Page 17 - MATLAB Recipes for Earth Sciences

1.4 Methods of Data Analysis 7

Most of these data require special methods to be analyzed, that are outlined
in the next chapter.

1.4 Methods of Data Analysis

Data analysis methods are used to describe the sample characteristics as

precisely as possible. Having defined the sample characteristics we proceed
to hypothesize about the general phenomenon of interest. The particular
method that is used for describing the data depends on the data type and the
project requirements.

1. Univariate methods – Each variable in a data set is explored separately
assuming that the variables are independent from each other. The data are
presented as a list of numbers representing a series of points on a scaled
line. Univariate statistics includes the collection of information about
the variable, such as the minimum and maximum value, the average and
the dispersion about the average. Examples are the investigation of the
sodium content of volcanic glass shards that were affected by chemical
weathering or the size of fossil snail shells in a sediment layer.

2. Bivariate methods – Two variables are investigated together in order to
detect relationships between these two parameters. For example, the cor-

relation coefficient may be calculated in order to investigate whether there
is a linear relationship between two variables. Alternatively, the bivariate
regression analysis may be used to describe a more general relationship
between two variables in the form of an equation. An example for a bi-
variate plot is the Harker Diagram, which is one of the oldest method
to visualize geochemical data and plots oxides of elements against SiO2
from igneous rocks.

3. Time-series analysis – These methods investigate data sequences as a
function of time. The time series is decomposed into a long-term trend,
a systematic (periodic, cyclic, rhythmic) and an irregular (random, sto-
chastic) component. A widely used technique to analyze time series is
spectral analysis, which is used to describe cyclic components of the
time series. Examples for the application of these techniques are the
investigation of cyclic climate variations in sedimentary rocks or the
analysis of seismic data.