Biomedical Engineering Reference
In-Depth Information
C
OMBINING
U
NCERTAINTIES
When analyzing the causes of error in a particular problem, one finds
a number of contributing factors; some random, some systematic. In
most circumstances, the rule for combining these is very simple:
make sure that all the uncertainties that are to be combined are
associated with the same level of confidence - you don't want to
combine standard deviations with 95% confidence limits;
combine all type A (random) uncertainties in quadrature;
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combine all type B (systematic) uncertainties in quadrature;
combine the type A and type B uncertainties in quadrature.
−
and that is the combined uncertainty, for the same level of confidence
as is associated with the individual components. When the individual
uncertainties are standard uncertainties, then the combined uncertainty
is known as the
combined standard uncertainty
.
In practice, the last three steps of this prescription can be combined.
One gets the identical answer if one just combines all uncertainties, of
no matter which type, in quadrature. However, knowing the overall
type A and type B uncertainties separately can be very informative.
U
NCERTAINTY
M
UST BE
M
ADE
E
XPLICIT
ISO (1995) states that “the result of a measurement [or calculation] …
is complete only when accompanied by a statement of uncertainty.”
Put more strongly,
a measured or computed value which is not ac-
companied by an uncertainty estimate is meaningless
. One simply does
not know what to make of it. For reasons which I do not understand,
and vehemently disapprove of, the statement of uncertainty in the clini-
cal setting is very often absent. And, when one is given, it is usually
unaccompanied by the qualifying information as to the confidence
associated with the stated uncertainty interval - which largely invali-
dates the statement of uncertainty.
The importance of first estimating and then providing an estimate of
uncertainty has led me to promulgate the following law:
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The sum in quadrature of a set of numbers is the square root of the sum of
the squared numbers.
