Statistical Graphics in QUAIL: An Overview

Hurley, Catherine B. and Oldford, R.W. (1999) Statistical Graphics in QUAIL: An Overview. Bulletin of the International Statistical Institute, 58. pp. 113-116.

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Abstract

It has been suggested (Wainer, 1989) that the system first proposed by C.S. Peirce to organise knowledge is particularly suited to describing statistical graphics. Peirce felt that all information could be broken down into three different types { monadic information, which describes something in and of itself, dyadic information, which describes a relationship between two things, and triadic information, which describes the relation between two things mediated by a third. We can see how this applies in statistical graphics by considering the scatterplot. There, each case in a dataset is represented in the display by a glyph, which is monadic in nature. The scatterplot is a dyad; by positioning the case glyphs in the plane according to the values each case has on two variates X and Y , any empirical relationship between the variates can be seen. Triadic information is available by linking the scatterplot with another plot, say a dot-plot of a third variate, Z. Colouring the glyphs in the dot-plot within a given range of Z values, causes the corresponding glyphs in the scatterplot to be coloured in the same way. Here the relationship between X and Y is seen mediated by the third variate Z. This description of information is reflected in the design and implementation of our graphics software, which is part of the QUAIL system (Oldford et al). Quail (for QUantitative Analysis in Lisp) is a programming environment for statistical and quantitative computing. It has extensive arithmetical, mathematical, statistical and display facilities. This paper gives a brief overview of the principles underlying the statistical graphics facilities. The original software model was first illustrated in a video (Hurley and Oldford, 1988), and was described in Hurley and Oldford (1991). Perhaps surprisingly, we have not altered the original software model, rather we have extended and enriched its scope over the intervening years. The statistical graphics system in Quail has an object-oriented design, which we outline in Section 2. In the language of Peirce, individual objects have a monadic nature. We provide basic building blocks consisting of simple graphical objects such as point symbols and lines and container objects within which the simple objects are positioned to display relationships, ultimately forming plots. Container objects present dyadic information; Section 3 describes some such objects available in Quail. In Section 4, we outline a few of the ways triadic information is available; generally this involves comparison of plots, and, if the plots are displayed over time, interactive graphics.

Item Type: Article Statistical Graphics; QUAIL; QUantitative Analysis in Lisp; Faculty of Science and Engineering > Mathematics and Statistics 5476 Dr. Catherine Hurley 08 Oct 2014 16:22 Bulletin of the International Statistical Institute ISI No This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here