropriate
reference
value
of
the
t­
ratio
(
as
a
rule,
larger
than
21,
then
there
is
evidence
of
curvature;
the
simple
power­
law
model
is
not
adequate.
If
the
t­
ratio
associated
with
b
is
notably
smaller
than
2,
there
is
no
fir
evidence
of
curvature;
the
power­
law
model
is
adequate;
attempting
to
f
t
h
e
data
to
a
more
.
complex
model
to
account
for
curvature
is
pointless
and
misleading.
b[
Ln(
C)
I2
to
the
model.
If
the
t­
ratio
3.
The
purpose
of
(
2)
above
is
not
to
build
a
completed
model.
The
purpose
is
to
test
for
the
presence
of
curvature
beyond
that
which
is
accommodated
by
the
power­
law
model.
If
curvature
is
detected
(
t­
ratio
for
b
is
larger
than,
say,
2),
then
we
may
be
justified
in
considering
an
alternative
model.
S
=
a
+
kCp
would
be
a
candidate.
F"

L
F
!

U
0
0
P
0
0
T­
O
T
0
0
0
0
0
r
M
p
paae
32
This
process
was
followed
to
make
that
judgement
about
these
data.

AS
A
S
248.5
7.28
2375.0
58.34
235.5
2.55
1622.0
77.78
147.3
5
­
37
234.0
233.5
23.9
24.4
150.4
12.16
.
­
220.8
.
17.54
146.7
9.69
1281.0
67.18
2189.0
189.29
2071.0
7
9
.
9
2056.0
11.6
1906.0
138.1
18.6
6.48
26.
1.19
.
23.
5.18
32.4
12.06
34.6
3.12
39.6
12.82
45.7
2.96
4
8
.
9
7
.
1
0
In
Fig.
8
t
h
e
power­
law
mod
explained
66.5%
of
the
variation
in
Ln(
S).
In
Fig.
9
the
model
was
extended
by
adding
a
as
suggested
on
page
30.
This
extended
model
expla
variation
in
Ln(
S).
coefficient;
this
increas
in
R­
sq
does
not
is
important.
The
t­
ra
ratic
term
is
an
indication
of
whether
that
term
is
a
w
to
the
model.
adratic
coefficient
69.2%
of
the
R­
sq
will
always
increas
when
we
add
another
model
rove
that
the
quadratic
term
The
t­
ratio
for
t
h
e
quadratic
coefficient
is
on
3
6
;
far
below
the
reference
value
of
2.08
(
with
we
do
not
have
sufficient
evi
power­
law
model
S
=
kCP.
What
have
come
from
a
straight­
line
rela
This
does
not
mean
we
have
"
prove
relationship
prevails
in
Ln­
Ln
coordin
evidence
in
favor
of
a
more
complex
justification
for
adding
a
quadratic
term
to
little
justification
for
pursuing
an
alternative
model
such
as
S
=
a
+
kCP.

It
is
possible
t
h
a
t
with
additional
data
we
may
learn
that
curvature
is
actually
present,
and
that
an
extended
model
form
was
justified.
attempting
to
build
a
model
more
complex
than
S
=
kCp
is
not
appropriate
with
the
existing
data.
(
say,
S
=
a
+
kCp).­.
then
the
coefficients
in
that
model
will
be
poorly
estimated;
the
confidence
intervals
on
those
coefficients
will
be
extremely
wide;
and
we
have
gained
nothing
more
than
t
h
e
satisfaction
of
explaining
a
little
more
of
t
h
e
variation
in
t
h
e
data.
But
If
we
pursue
this
...
if
we
build
an
extended
model
Figure
8
page
33
smm.
2
Dstenninant
=
1.0000
mi?.
1
GOING
IN
VX?
IABUS
comrcms
SE
OF
am
T­
IIATIO
T­
CFUT
0.05
&
0.01
=
2.07
&
2.80
0
Intercept
2.77468
1
average
conc
0
.
68217
0.10316
6.61
ESSUMSQ
S?
pDEvOFRES
DF
R­
SQ
16.02539
0.85348
22
0.6653
<­­­
66.5%

In
In
Units
In
Original
Units
OBSVD
PREl
RESID
STD
RES
Observed
Pr&
i.
ct&
Diff
1.985
2.826
­
0.841
­
0.99
7.28
16.88
­
9.60
0.936
2.789
­
1.853
­
2.17
1.681
2.469
­
0.789
­
0.92
5.37
11.82
­
6­
45
3.174
2.784
0.390
0.46
23.90
16.18
7.72
3.195
2.644
0.550
0.64
24.40
14.08
10
.
32
2.498
2.484
0.015
0.02
12.16
If.
98
0.18
2.864
2.746
0.119
0.14
17.54
15.57
1.97
2.271
2.467
­
0.196
­
0.23
9.69
11.78
­
2
.
09
4.207
3.945
0.263
0.31
67.18
51
.
67
15
.
51
5.243
4.310
0.933
1.09
189.29
74.47
114.82
4.381
4.273
0.108
0.13
79.90
71.71
8­
19
2.451
4.268
­
1.817
­
2.13
11.60
71.35
­
59.7
4.066
4.366
­
0.300
­
0.35
58.34
78.73
­
20.3
4.354
4.106
0.248
0.29
77.78
60.70
17.08
5.4
4.352
1.104
1.29
234.00
77.62
156.38
16
0.712
0.83
138.10
67.76
70.34
1.869
1.058
0.811
0.95
0.174
1.294
­
1.120
­
1.31
1­
645
1.312
0.333
0.39
2­
40
1.436
1.054
1.23
1.138
1.481
­
0.343
­
0.40
2,551
1.573
0.978
1.15
1.085
1.686
­
0.601
­
0.70
1.960
1.717
0.243
0.28
2.55
16.27
­
13.72**

s
SQSQ
FEicM
REQESSION
=
16.02539
RES
rage
&.
served
=
42.0829
Average
Predi
Figure
9
page
34
s
w
m
.
3
Determinant
=
0.9
WRLABLES
S
SE
OF
EEET
T­
EAT10
=
2*
08
6r
2*
82
0
Intercept
1
average
conc
6.39
2
quadratic
0.08073
1.36
<­­­

14.12537
0.83738
21
0.6924
69.2%
­
.
.
­
66.5%
.
=
2.7%
_
.
RESSUJSQ
STDDEVOFWS
DF
R­
SQ
Note
Ln(
S)
=
2.461
+
0.657*(
Ln(
C)
­
5.44)
+
O.
ll*(
Ln(
C)
­
5.44)­
sq
1
2
3
4
5
6
I
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
In
Ln
U
n
i
t
s
In
Original
Units
OBSVD
PPED
RESID
STDRES
Observed
Predicted
D
i
f
f
1.985
2.511
­
0.526
­
0.63
7.28
12.32
­
5.04
1.681
2.
­
0.508
­
0.61
5.37
8.93
­
3.56
3.174
2.470
0.
23.90
11.82
12
.
08
24.40
10.38
14.02
12.16
9.03
3.13
2.864
2.433
0
17.54
11..
40
6.14
2.271
2.187
0
9.69
8.91
0
­
78
4.207
3.912
0.295
0.35
67
.
18
50.01
17.17
5.243
4,498
0.745
0.
189.29
89.83
99.46
4.381
4.434
­
79.90
84.31
­
4
.
41
2.451
4.426
­
11.60
83.61
­
72.01**
~

4.066
4.593
­
58.34
98.76
­
40
.
42
4.354
4.162
77*
78
64.23
13.55
5.455
4.568
0.887
1.06
234.00
96.38
137.62
4.928
4.341
0.
0.70
138.10
76.75
61.35
1.869
1.503
0.
6.48
4.50
1.98
1.645
1.557
0.
5.18
4.75
0.43
2.490
1,595
0.895
1.07
12
.
06
4.93
7.13
1.138
1.610
­
0.472
­
0.56
3.12
5.00
­
1.88
2.551
1.645
0.906
1.08
12.82
5.18
7.64
1.085
1.692
­
0.607
­
0.72
2.96
5.43
­
2.47
1.960
1.706
0
5­
51
1.59
0.936
2.476
­
1.539
­
1.84
2.55
11.89
­
9
.
34
0.174
1.552
­
1.
1.19
4.72
­
3
.
53
EES
SmSQ
rn
REGRESSION
Average
Cbserved
=
42,0829
D
I
E
C
T
=
14.72535
Average
Predicted
=
32.0234
lxLaa5
The
foregoing
data
can
be
fit
directly
to
a
model
of
the
form
S
=
a
+
kCP
using
t
h
e
following
technique.
Set
p
to
a
constant
(
say,
0.6)
and
fit
S
=
a
+
kC0.6.
Since
this
model
is
linear
in
the
coefficients
a
and
k,
ordinary
least
squares
methods
can
be
used
to
estimate
those
coefficients.
Repeat
this
process
for
p
=
0.8,
1.0,
etc.
When
this
is
done:

0
a
k
Resi&
zl
Sum
S
a
0.6
­
10.27
1.24
40.52
0.8
­
1.61
0.25
39.96
1.0
2.95
0.053
39.66
1.2
5.60
0.012
39­
50
1.4
7.26
0.0024
39.43
1.6
8.39
0.00052
39.41
The
coefficient
a
is
an
estimate
of
(
r
when
C
=
0.
Negative
values
of
a
imply
that
CT
becomes
negative
as
the
average
concentration
approaches
zero.
So
p
c
1
is
certainly
not
acceptable.

The
residual
SUM
of
squares
...
a
direct
measure
of
how
well
a
model
explains
the
variation
in
S,
is
insensitive
to
the
least
squares
combinations
of
a,
k,
and
p.
The
estimates
o
f
all
three
coefficients
are
highly
correlated.
minimizes
the
r
er.
This
m
very
wide.
This
will
happen
when
the
data
is
not
cap
There
is
no
unique
combination
of
coefficients
`
that
ual
sum
of
squares;
one
combination
is
as
good
as
any
that
the
confidence
intervals
on
the
model
coefficients
of
accurately
able
situation
estimating
the
coefficients
in
the
residual
s
u
m
of
squares
I{
have
a
"
sharp"
well­
defined
minimum.

The
underlying
chemistry
or
physics
may
suggest
that
G
converges
to
a
iimit
greater
than
zero;
Fig.
7
suggests
this.
What
harm
is
done
by
fitting
the
S
vs.
C
data
to
a
model
...
viz.,
S
=
a
+
kC
p...
that
supports
this
theory
about
the
lower
bound
on
o?
That
depends
on
t
h
e
definition
of
harm.
The
prior
analysis
showed
there
is
insufficient
evidence
to
support
"
curvature"
in
Ln­
Ln
coordinates.
If
an
alternative
model
is
used
to
claim
that
t
h
e
data
follows
a
certain
theory,
when
in
fact
the
model
coefficient
that
wouJd
support
that
theory
is
not
supported
by
the
data,
then
that
is
a
poorly
founded
claim.
The
resolution
to
this
is
to
g.
et
data
.
that
wilt
rr
properly
test
theory;
in
this
instance,
iet
data
at
very
low
levels
of
C.
In
any
event,
confidence
intervals
on
a,
k,
and
p
should
be
repofied.
,

h­
np
paae
36
The
Performance
of
t
h
e
ReMAP
Process
The
ReMAP
process
i
ing
relationships
between
estimates
of
sigm
degrees
of
freedo
derived
from
small
samples
process
can
be
found
in
text
statistical
procedure.
It
is
ther
the
ReMAP.
process
perform
Monte
Carlo
simulati
ReMAP
process.
By
perfu
intervals
on
sigma
encu
verify
that
statements
interval
has
encompassed
sigma"
are
accurate.

The
simulations
are
comprised
of
the
following
s
I
.
Generate
data
that
lese
bles
actual
data.
The
model
used
to
models
cited
in
the
were
clustered
near
.2*
Co.
8
This
resembles
simulated
data
tions
they
were
scattered
d
we
mean
the
data
and
in
another
band
to
generate
the
random
normal
deviates
3.
Steps
1
­
2.
were
repeated
(
say)
20
times
to
generate
20
sets
of
simultaneous
samples,
each
comprised
of
a
pair
(
N
=
2)
of
4.
The
sample
average
and
sample
standard
deviation
S
were
calculated
for
each
pair
of
data.
of
S
was
m
by
the
small
sample
correction
factor
1.253
to
obtain
un
estimates
of
sigma.
L­
paae
37
of
the
form
Ln(
S)
=
Ln(
K)
+
p'Ln(
C).
This
equation
was
used
to
predict
Ln(
S)
for
each
of
the
20
combinations.
5.
The
(
sample
average,
S)­
combinations
were
used
to
build
a
model
­
I­

­
r
b.
2
Estimates
of
1
Ln(
S)
were
converted
to
estimates
of
S
by
Exp(
Ln(
S)).

L
A
a.

6.
As
in
the
ReMAP
process,
the
ratio
of
the
average
of
the
observed
vatues
of
S
to
the
average
of
the
predicted
values
of
S
was
used
to
calculate
the
bias
correction
factor,
BCF.

7.
95%
confidence
intervals
were
calculated
in
terms
of
Ln(
Sj
and
8.
The
predicted
values
of
Ln(
S)
and
the
intervals
OR
Ln(
S)
were
'

r­

kJ
F­=

i
c
i
L
intervals
on
Ln{
S).
irrm
I
ienr
to
estimates
of
sigma
and
the
confidence
intervals
on
ugh
Exp(
Ln(
S)).
The
completed
prediction
equation
is
of
/
bR14
bur
t
h
e
form
Est
Sigma
=
BCF'kCP.

$""

9.
This
equation
...
the
line
of
regression
...
was
traversed
in
small
steps
along
t
h
e
entire
length
of
the
line
(
from
C
=
500
to
C
=
5000.
The
upper
and
lower
confidence
limits
were
calculated
The
frequency
with
which
those
intervals
the
true
values
of
Sigma
(
the
true
values
of
sigma
m
Sigma
=
0.2'
co.*)
was
recorded.
L
P
r
kn­
n
8.
This
entire
process
from
Step
1
through
Step
9
was
repeated
The
foregoi
imulates
getting
10,000
complete
sets
of
ReMAP
data;
fitting
those
vto
the
model
Ln(
S)
=
Ln(
K)
+
p*
Ln(
C);
applying
the
L+
appropriate
bias
correction
factors;
and
(
because
we
know
the
true
value
of
Sigma
in
these
simulations)
observing
bow
frequently
the
population
of
confidence
intervals
actually
encompass
the
true
values
of
sigma.
..
­
.
­
...
""""
10,000
times;
in
some
instances
30,000
times.

L
UIIY
The
simulations
also
provided
information
about
biases
in
I
estimating
sigma
usi
the
ReMAP
process.
The
bias...
100'(
Est
Sigma
­
S
a)/
Sigma..,
ranged
from
­
0.1%
at
low
levels
of
C
(
hence
low
values
of
sigma)
to
+
1.1%
at
high
levels
of
C
(
high
levels
of
Y"
S
sigma).
This
means
that
hen
the
estimated
value
of
sigma
is,
for
example,
10,
the
true
of
sigma
could
be
as
low
as
9.89.
Using
the
*
same
examp
vel
of
concentration,
the
true
value
of
sigma
l__
y
could
be
10.
P
L
e
This
bias
is
trivial
when
compared
to
other
considerations
such
as
the
the
confidence
intervals
on
sigma.

I
*_
Y
~­

~~
~
­
­~
C~

­

oaae38
To
verify
the
software
of
this
software
was
written
generating
data
from
the
Y
=
60
+
0.3'
X
was
use
fitting
the
data
to
the
m
to
a
model
of
t
h
e
form
Y
=

?
he
usual
95%
confi
value
of
Y
in
the
mann
d
for
these
simulations,
an
identical
copy
h
the
following
changes.
Instead
of
...
these
data
were
fit
the
95%
confiden
designed
to
perform;
an
for
simulating
the
ReMA
3
that
purpose,
between
97%
a
encompassed
the
true
values
o
"
95%
confidence
intervals"
act
the
frequency
of
capturing
data;
simulations
were
run
z
I;
u
97%
of
the
intervals
calculat
the
frequency
of
capture
is
prese
ReMAP
process.

Simulations
were
run
to
understand
t
r,
The
magnitude
of
this
increase
Lui
i
1
compared
to
95%)
depends
up0
When
we
have
two
simultaneous
sarn
97%
­
98%
intervals.
Whe
"
95%
intervals"
are
actual1
produce
a
distribution
of
S
that
is
hig
will
produce
a
distribution
of
S
that
i
cause
of
intervals
t
h
a
t
are
somewhat
broader
t
h
a
n
expected.
paae
39
No
real
harm
has
been
done
by
this
small
deviation
from
expected.
it
just
means
that
we
should
remember
that
what
we
are
calling
95%
intervals
are
closer
to
97%
­
98%
intervals.
Our
probabifity
of
capturing
sigma
with
these
intervals
is
a
little
higher
than
anticipated,

In
the
foregoing
discussion
we
have
described
the
performance
of
the
ReMAP
process
in
terms
of
individual
confidence
intervals.
These
intervals
are
calculated
and
presented
throughout
this
report.
This
means
that
when
we
estimate
a
confidence
interval
at
a
point
along
the
scale
of
C,
we
can
declare
that
"
95%
of
the
intervals
calculated
in
this
manner
value
of
sigma.
(
We
know
it's
really
97%
­
98%,
but
is
discussion
we'll
skip
that
detail.)
This
also
means
n
the
scale
of
C)
"
the
probability
that
this
confidence
sigma
is
95%".
S
there
is
a
probability
that
sigma
is
a
litt
larger
than
the
calcu
ller
than
the
calcufated
lower
limit.
In
ity
of
"
about
1%
in
each
tail."
limit,
or
a
littl
reduces
to
a
There
is
another
concept
that
should
be
considered.
This
is
the
concept
of
a
confidence
interval
on
a
line
as
a
whole.
These
intervals
are
concerned
with
probability
that
a
confidence
interval
captures
the
true
values
of
sigma
at
every
point
along
a
line,
(
over
t
h
e
range
of
the
tated
as
"
the
probability
is
X%
that
this
confidence
the
true
values
of
sigma
at
all
points
alo
e
intervals
that
f
capture
sigma.
In
this
n
is
directed
to
the
frequency
at
which
sig
d
of
the
line
to
the
other,
rather
than
at
i
Thus
the
frequ
captured",
not
in
terms
of
individual
scale
of
c
u
m
on.
This
is
also
th
of
capturing
is
in
terms
of
"
lines
ts
captured.
Capturing
the
entire
line
(
the
line
is
Sigma
=
0.2`
Co.
8)
as
opposed
line
is
a
rather
stringent
requirement.

In
this
report
the
cited
confidence
intervals
intervals,
or
points
on
the
line,
not
whole
line
statement
"
95%
of
the
intervals
calculated
in
sigma"
means
95%
of
the
individual
intervals.
interpretation
of
confidence
intervals.
to
individual
points
on
the
are
in
terms
of
individual
intervals.
Thus
the
this
manner
will
encompass
This
is
the
usual
For
more
information
concerning
whole
line
confidence
intervals,
see
Natrella,
M.
G.;
Experimental
Statistics;
National
Bureau
of
Standards
Handbook
91;
August
7963;
pages
5­
15
and
5­
16.,
paae
40
Simulations
with
the
model
Y
=
60
+
0.3'
X
(
with
the
usual
confidence
interval
reporting
95%
ind
confidence
intervals
our
95%
confiden
s
of
the
mean
of
Y
at
.

every
point
along
t
h
e
entir
at
when
we
are
equivalent
to
86%
obability
is
86%
that
Simulations
of
the
ReM
with
the
model
)
show
that
the
fr
wal
is
91%
­
92%.
Th
ct
that
individual
ot
95%.
Thus
in
the
y
is
about
91%
­
92%
t
true
values
of
sigma
ai
the
line.
This
c
Remember,
in
the
context
of
a
whoie
line
"
failure
to
capture
the
indeed.
The
P
nfidence
interval,
a
would
be
counted
as
a
t
al
confidence
interv
uch
that
the
tr
wals.
This
is
'
The
precise
outcomes
from
these
simulations
are
dependent
on
several
factors:
7
1.
The
constants
k
and
p
in
the
underlying
model
Sig
i
1
­
2.
The
amount
of
data
in
the
simultaneous
samples.
3.
The
number
of
samples
us
to
build
the
models.
4.
The
points
at
which
predic
n
t
h
e
scale
of
C.

6
!
LJ
L
This
proprietary
simulation
software
can
be
modified
to
study
specific
situations
in
more
detail.
paae
41
What
If
There
Is
No
Relationshb
Betwe
en
Est
cs
a
nd
Co
ncen
tration
?

If
the
t­
ratio
associated
with
p
is
trivial
(
notably
less
than
2)
then
we
have
failed
to
detect
a
relationship
between
Est
CY
and
C.
This
dues
not
mean
there
is
no
relationship;
it
only
means
that
whatever
relationship
there
may
be,
it
was
not
detected
in
this
set
of
data.

Our
ability
to
detect
such
a
relationship
is
influenced
by
the
range
over
which
the
concentration
w
varied.
If
the
data
span
a
narrow
range
(
viz.,
only
about
one
decade,
or
a
factor
of
10)
the
dispersion
in
the
values
of
S
may
be
too
small
to
detect
the
actual
change
in
0.

If
the
data
are
badly
distributed
along
the
scale
of
C...
for
instance,
concentrated
near
the
centroid
instead
of
near
the
ends
of
the
scale
...
our
ability
to
establish
the
relationship
between
0
and
C
may
be
degraded.
Thus
our
inability
to
establish
a
relationship
may
simply
be
due
to
data
that
are
poorly
distributed
on
the
scale
of
concentration.

The
inherent
variation
among
individual
values
of
S,
cannot
be
Attempting
to
establish
a
overcome
unless
we
have
sufficient
data.
relationship
between
G
and
C
with
insufficient
data
spread
over
narrow
ranges
virtualty
insures
that
the
t­
ratio
for
p
will
be
low;
so
low,
in
fact,
that
we
may
not
detect
the
presence
of
a
relationship
much
less
establish
the
nature
of
it.

Any
of
the
foregoing
factors,
or
combinations
of
those
factors,
can
be
responsible
for
a
failure
to
detect
a
relationship
between
cr
and
C.
It.
cannot
be
overemphasized
that
a
"
failure
to
detect"
does
not
imply
there
is
no
relationship.
data
spread
over
a
wide
range
of
concentrations.
Rather,
it
implies
that
we
did
not
have
sufficient
If
the
t­
ratio
for
p
is
low
(
notably
smaller
than
2)
then
we
may
decide
to
take
the
following
position.
Since
we
have
not
established
a
hip,
then
we
may
deciare
that
G
is
a
constant.
This
is
equivalent
ring
that
the
individual
vafues
of
S
effectively
came
from
one
ommon
source
whose
true
standard
deviation
is
G,
Under
this
practice
we
coutd
...
if
we
elect
to
do
so
....
simply
pool
the
individual
values
of
S
and
use
that
as
the
estimate
of
G.
When
doing
this,
it
is
appropriate
to
use
the
factors
in
Table
1
to
calculate
confidence
bounds
an
0.
L
paae
42
The
ITEQ
data
(
Table
12
of
the
main
body
of
this
report)
will
be
used
to
illustrate
this
practice.
The
reported
as
0.0457,
0.001
2,
...
of
these
provides
a
1
df
estirn
sum
and
divide
by
2
Variance
=
0.00071
2.
deviation;
pooled
S
=
1.40
(
interpolated
in
0.0207
and
0.0374;­
equivalent
to
drawi
limits
are
re1
uncertainly
in
estimating
the
slope,
1
i
Pooling
is
not
the
same
as
averaging
standard
deviations
­
The
small­
sample
bias
correction
factor
is
not
needed
when
pooling
if
the
number
of
pooled
degrees
of
freedom
is
greater
than
10.
Llau.
3
Recommendations
Although
the
variation
in
simultaneocsly
sampled
data
causes
uncertainly
in
the
relationship
between
G
and
C,
the
width
of
the
confidence
intervals
on
G
can
be
minimized
by
acquiring
data
at
well­
chosen
points
along
the
scale
of
C.
In
planning
for
future
data
...
anticipating
a
model
of
the
form
Est
ci
=
kCP
...
about
one­
half
of
the
data
"
high"
level
of
each
pollutant.
t
h
e
t­
ratio
on
the
power
coefficient,
and
minimize
the
width
of
the
confidence
intervals
on
(
r
for
a
given
amount
of
data.
Id
be
collected
at
a
"
low"
level
and
one­
half
should
be
collected
at
a
This
will
minimize
SE(
coeff),
maximize
if
there
is
interest
in
pursuing
alternative
models,
then
the
For
every
coefficient
in
the
model
used
to
following
rules
apply.
associate
0
with
C,
data
should
be
Concentrated
at
a
point
along
the
scale
of
C.
This
means
that
for
a
model
with
two
estimated
coefficients
(
viz.,
Est
CT
=
kCP)
the
experimental
data
should
be
concentrated
at
two
points'
on
the
scale
of
C,
as
in
Table
5
and
Fig.
5.
For
a
model
of
the
form
Est
CT
=
a
+
kCP
the
data
should
be
concentrated
at
three
distinct
points'
on
the
scale
of
C.
If
the
data
are
poorly
dispersed,
as
in
Table
2
and
Fig.
2
then
the
SE(
Coeffs)
will
be
large
and
the
confidence
intervals
on
estimates
of
Est
0
may
be
wide.
Attempting
to
estimate
three
model
coefficients
from
poorly
dispersed
data
can
only
lead
to
confusion.

There
is
no
justification
for
using
models
more
complex
than
Est
ci
=
kCp
with
the
ReMAP
data
at
this
time.

Within
this
report
there
is
sufficient
information
to
allow
u
s
to
estimate
the
amount
of
data
needed
and
the
best
positioning
of
that
data
on
the
scale
of
C
so
as
to
reduce
the
confidence
intervals
on
0
to
pre­
specified
widths.
AIthoug
h
these
calculations
could
be
done
analytically,
it
is
better
to
do
them
with
Monte
Carlo
simulations
because
of
the
complexity
introduced
by
the
bias
corrections.
Moreover,
with
simulations
we
can
quickly
explore
"
what
if
cases"
before
investing
in
additional
data,
A
further
advantage
of
Monte
Carlo
is
that
it
makes
the
underlying
models
(
and
the
assumptions)
completely
visible
and
unambiguous
as
compared
to
analytical
methods
that
require
in­
depth
knowledge
of
statistical
methods.

*
Data
should
be
concentrated
at
additional
points
on
the
scale
of
C
in
order
to
test
for
lack­
of­
fit.