New Statistical Algorithms for the Analysis of Mass - FU Berlin, FB MI ...

Figure 4.2.1: A monotonic
relationship associated
with a measuring
process.
68 CHAPTER 4. (BIO-)MEDICAL APPLICATIONS
4.2 Statistical Remarks
4.2.1 Measurement Fundamentals
Campbell defines measurement as the “assignment of numerals to represent
properties” (Campbell, 1920). This very general statement fits with the common
perception of this term and is used in many different application domains:
people are measuring the diameter of the sun, the mass of an electron, the intelligence
of a human being, or the popularity of a television show. In other
words, measurement is the objective representation of objects, processes, and
phenomenon (Finkelstein and Leaning, 1984). Measurement captures information
about a system through its properties (also called characteristics, features,
or attributes) which can be either directly or indirectly observable. Additionally,
there exist relationships between the properties and the elements (i.e.
measured representations) of a system. Thus, a system X is defined by the
properties xi chosen to represent it:
X = (x1, x2, . . . , xi)
Mostly, there are three elements present: a property to be determined (P), a
measured quantity (M) and a relationship between these two quantities:
M = f(P )
Figure 4.2.1 is a graphical representation of the relationship associated with a
measuring process.
Since this formulation only addressed the properties selected to represent
the system one easily notices that, although being objective, it is an abstraction,
and many important properties of the systems might not be included.
Property selection is crucial since the validity of a system measurement is
influenced by the number of properties used in the measurement. Clearly,
properties affect the validity of a measure. Therefore, formalized frameworks
and theories are required to clarify concepts about measurement within a particular
domain.
Obviously there is a catch here with regard to property selection:
In order to measure a system properly, one needs to know something
about it - however, the main reason to measure a system is to gain an
understanding of it. Therefore, for most complex systems the properties
that best define such a system are unknown, inaccessible, or only
visible as an outcome. Measurement of these systems requires use of a
proxy or indirect measuring method which is essentially a model or approximation
of the system property of interest. The process of deriving
these proxies usually involves reducing complex aspects of a system into
understandable, measurable components.
Having defined or selected the properties the subsequent measurement
can be thought of as a process of assigning numbers (or generally
symbols) to the properties of a system such that these symbols reflect the
underlying relationships (or nature) of the properties (Caws, 1959).
Having performed the measurements one should analyze its main characteristics
(Geisler, 2000), namely: