The Earth Sciences have entered an era of ‘Big Data’. Much research nowadays involves large datasets of numerical data. These may include (1) compositional data such as chemical concentrations; (2) spatial data (X,Y,Z); (3) spherical data such as latitudes and longitudes; (4) directional data such as strikes and dips; (5) time series data such as the oxygen and Sr isotope curves; and (6) point-counting data such as petrographic compositions and fossil assemblages, to name but a few.
This module will introduce basic statistical principles and methods to extract geologically meaningful information from such datasets. The module consists of 20 sessions that are divided into a theoretical introduction followed by practical exercises using the R programming language.
The first 14 sessions of the module will provide a general introduction to statistics, covering a basic introduction to R; exploratory data analysis and data visualisation; descriptive summary statistics to quantify the average and dispersion of datasets; combinatorics; the binomial, Poisson and normal distributions; fractal distributions and chaos; hypothesis tests and confidence intervals; error propagation; linear regression; principal component analysis and discriminant analysis.
The remaining 6 sessions will focus on issues that are specific to the Earth Sciences and that are not covered by most introductory statistics textbooks. The main purpose of these sessions is to instill a critical attitude towards the use of statistical ‘black boxes’ to geoscience research. We will see that basic statistical operations such as averaging, confidence intervals and least squares regression can yield nonsensical results when applied to geological data. For example, suppose that you take two strike measurements on a tilted bedding plane. Let the first strike be 359° and the second strike 1°. Then the arithmetic mean of the two measurements is 180°, which is exactly the opposite of what one would expect! We will see that this and many other similar problems can be solved by simple data transformations such as Aitchison’s logratio transformation for compositional data, and the cosine transformation for directional data.
This module makes frequent use of basic mathematical operations such as logarithms, trigonometry, solving simple equations, and simple calculus. Prerequisites are fulfilled by GEOL0005 (Foundations of Physical Geoscience) or equivalent.