Geoscience Reference
In-Depth Information
3 Univariate Statistics
Pebbles on the beach near the Långe Erik
lighthouse, at the northern end of the island
of Öland in Sweden. The average composition
and dispersion of this deposit can be used
to determine the origin of the rocks. In this
example the rock fragments, which are mainly
of granite and gneiss, were eroded on the
Swedish mainland by the Baltic ice sheet
during the last glacial period and transported
to their present location.
3.1 Introduction
h e statistical properties of a single parameter are investigated by means
of univariate analysis. Such a parameter could, for example, be the organic
carbon content of deep-sea sediments, the sizes of grains in a sandstone layer,
or the ages of sanidine crystals in a volcanic ash. Both the number and the
size of
samples
that we collect from a larger
population
are ot en limited by
i nancial and logistical constraints. h e methods of univariate statistics assist
us to draw from the sample conclusions that apply to the population as a
whole. For univariate analysis we use the Statistics Toolbox (MathWorks
2014), which contains all the necessary routines.
We i rst need to describe the characteristics of the sample using statistical
parameters, and to compute an
empirical distribution
(
descriptive statistics
)
(Sections 3.2 and 3.3). A brief introduction is provided to the most
important statistical parameters (such as the
measures of central tendency
and dispersion
), followed by MATLAB examples. We then select a
theoretical
distribution
that shows similar characteristics to the empirical distribution
(Sections 3.4 and 3.5). A suite of theoretical distributions is introduced
and their potential applications outlined prior to using MATLAB tools
