TABLE
OF
CONTENTS
Page
No.

2.
VARIABILITY
AND
UNCERTAINTY
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
1
2.1.
VARIABILITY
VERSUS
UNCERTAINTY
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
1
2.2.
TYPES
OF
VARIABILITY
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
2
2.3.
CONFRONTING
VARIABILITY
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
3
2.4.
CONCERN
ABOUT
UNCERTAINTY
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
3
2.5.
TYPES
OF
UNCERTAINTY
AND
REDUCING
UNCERTAINTY
.
.
.
.
.
.
.
.
.
4
2.6.
ANALYZING
VARIABILITY
AND
UNCERTAINTY
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
4
2.7.
PRESENTING
RESULTS
OF
VARIABILITY
AND
UNCERTAINTY
ANALYSIS
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
6
2.8.
REFERENCES
FOR
CHAPTER
2
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
7
ADD
pot
'
Contaminant
Concentration
x
Intake
Rate
x
Exposure
Duration
Body
Weight
x
Averaging
Time
Volume
I
­
General
Factors
Chapter
2
­
Variability
and
Uncertainty
Exposure
Factors
Handbook
Page
August
1997
2­
1
(
Eqn.
2­
1)
2.
VARIABILITY
AND
UNCERTAINTY
The
chapters
that
follow
will
discuss
exposure
process
of
conducting
risk
assessments;
because
exposure
factors
and
algorithms
for
estimating
exposure.
Exposure
assessment
is
a
component
of
risk­
assessment
process,
the
factor
values
can
be
used
to
obtain
a
range
of
exposure
general
concepts
apply
equally
to
the
exposure­
assessment
estimates
such
as
average,
high­
end
and
bounding
component.
estimates.
It
is
instructive
here
to
return
to
the
general
equation
for
potential
Average
Daily
Dose
(
ADD
)
that
pot
was
introduced
in
the
opening
chapter
of
this
handbook:
While
some
authors
have
treated
variability
as
a
With
the
exception
of
the
contaminant
concentration,
affecting
exposure
or
risk,
whereas
variability
arises
from
all
parameters
in
the
above
equation
are
considered
true
heterogeneity
across
people,
places
or
time.
In
other
exposure
factors
and,
thus,
are
treated
in
fair
detail
in
other
words,
uncertainty
can
lead
to
inaccurate
or
biased
chapters
of
this
handbook.
Each
of
the
exposure
factors
estimates,
whereas
variability
can
affect
the
precision
of
the
involves
humans,
either
in
terms
of
their
characteristics
estimates
and
the
degree
to
which
they
can
be
generalized.
(
e.
g.,
body
weight)
or
behaviors
(
e.
g.,
amount
of
time
spent
Most
of
the
data
presented
in
this
handbook
concerns
in
a
specific
location,
which
affects
exposure
duration).
variability.
While
the
topics
of
variability
and
uncertainty
apply
equally
Variability
and
uncertainty
can
complement
or
to
contaminant
concentrations
and
the
rest
of
the
exposure
confound
one
another.
An
instructive
analogy
has
been
factors
in
equation
2­
1,
the
focus
of
this
chapter
is
on
drawn
by
the
National
Research
Council
(
NRC,
1994:
variability
and
uncertainty
as
they
relate
to
exposure
factors.
Chapter
10),
based
on
the
objective
of
estimating
the
Consequently,
examples
provided
in
this
chapter
relate
distance
between
the
earth
and
the
moon.
Prior
to
fairly
primarily
to
exposure
factors,
although
contaminant
recent
technology
developments,
it
was
difficult
to
make
concentrations
may
be
used
when
they
better
illustrate
the
accurate
measurements
of
this
distance,
resulting
in
point
under
discussion.
measurement
uncertainty.
Because
the
moon's
orbit
is
This
chapter
also
is
intended
to
acquaint
the
elliptical,
the
distance
is
a
variable
quantity.
If
only
a
few
exposure
assessor
with
some
of
the
fundamental
concepts
measurements
were
to
be
taken
without
knowledge
of
the
and
precepts
related
to
variability
and
uncertainty,
together
elliptical
pattern,
then
either
of
the
following
incorrect
with
methods
and
considerations
for
evaluating
and
conclusions
might
be
reached:
presenting
the
uncertainty
associated
with
exposure
estimates.
Subsequent
sections
in
this
chapter
are
devoted
°
That
the
measurements
were
faulty,
thereby
to
the
following
topics:
ascribing
to
uncertainty
what
was
actually
°
Distinction
between
variability
and
°
That
the
moon's
orbit
was
random,
thereby
not
uncertainty;
allowing
uncertainty
to
shed
light
on
seemingly
°
Types
of
variability;
unexplainable
differences
that
are
in
fact
C
Methods
of
confronting
variability;
variable
and
predictable.
°
Types
of
uncertainty
and
reducing
uncertainty;
°
Analysis
of
variability
and
uncertainty;
and
A
more
fundamental
error
in
the
above
situation
°
Presenting
results
of
variability/
uncertainty
would
be
to
incorrectly
estimate
the
true
distance,
by
analysis.
assuming
that
a
few
observations
were
sufficient.
This
Fairly
extensive
treatises
on
the
topic
of
uncertainty
were
invariant
or
only
uncertain
­­
is
probably
the
most
have
been
provided,
for
example,
by
Morgan
and
Henrion
relevant
to
the
exposure
or
risk
assessor.
(
1990),
the
National
Research
Council
(
NRC,
1994)
and,
Now
consider
a
situation
that
relates
to
exposure,
to
a
lesser
extent,
the
U.
S.
EPA
(
1992;
1995).
The
topic
such
as
estimating
the
average
daily
dose
by
one
exposure
commonly
has
been
treated
as
it
relates
to
the
overall
2.1.
VARIABILITY
VERSUS
UNCERTAINTY
specific
type
or
component
of
uncertainty,
the
U.
S.
EPA
(
1995)
has
advised
the
risk
assessor
(
and,
by
analogy,
the
exposure
assessor)
to
distinguish
between
variability
and
uncertainty.
Uncertainty
represents
a
lack
of
knowledge
about
factors
caused
by
variability;
or
latter
pitfall
­­
treating
a
highly
variable
quantity
as
if
it
Volume
I
­
General
Factors
Chapter
2
­
Variability
and
Uncertainty
Page
Exposure
Factors
Handbook
2­
2
August
1997
route
­­
ingestion
of
contaminated
drinking
water.
Suppose
location
might
vary
in
response
to
weather
conditions,
or
that
it
is
possible
to
measure
an
individual's
daily
water
between
weekdays
and
weekends.
consumption
(
and
concentration
of
the
contaminant)
At
a
more
fundamental
level,
three
types
of
exactly,
thereby
eliminating
uncertainty
in
the
measured
variability
can
be
distinguished:
daily
dose.
The
daily
dose
still
has
an
inherent
day­
to­
day
variability,
however,
due
to
changes
in
the
individual's
daily
°
Variability
across
locations
(
Spatial
water
intake
or
the
contaminant
concentration
in
water.
Variability);
It
is
impractical
to
measure
the
individual's
dose
°
Variability
over
time
(
Temporal
Variability);
every
day.
For
this
reason,
the
exposure
assessor
may
and
estimate
the
average
daily
dose
(
ADD)
based
on
a
finite
°
Variability
among
individuals
(
Internumber
of
measurements,
in
an
attempt
to
"
average
out"
the
individual
Variability).
day­
to­
day
variability.
The
individual
has
a
true
(
but
unknown)
ADD,
which
has
now
been
estimated
based
on
a
sample
of
measurements.
Because
the
individual's
true
average
is
unknown,
it
is
uncertain
how
close
the
estimate
is
to
the
true
value.
Thus,
the
variability
across
daily
doses
has
been
translated
into
uncertainty
in
the
ADD.
Although
the
individual's
true
ADD
has
no
variability,
the
estimate
of
the
ADD
has
some
uncertainty.
The
above
discussion
pertains
to
the
ADD
for
one
person.
Now
consider
a
distribution
of
ADDs
across
individuals
in
a
defined
population
(
e.
g.,
the
general
U.
S.
population).
In
this
case,
variability
refers
to
the
range
and
distribution
of
ADDs
across
individuals
in
the
population.
By
comparison,
uncertainty
refers
to
the
exposure
assessor's
state
of
knowledge
about
that
distribution,
or
about
parameters
describing
the
distribution
(
e.
g.,
mean,
standard
deviation,
general
shape,
various
percentiles).
As
noted
by
the
National
Research
Council
(
NRC,
1994),
the
realms
of
variability
and
uncertainty
have
fundamentally
different
ramifications
for
science
and
judgment.
For
example,
uncertainty
may
force
decisionmakers
to
judge
how
probable
it
is
that
exposures
have
been
overestimated
or
underestimated
for
every
member
of
the
exposed
population,
whereas
variability
forces
them
to
cope
with
the
certainty
that
different
individuals
are
subject
to
exposures
both
above
and
below
any
of
the
exposure
levels
chosen
as
a
reference
point.

2.2.
TYPES
OF
VARIABILITY
Variability
in
exposure
is
related
to
an
individual's
location,
activity,
and
behavior
or
preferences
at
a
particular
point
in
time,
as
well
as
pollutant
emission
rates
and
physical/
chemical
processes
that
affect
concentrations
in
various
media
(
e.
g.,
air,
soil,
food
and
water).
The
variations
in
pollutant­
specific
emissions
or
processes,
and
in
individual
locations,
activities
or
behaviors,
are
not
necessarily
independent
of
one
another.
For
example,
both
personal
activities
and
pollutant
concentrations
at
a
specific
Spatial
variability
can
occur
both
at
regional
(
macroscale)
and
local
(
microscale)
levels.
For
example,
fish
intake
rates
can
vary
depending
on
the
region
of
the
country.
Higher
consumption
may
occur
among
populations
located
near
large
bodies
of
water
such
as
the
Great
Lakes
or
coastal
areas.
As
another
example,
outdoor
pollutant
levels
can
be
affected
at
the
regional
level
by
industrial
activities
and
at
the
local
level
by
activities
of
individuals.
In
general,
higher
exposures
tend
to
be
associated
with
closer
proximity
to
the
pollutant
source,
whether
it
be
an
industrial
plant
or
related
to
a
personal
activity
such
as
showering
or
gardening.
In
the
context
of
exposure
to
airborne
pollutants,
the
concept
of
a
"
microenvironment"
has
been
introduced
(
Duan,
1982)
to
denote
a
specific
locality
(
e.
g.,
a
residential
lot
or
a
room
in
a
specific
building)
where
the
airborne
concentration
can
be
treated
as
homogeneous
(
i.
e.,
invariant)
at
a
particular
point
in
time.
Temporal
variability
refers
to
variations
over
time,
whether
long­
or
short­
term.
Seasonal
fluctuations
in
weather,
pesticide
applications,
use
of
woodburning
appliances
and
fraction
of
time
spent
outdoors
are
examples
of
longer­
term
variability.
Examples
of
shorter­
term
variability
are
differences
in
industrial
or
personal
activities
on
weekdays
versus
weekends
or
at
different
times
of
the
day.
Inter­
individual
variability
can
be
either
of
two
types:
(
1)
human
characteristics
such
as
age
or
body
weight,
and
(
2)
human
behaviors
such
as
location
and
activity
patterns.
Each
of
these
variabilities,
in
turn,
may
be
related
to
several
underlying
phenomena
that
vary.
For
example,
the
natural
variability
in
human
weight
is
due
to
a
combination
of
genetic,
nutritional,
and
other
lifestyle
or
environmental
factors.
Variability
arising
from
independent
factors
that
combine
multiplicatively
generally
will
lead
to
an
approximately
lognormal
distribution
across
the
population,
or
across
spatial/
temporal
dimensions.
Volume
I
­
General
Factors
Chapter
2
­
Variability
and
Uncertainty
Exposure
Factors
Handbook
Page
August
1997
2­
3
2.3.
CONFRONTING
VARIABILITY
According
to
the
National
Research
Council
(
NRC
reliably
in
light
of
the
variability
(
e.
g.,
when
the
variability
1994),
variability
can
be
confronted
in
four
basic
ways
is
known
to
be
relatively
small,
as
in
the
case
of
adult
body
(
Table
2­
1)
when
dealing
with
science­
policy
questions
weight).
surrounding
issues
such
as
exposure
or
risk
assessment.
The
first
is
to
ignore
the
variability
and
hope
for
the
best.
This
strategy
tends
to
work
best
when
the
variability
is
relatively
small.
For
example,
the
assumption
that
all
adults
weigh
70
kg
is
likely
to
be
correct
within
±
25%
for
most
adults.
The
second
strategy
involves
disaggregating
the
time
period
(
e.
g.,
the
period
of
peak
exposure),
one
spatial
variability
in
some
explicit
way,
in
order
to
better
understand
it
or
reduce
it.
Mathematical
models
are
appropriate
in
some
cases,
as
in
fitting
a
sine
wave
to
the
annual
outdoor
concentration
cycle
for
a
particular
pollutant
and
location.
In
other
cases,
particularly
those
involving
human
characteristics
or
behaviors,
it
is
easier
to
disaggregate
the
data
by
considering
all
the
relevant
subgroups
or
subpopulations.
For
example,
distributions
of
body
weight
could
be
developed
separately
for
adults,
2.4.
CONCERN
ABOUT
UNCERTAINTY
adolescents
and
children,
and
even
for
males
and
females
within
each
of
these
subgroups.
Temporal
and
spatial
analogies
for
this
concept
involve
measurements
on
appropriate
time
scales
and
choosing
appropriate
subregions
or
microenvironments.
The
third
strategy
is
to
use
the
average
value
of
a
quantity
that
varies.
Although
this
strategy
might
appear
as
tantamount
to
ignoring
variability,
it
needs
to
be
based
on
a
decision
that
the
average
value
can
be
estimated
The
fourth
strategy
involves
using
the
maximum
or
minimum
value
for
an
exposure
factor.
In
this
case,
the
variability
is
characterized
by
the
range
between
the
extreme
values
and
a
measure
of
central
tendency.
This
is
perhaps
the
most
common
method
of
dealing
with
variability
in
exposure
or
risk
assessment
­­
to
focus
on
one
region
(
e.
g.,
in
close
proximity
to
the
pollutant
source
of
concern),
or
one
subpopulation
(
e.
g.,
exercising
asthmatics).
As
noted
by
the
U.
S.
EPA
(
1992),
when
an
exposure
assessor
develops
estimates
of
high­
end
individual
exposure
and
dose,
care
must
be
taken
not
to
set
all
factors
to
values
that
maximize
exposure
or
dose
­­
such
an
approach
will
almost
always
lead
to
an
overestimate.

Why
should
the
exposure
assessor
be
concerned
with
uncertainty?
As
noted
by
the
U.
S.
EPA
(
1992),
exposure
assessment
can
involve
a
broad
array
of
information
sources
and
analysis
techniques.
Even
in
situations
where
actual
exposure­
related
measurements
exist,
assumptions
or
inferences
will
still
be
required
because
data
are
not
likely
to
be
available
for
all
aspects
of
the
exposure
assessment.
Moreover,
the
data
that
are
available
may
be
of
questionable
or
unknown
quality.
Thus,
exposure
assessors
have
a
responsibility
to
present
not
just
numbers,
but
also
a
clear
and
explicit
explanation
of
the
implications
and
limitations
of
their
analyses.

Table
2­
1.
Four
Strategies
for
Confronting
Variability
Strategy
Example
Comment
Ignore
variability
Assume
that
all
adults
weigh
Works
best
when
variability
is
small
70
kg
Disaggregate
the
Develop
distributions
of
body
Variability
will
be
smaller
in
each
group
variability
weight
for
age/
gender
groups
Use
the
average
value
Use
average
body
weight
for
Can
the
average
be
estimated
reliably
given
what
is
adults
known
about
the
variability?

Use
a
maximum
or
Use
a
lower­
end
value
from
Conservative
approach
­­
can
lead
to
unrealistically
minimum
value
the
weight
distribution
high
exposure
estimate
if
taken
for
all
factors
Volume
I
­
General
Factors
Chapter
2
­
Variability
and
Uncertainty
Page
Exposure
Factors
Handbook
2­
4
August
1997
Morgan
and
Henrion
(
1990)
provide
an
argument
by
assessment
or
risk
characterization)
at
which
they
can
analogy.
When
scientists
report
quantities
that
they
have
occur.
A
more
abstract
and
generalized
approach
preferred
measured,
they
are
expected
to
routinely
report
an
estimate
by
some
scientists
is
to
partition
all
uncertainties
among
the
of
the
probable
error
associated
with
such
measurements.
three
categories
of
bias,
randomness
and
true
variability.
Because
uncertainties
inherent
in
policy
analysis
(
of
which
These
ideas
are
discussed
later
in
some
examples.
exposure
assessment
is
a
part)
tend
to
be
even
greater
than
The
U.
S.
EPA
(
1992)
has
classified
uncertainty
in
those
in
the
natural
sciences,
exposure
assessors
also
should
exposure
assessment
into
three
broad
categories:
be
expected
to
report
or
comment
on
the
uncertainties
associated
with
their
estimates.
1.
Uncertainty
regarding
missing
or
incomplete
Additional
reasons
for
addressing
uncertainty
in
information
needed
to
fully
define
exposure
and
exposure
or
risk
assessments
(
U.
S.
EPA,
1992,
Morgan
and
dose
(
Scenario
Uncertainty).
Henrion,
1990)
include
the
following:
2.
Uncertainty
regarding
some
parameter
°
Uncertain
information
from
different
sources
of
3.
Uncertainty
regarding
gaps
in
scientific
theory
different
quality
often
must
be
combined
for
the
required
to
make
predictions
on
the
basis
of
assessment;
causal
inferences
(
Model
Uncertainty).
°
Decisions
need
to
be
made
about
whether
or
how
to
expend
resources
to
acquire
additional
Identification
of
the
sources
of
uncertainty
in
an
exposure
information,;
assessment
is
the
first
step
in
determining
how
to
reduce
°
Biases
may
result
in
so­
called
"
best
estimates"
that
uncertainty.
The
types
of
uncertainty
listed
above
can
that
in
actuality
are
not
very
accurate;
and
be
further
defined
by
examining
their
principal
causes.
°
Important
factors
and
potential
sources
of
Sources
and
examples
for
each
type
of
uncertainty
are
disagreement
in
a
problem
can
be
identified.
summarized
in
Table
2­
2.

Addressing
uncertainty
will
increase
the
likelihood
fundamentally
tied
to
a
lack
of
knowledge
concerning
that
results
of
an
assessment
or
analysis
will
be
used
in
an
important
exposure
factors,
strategies
for
reducing
appropriate
manner.
Problems
rarely
are
solved
to
uncertainty
necessarily
involve
reduction
or
elimination
of
everyone's
satisfaction,
and
decisions
rarely
are
reached
on
knowledge
gaps.
Example
strategies
to
reduce
uncertainty
the
basis
of
a
single
piece
of
evidence.
Results
of
prior
include
(
1)
collection
of
new
data
using
a
larger
sample
analyses
can
shed
light
on
current
assessments,
particularly
size,
an
unbiased
sample
design,
a
more
direct
measurement
if
they
are
couched
in
the
context
of
prevailing
uncertainty
method
or
a
more
appropriate
target
population,
and
(
2)
use
at
the
time
of
analysis.
Exposure
assessment
tends
to
be
an
of
more
sophisticated
modeling
and
analysis
tools.
iterative
process,
beginning
with
a
screening­
level
assessment
that
may
identify
the
need
for
more
in­
depth
assessment.
One
of
the
primary
goals
of
the
more
detailed
assessment
is
to
reduce
uncertainty
in
estimated
exposures.
Exposure
assessments
often
are
developed
in
a
This
objective
can
be
achieved
more
efficiently
if
guided
by
phased
approach.
The
initial
phase
usually
screens
out
the
presentation
and
discussion
of
factors
thought
to
be
exposure
scenarios
or
pathways
that
are
not
expected
to
primarily
responsible
for
uncertainty
in
prior
estimates.
pose
much
risk,
to
eliminate
them
from
more
detailed,

2.5.
TYPES
OF
UNCERTAINTY
AND
REDUCING
UNCERTAINTY
The
problem
of
uncertainty
in
exposure
or
risk
screening­
level
analyses
usually
are
included
in
the
final
assessment
is
relatively
large,
and
can
quickly
become
too
exposure
assessment,
the
final
document
may
contain
complex
for
facile
treatment
unless
it
is
divided
into
smaller
scenarios
that
differ
quite
markedly
in
and
more
manageable
topics.
One
method
of
division
(
Bogen,
1990)
involves
classifying
sources
of
uncertainty
according
to
the
step
in
the
risk
assessment
process
(
hazard
identification,
dose­
response
assessment,
exposure
(
Parameter
Uncertainty).

Because
uncertainty
in
exposure
assessments
is
2.6.
ANALYZING
VARIABILITY
AND
UNCERTAINTY
resource­
intensive
review.
Screening­
level
assessments
typically
examine
exposures
that
would
fall
on
or
beyond
the
high
end
of
the
expected
exposure
distribution.
Because
Volume
I
­
General
Factors
Chapter
2
­
Variability
and
Uncertainty
Exposure
Factors
Handbook
Page
August
1997
2­
5
Table
2­
2.
Three
Types
of
Uncertainty
and
Associated
Sources
and
Examples
Type
of
Uncertainty
Sources
Examples
Scenario
Uncertainty
Descriptive
errors
Incorrect
or
insufficient
information
Aggregation
errors
Spatial
or
temporal
approximations
Judgment
errors
Selection
of
an
incorrect
model
Incomplete
analysis
Overlooking
an
important
pathway
Parameter
Uncertainty
Measurement
errors
Imprecise
or
biased
measurements
Sampling
errors
Small
or
unrepresentative
samples
Variability
In
time,
space
or
activities
Surrogate
data
Structurally­
related
chemicals
Model
Uncertainty
Relationship
errors
Incorrect
inference
on
the
basis
for
correlations
Modeling
errors
Excluding
relevant
variables
sophistication,
data
quality,
and
amenability
to
quantitative
the
assessor
may
use
order­
of­
magnitude
bounding
expressions
of
variability
or
uncertainty.
estimates
of
parameter
ranges
(
e.
g.,
from
0.1
to
10
liters
for
According
to
the
U.
S.
EPA
(
1992),
uncertainty
daily
water
intake).
Another
method
describes
the
range
for
characterization
and
uncertainty
assessment
are
two
ways
of
each
parameter
including
the
lower
and
upper
bounds
as
describing
uncertainty
at
different
degrees
of
sophistication.
well
as
a
"
best
estimate"
(
e.
g.,
1.4
liters
per
day)
determined
Uncertainty
characterization
usually
involves
a
qualitative
by
available
data
or
professional
judgement.
discussion
of
the
thought
processes
used
to
select
or
reject
When
sensitivity
analysis
indicates
that
a
parameter
specific
data,
estimates,
scenarios,
etc.
Uncertainty
profoundly
influences
exposure
estimates,
the
assessor
assessment
is
a
more
quantitative
process
that
may
range
should
develop
a
probabilistic
description
of
its
range.
If
from
simpler
measures
(
e.
g.,
ranges)
and
simpler
analytical
there
are
enough
data
to
support
their
use,
standard
techniques
(
e.
g.,
sensitivity
analysis)
to
more
complex
statistical
methods
are
preferred.
If
the
data
are
inadequate,
measures
and
techniques.
Its
goal
is
to
provide
decision
expert
judgment
can
be
used
to
generate
a
subjective
makers
with
information
concerning
the
quality
of
an
probabilistic
representation.
Such
judgments
should
be
assessment,
including
the
potential
variability
in
the
developed
in
a
consistent,
well­
documented
manner.
estimated
exposures,
major
data
gaps,
and
the
effect
that
Morgan
and
Henrion
(
1990)
and
Rish
(
1988)
describe
these
data
gaps
have
on
the
exposure
estimates
developed.
techniques
to
solicit
expert
judgment.
A
distinction
between
variability
and
uncertainty
was
Most
approaches
to
quantitative
analysis
examine
made
in
Section
2.1.
Although
the
quantitative
process
how
variability
and
uncertainty
in
values
of
specific
mentioned
above
applies
more
directly
to
variability
and
the
parameters
translate
into
the
overall
uncertainty
of
the
qualitative
approach
more
so
to
uncertainty,
there
is
some
assessment.
Details
may
be
found
in
reviews
such
as
Cox
degree
of
overlap.
In
general,
either
method
provides
the
and
Baybutt
(
1981),
Whitmore
(
1985),
Inman
and
Helton
assessor
or
decision­
maker
with
insights
to
better
evaluate
(
1988),
Seller
(
1987),
and
Rish
and
Marnicio
(
1988).
the
assessment
in
the
context
of
available
data
and
These
approaches
can
generally
be
described
(
in
order
of
assumptions.
The
following
paragraphs
describe
some
of
increasing
complexity
and
data
needs)
as:
(
1)
sensitivity
the
more
common
procedures
for
analyzing
variability
and
analysis;
(
2)
analytical
uncertainty
propagation;
uncertainty
in
exposure
assessments.
Principles
that
pertain
(
3)
probabilistic
uncertainty
analysis;
or
(
4)
classical
to
presenting
the
results
of
variability/
uncertainty
analysis
statistical
methods
(
U.
S.
EPA
1992).
The
four
approaches
are
discussed
in
the
next
section.
are
summarized
in
Table
2­
3.
Several
approaches
can
be
used
to
characterize
uncertainty
in
parameter
values.
When
uncertainty
is
high,
Volume
I
­
General
Factors
Chapter
2
­
Variability
and
Uncertainty
Page
Exposure
Factors
Handbook
2­
6
August
1997
Table
2­
3.
Approaches
to
Quantitative
Analysis
of
Uncertainty
Approach
Description
Example
Sensitivity
Analysis
Changing
one
input
variable
at
a
time
while
leaving
others
constant,
to
examine
effect
on
output
Fix
each
input
at
lower
(
then
upper)
bound
while
holding
others
at
nominal
values
(
e.
g.,
medians)

Analytical
Uncertainty
Propagation
Examining
how
uncertainty
in
individual
parameters
affects
the
overall
uncertainty
of
the
exposure
assessment
Analytically
or
numerically
obtain
a
partial
derivative
of
the
exposure
equation
with
respect
to
each
input
parameter
Probabilistic
Uncertainty
Analysis
Varying
each
of
the
input
variables
over
various
values
of
their
respective
probability
distributions
Assign
probability
density
function
to
each
parameter;
randomly
sample
values
from
each
distribution
and
insert
them
in
the
exposure
equation
(
Monte
Carlo)

Classical
Statistical
Methods
Estimating
the
population
exposure
distribution
directly,
based
on
measured
values
from
a
representative
sample
Compute
confidence
interval
estimates
for
various
percentiles
of
the
exposure
distribution
2.7.
PRESENTING
RESULTS
OF
VARIABILITY
AND
UNCERTAINTY
ANALYSIS
Comprehensive
qualitative
analysis
and
rigorous
Although
assessors
have
always
used
descriptors
to
quantitative
analysis
are
of
little
value
for
use
in
the
communicate
the
kind
of
scenario
being
addressed,
the
decision­
making
process,
if
their
results
are
not
clearly
1992
Exposure
Guidelines
establish
clear
quantitative
presented.
In
this
chapter,
variability
(
the
receipt
of
definitions
for
these
risk
descriptors.
These
definitions
different
levels
of
exposure
by
different
individuals)
has
were
established
to
ensure
that
consistent
terminology
is
been
distinguished
from
uncertainty
(
the
lack
of
knowledge
used
throughout
the
Agency.
The
risk
descriptors
defined
about
the
correct
value
for
a
specific
exposure
measure
or
in
the
Guidelines
include
descriptors
of
individual
risk
and
estimate).
Most
of
the
data
that
are
presented
in
this
population
risk.
Individual
risk
descriptors
are
intended
to
handbook
deal
with
variability
directly,
through
inclusion
of
address
questions
dealing
with
risks
borne
by
individuals
statistics
that
pertain
to
the
distributions
for
various
within
a
population,
including
not
only
measures
of
central
exposure
factors.
tendency
(
e.
g.,
average
or
median),
but
also
those
risks
at
Not
all
approaches
historically
used
to
construct
the
high
end
of
the
distribution.
Population
risk
descriptors
measures
or
estimates
of
exposure
have
attempted
to
refer
to
an
assessment
of
the
extent
of
harm
to
the
distinguish
between
variability
and
uncertainty.
The
population
being
addressed.
It
can
be
either
an
estimate
of
assessor
is
advised
to
use
a
variety
of
exposure
descriptors,
the
number
of
cases
of
a
particular
effect
that
might
occur
and
where
possible,
the
full
population
distribution,
when
in
a
population
(
or
population
segment),
or
a
description
of
presenting
the
results.
This
information
will
provide
risk
what
fraction
of
the
population
receives
exposures,
doses,
managers
with
a
better
understanding
of
how
exposures
are
or
risks
greater
than
a
specified
value.
The
data
presented
distributed
over
the
population
and
how
variability
in
in
the
Exposure
Factors
Handbook
is
one
of
the
tools
population
activities
influences
this
distribution.
available
to
exposure
assessors
to
construct
the
various
risk
Although
incomplete
analysis
is
essentially
descriptors.
unquantifiable
as
a
source
of
uncertainty,
it
should
not
be
However,
it
is
not
sufficient
to
merely
present
the
ignored.
At
a
minimum,
the
assessor
should
describe
the
results
using
different
exposure
descriptors.
Risk
managers
rationale
for
excluding
particular
exposure
scenarios;
should
also
be
presented
with
an
analysis
of
the
characterize
the
uncertainty
in
these
decisions
as
high,
uncertainties
surrounding
these
descriptors.
Uncertainty
medium,
or
low;
and
state
whether
they
were
based
on
data,
may
be
presented
using
simple
or
very
sophisticated
analogy,
or
professional
judgment.
Where
uncertainty
is
techniques,
depending
on
the
requirements
of
the
high,
a
sensitivity
analysis
can
be
used
to
credible
upper
limits
on
exposure
by
way
of
a
series
of
"
what
if"
questions.
Volume
I
­
General
Factors
Chapter
2
­
Variability
and
Uncertainty
Exposure
Factors
Handbook
Page
August
1997
2­
7
assessment
and
the
amount
of
data
available.
It
is
beyond
Table
2­
2
summarizes
the
three
types
of
uncertainty,
the
scope
of
this
handbook
to
discuss
the
mechanics
of
associated
sources,
and
examples.
Table
2­
3
summarizes
uncertainty
analysis
in
detail.
At
a
minimum,
the
assessor
four
approaches
to
analyze
uncertainty
quantitatively.
should
address
uncertainty
qualitatively
by
answering
These
are
described
further
in
the
1992
Exposure
questions
such
as:
Guidelines.

°
What
is
the
basis
or
rationale
for
selecting
these
assumptions/
parameters,
such
as
data,
Bogen,
K.
T.
(
1990)
Uncertainty
in
environmental
health
modeling,
scientific
judgment,
Agency
policy,
risk
assessment.
Garland
Publishing,
New
York,
"
what
if"
considerations,
etc.?
NY.

°
What
is
the
range
or
variability
of
the
key
analysis.
A
comparative
survey.
Risk
Anal.
parameters?
How
were
the
parameter
values
1(
4):
251­
258.
selected
for
use
in
the
assessment?
Were
Duan,
N.
(
1982)
Microenvironment
types:
A
model
for
average,
median,
or
upper­
percentile
values
human
exposure
to
air
pollution.
Environ.
Intl.
chosen?
If
other
choices
had
been
made,
how
8:
305­
309.
would
the
results
have
differed?
Inman,
R.
L.;
Helton,
J.
C.
(
1988)
An
investigation
of
°
What
is
the
assessor's
confidence
(
including
computer
models.
Risk
Anal.
8(
1):
71­
91.
qualitative
confidence
aspects)
in
the
key
Morgan,
M.
G.;
Henrion,
M.
(
1990)
Uncertainty:
A
guide
parameters
and
the
overall
assessment?
What
to
dealing
with
uncertainty
in
quantitative
risk
and
are
the
quality
and
the
extent
of
the
data
base(
s)
policy
analysis.
Cambridge
University
Press,
New
supporting
the
selection
of
the
chosen
values?
York,
NY.

Any
exposure
estimate
developed
by
an
assessor
will
judgment
in
risk
assessment.
National
Academy
have
associated
assumptions
about
the
setting,
chemical,
Press,
Washington,
DC.
population
characteristics,
and
how
contact
with
the
Rish,
W.
R.
(
1988)
Approach
to
uncertainty
in
risk
chemical
occurs
through
various
exposure
routes
and
analysis.
Oak
Ridge
National
Laboratory.
pathways.
The
exposure
assessor
will
need
to
examine
ORNL/
TM­
10746.
many
sources
of
information
that
bear
either
directly
or
Rish,
W.
R.;
Marnicio,
R.
J.
(
1988)
Review
of
studies
indirectly
on
these
components
of
the
exposure
assessment.
related
to
uncertainty
in
risk
analysis.
Oak
Ridge
In
addition,
the
assessor
will
be
required
to
make
many
National
Laboratory.
ORNL/
TM­
10776.
decisions
regarding
the
use
of
existing
information
in
Seller,
F.
A.
(
1987)
Error
propagation
for
large
errors.
constructing
scenarios
and
setting
up
the
exposure
Risk
Anal.
7(
4):
509­
518.
equations.
In
presenting
the
scenario
results,
the
assessor
U.
S.
EPA
(
1992)
Guidelines
for
exposure
assessment.
should
strive
for
a
balanced
and
impartial
treatment
of
the
Washington,
DC:
Office
of
Research
and
evidence
bearing
on
the
conclusions
with
the
key
Development,
Office
of
Health
and
Environmental
assumptions
highlighted.
For
these
key
assumptions,
one
Assessment.
EPA/
600/
2­
92/
001.
should
cite
data
sources
and
explain
any
adjustments
of
the
U.
S.
EPA
(
1995)
Guidance
for
risk
characterization.
data.
Science
Policy
Council,
Washington,
DC.
The
exposure
assessor
also
should
qualitatively
Whitmore,
R.
W.
(
1985)
Methodology
for
describe
the
rationale
for
selection
of
any
conceptual
or
characterization
of
uncertainty
in
exposure
mathematical
models
that
may
have
been
used.
This
assessments.
EPA/
600/
8­
86/
009.
discussion
should
address
their
verification
and
validation
status,
how
well
they
represent
the
situation
being
assessed
(
e.
g.,
average
versus
high­
end
estimates),
and
any
plausible
alternatives
in
terms
of
their
acceptance
by
the
scientific
community.
2.8.
REFERENCES
FOR
CHAPTER
2
Cox,
D.
C.;
Baybutt,
P.
C.
(
1981)
Methods
for
uncertainty
uncertainty
and
sensitivity
analysis
techniques
for
National
Research
Council
(
NRC).
(
1994)
Science
and
