Kipp&Zonen BSRN Scientific Solar Monitoring System User Manual

Page 174

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Experimental standard deviation

For a series of n m easurem ents of the sam e measurand, the quantity

characterizing the dispersion

of the results and given by the form ula:

being the result of the

m easurem ent and

being the arithm etic m ean of the n results considered.

Notes:

Considering the series of n values as a sam ple of a distribution,

is an unbiased estim ate of

the m ean

, and

is an unbiased estim ate of the variance

, of that distribution.

The expression

is an estim ate of the standard deviation of the distribution of

and

is called the experimental standard deviation of the mean.

“Experim ental standard deviation of the m ean” is som etim es incorrectly called standard error
of the mean.

Uncertainty (of measurement)

Param eter, associated with the result of a m easurem ent that characterizes the dispersion of the values
that could reasonably be attributed to the m easurand.

Notes:
a.

The param eter m ay be, for exam ple, a standard deviation (or a given m ultiple of it), or the half-width
of an interval having a stated level of confidence.

Uncertainty of m easurem ent com prises, in general, m any com ponents. Som e of these com ponents
m ay be evaluated from the statistical distribution of the results of series of m easurem ents and
can be characterized by experim ental standard deviations. The other com ponents, which can
also be characterized by standard deviations, are evaluated from assum ed probability distributions
based on experience or other inform ation.

It is understood that the result of the m easurem ent is the best estim ate of the value of the measurand,
and that all com ponents of uncertainty, including those arising from system atic effects, such
com ponents associated with corrections and reference standards, contribute to the dispersion.

Error (of measurement)

Result of a m easurem ent m inus a true value of the m easurand.

Notes:
a.

Since a true value cannot be determ ined, in practice a conventional true value is used.

W hen it is necessary to distinguish “error” from “relative error,” the form er is som etim es called
absolute error of m easurem ent. This should not be confused with absolute value of error, which
is the m odulus of the error.

Relative error

Error of m easurem ent divided by a true value of the m easurand.

Note:
a.

Since a true value cannot be determ ined, in practice a conventional true value is used.

Random error

Result of a m easurem ent m inus the m ean that would result from an infinite num ber of m easurem ents
of the sam e m easurand carried out under repeatability conditions.

Notes:
a.

Random error is equal to error m inus system atic error.