Biomedical Engineering Reference
In-Depth Information
Figure 2.2. The Gaussian distribution. Both the yellow and orange shaded
areas extend out to infinity. Verse by the author.
confidence interval
. An uncertainty of 1SD is termed a
standard
uncertainty
. The uncertainty in a measurement has the same physical
units as the measurement itself.
Sometimes it is useful to use the
relative standard uncertainty
,
f
, of a
value. This is given by
f
= σ
v
and it follows that the standard con-
f
( )
fidence interval can be expressed as
v
± σ ≡
v
1
±
. The relative
uncertainty, being the ratio of two values with the same units, is itself
unit-less.
3
O n a somewhat pedantic note, the International Organization for Standardi-
zation (ISO, 1995) discourages the term “true value” on the grounds that
the word “true” is redundant; they take the position that one should not
say, for example, “the true value was …”; it is sufficient, and better, to
simply state that the “the value was …”.
4
More correctly one should state that, if the value were measured a large
number of times, 68% of the time it would fall within
1SD.
5
The definition of and estimate of the standard deviation does not depend on
the probability density function being Gaussian. One can define a standard
deviation for a triangle, a square function, and so forth. However, it is
only when the probability density function is Gaussian that the
±
±
1SD
interval, for example, corresponds to a 68% level of confidence.
