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

4.2. STATISTICAL REMARKS 69
1. Validity: characterizes how well a measure reflects the system properties
it was supposed to represent.
2. Reliability (or precision): addresses the consistency or repeatability of
the measurement process.
3. Amplitude: how well a measure represents abstract or higher order constructs
and complex properties.
4.2.2 Making Errors
Measurements are generally made through the use of a measurement instrument,
which is based on a scale that should have the same underlying relationships
as the system property being measured. Formally put, a scale is a
predefined mapping from one domain to another (e.g. the volume expansion of
mercury to degrees of Celsius). The mappings can of course induce uncertainty
e.g. through the use of fuzzy scales to represent the degree to which a property
is considered present (Benoit and Foulloy, 2003). Obviously, the construction
of a scale can be a source of error as well as each observation itself, which is
a random variable with an underlying distribution (Potter, 2000). Basically,
there are four primary sources of measurement error:
� Random error: non-deterministic variation from any source impacting
the system including the system itself.
� Systemic error: derives from construction of the measure or definition of
the measurement process and comes in form of measurement bias.
� Observational error: the oversight of key system properties requiring
measurement or using the wrong measures for identified system properties.
� Experimental error: the influence of environment conditions (such as
temperature, air pressure, or response time of the operator) which affects
the measurement process
These errors create divergences between the perceived state of a system
and the true state and can yield misleading insights and thus, must be addressed
in any measurement framework. They will be part of the measurement
process even when the system is welldefined (Krantz et al., 1971). Error is
an inescapable feature of measurement (Mitchell, 2003) and can be partially
addressed with statistical theory as described in chapter 3.
4.2.3 Experiment and Inference
As mentioned in the previous sections when experiments are carried out, the
results of the measurements and the subsequent statistical analyses are often
stated in the language of mathematics or, more precisely, in that of the theory
of probability. These mathematical statements have the beauty of being
objective, precise and clear. On the other hand, this might induce people to
hide inadequate experimentation behind a brilliant (mathematical) facade. A
fact, unfortunately often seen in scientific publications. Let discuss a simple
example: data consisting of two columns of numbers, say x and y, can always