Page 38 - MATLAB Recipes for Earth Sciences

3 Univariate Statistics

3.1 Introduction

The statistical properties of a single parameter are investigated by means of
univariate analysis. Such variable could be the organic carbon content of a
sedimentary unit, thickness of a sandstone layer, age of sanidine crystals in a
volcanic ash or volume of landslides in the Central Andes. The number and
size of samples we collect from a larger population is often limited by fi nan-
cial and logistical constraints. The methods of univariate statistics help to
conclude from the samples for the larger phenomenon, i.e., the population.
Firstly, we describe the sample characteristics by means of statistical
parameters and compute an empirical distribution ( descriptive statistics)
(Chapters 3.2 and 3.3). A brief introduction to the most important measures
of central tendency and dispersion is followed by MATLAB examples.
Next, we select a theoretical distribution, which shows similar characteris-
tics as the empirical distribution (Chapters 3.4 and 3.5). A suite of theoreti-
cal distributions is then introduced and their potential applications outlined,
before we use MATLAB tools to explore these distributions. Finally, we try
to conclude from the sample for the larger phenomenon of interest ( hypoth-
esis testing) (Chapters 3.6 to 3.8). The corresponding chapters introduce the
three most important statistical tests for applications in earth sciences, the
t-test to compare the means of two data sets, the F-test comparing variances
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and the χ -test to compare distributions.

3.2 Empirical Distributions

Assume that we have collected a number of measurements of a specifi c ob-
ject. The collection of data can be written as a vector x