Investigations in Graphical Statistics

Abstract

This thesis is concerned with the design and development of statistical graphics software – programs to help draw graphs. Graphs serve two major functions in statistics. Firstly, graphs are used for exploratory data analysis – for detecting the message in a set of data – and secondly, graphs are used for data display – for presenting the message in a set of data.

The most important feature of software for exploratory data analysis is extensibility. This is the ability to quickly and easily develop new graphical images and is vital for being able to explore a data set in many different ways. The most important feature of software for data display is customisation. This is the ability to fine-tune a graphical image in great detail and is vital for the production of presentation-quality graphics. In both cases it is important that a graphical image should be constructed to best explore or show-off the peculiarities of a specific data set.

A pervading theme of this thesis is that statistical graphics software should be flexible. The software tools described herin allow graphical images to be modified in arbitrary ways; the structure of graphical images is also arbitrary and not restricted to standard graph formats; a simple, coherent method, based on a general constraint system, for developing novel graphical images is explored; and a mechanism for specifying the arrangement of the components of a graphical image is introduced. Some of these ideas are incorporated within an existing statistical analysis package.