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Stereoscopic Scatter Diagrams for Illustrating Population Distributions

Published online by Cambridge University Press:  03 November 2016

C. J. Lawrance
Affiliation:
Soil Science Laboratory, Oxford

Extract

Statisticians are commonly confronted with the problem of expressing the relationships among three variables and often wish to illustrate these relationships. Various ways have been tried with more or less success. For some types of data isometric block diagrams or graphs have been found satisfactory. But unless there is a fairly steady surface trend this solution is not practicable, and the whole picture can be seen only in a solid model. Where the data are a number of points the information can be represented as small balls or other symbols standing on stalks . The co-ordinates of each point are given by the height of its stalk and the position of the base of the stalk on the horizontal plane. But the problem becomes acute with scatter diagrams where the purpose of the exercise is to see the relationships among the points and to identify clusters, particularly when the variables themselves are principal components and of little interest or meaning. Gyllenberg and Rauramaahave attempted a solution by plotting the points from a component analysis with respect to two perpendicular axes and representing the distance in the third dimension, i.e. height above the plane of the paper, by symbols. Although the height of each individual point can be roughly inferred, it is impossible to see the overall distribution of the points. Other similar techniques are commonly employed, but the impressions they give are usually rather confused.

Type
Research Article
Copyright
Copyright © Mathematical Association 1972

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Footnotes

*

Transport and Road Research Laboratory, Crowthorne, Berkshire

*

Soil Survey of England and Wales, Rothamsted Experimental Station, Harpenden, Herts)

References

1. Gyllenberg, H. G. and Rauramaa, V.: Taxonometric Models of Bacterial Soil Populations, wActa Agriculturae Scandinavica, 16 (1966) 3039.CrossRefGoogle Scholar
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4. Yule, G. U. and Kendall, M. G.: An Introduction to the Theory of Statistics, Griffin (1965).Google Scholar