Hurley, Catherine B. and Oldford, R.W.
(1999)
Statistical Graphics in QUAIL: An Overview.
Bulletin of the International Statistical Institute, 58.
pp. 113116.
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 dotplot of a third variate, Z. Colouring the glyphs in the dotplot 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 objectoriented 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

Keywords: 
Statistical Graphics; QUAIL; QUantitative Analysis in Lisp; 
Academic Unit: 
Faculty of Science and Engineering > Mathematics and Statistics 
Item ID: 
5476 
Depositing User: 
Dr. Catherine Hurley

Date Deposited: 
08 Oct 2014 16:22 
Journal or Publication Title: 
Bulletin of the International Statistical Institute 
Publisher: 
ISI 
Refereed: 
No 
URI: 

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