[unitsml] Uncertainty representation and the Guide to theExpression of Uncertainty in Measurement

["Linstrom, Peter" <peter.linstrom@nist.gov>]

All,

   This message is intended to be part of the asynchronous
UnitsML meeting for February.

   During our discussion on Wednesday, the issue of how
uncertainty in unit conversions should be expressed came up.
I looked at the BIPM / ISO publication "Guide to the Expression
of Uncertainty in Measurement" (1995 edition) and it defines
two ways of presenting uncertainties. "Standard uncertainty"
is the uncertainty of a measurement expressed as a standard
deviation. "Expanded uncertainty" is a quantity defining an
interval about the result of the measurement which encompasses
a large portion of the distribution of possible values. A
value called the "coverage factor" relates these two values.
The expanded uncertainty is equal to the standard uncertainty
multiplied by the coverage factor.

   During our discussion on Wednesday I indicated that I
believed that the Guide effectively specified a coverage
factor of 2; this was completely incorrect. The Guide indicates
the coverage factors typically range from 2 to 3 and should
be indicated when reporting expanded uncertainty values.
The Guide also indicates that metrology institutes should
report standard uncertainties (standard deviations).

   I'm not sure how UnitsML should be changed to cope with
this (or if it should). I can see three options:

1.) Leave things as they are.
2.) Use standard uncertainties instead of expanded uncertainties
    (rename ...U95UncertaintyRadius to ...StandardUncertainty
    or ...StandardDeviation)
3.) Allow the uncertainty and the coverage factor to be specified.

I don't like the third option because creates extra work for
processors and could make things more difficult down the road.
Option 2 has the advantage that BIPM / ISO / IEC / (other
international organizations) endorse it. The only disadvantage
of option 2 is that it provides a radius which only encompasses
68.27 percent of the normal distribution, something which may
not be obvious to users. The choice of the best option may depend
on the form most commonly encountered for the data.

Just for your information, the Guide (in table G-1) provides
coverage factors for various confidence levels in a normal
distribution. These factors are noted below:

Confidence level        Coverage factor
    68.27                    1.        (standard uncertainty)
    90                       1.645
    95                       1.960
    95.45                    2.
    99                       2.576
    99.73                    3.

Thus to convert a 95 % expanded uncertainty to a standard
uncertainty one would divide by 1.96 (for a normal distribution).

Peter Linstrom

======================================================
Peter J. Linstrom
(301) 975-5422
NIST, Chemical and Biochemical Reference Data Division
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