Relationships between three or more variables

The relationship between two variables is captured completely by a scatterplot. However there is no comparable display of three or more variables that clearly expresses their relationships.

Various displays have been proposed for multivariate data, each of which extends the scatterplot in a different way. None of them have the same descriptive power that a simple scatterplot has for bivariate data but, with experience, they can give some insight into the relationships between the variables. The pages in this section describe some such displays.

Use different plotting symbols to represent a third variable

For data sets that contain three numerical variables, the simplest display is based on a scatterplot of two of the variables. The third variable is represented by the use of differing symbols instead of identical 'crosses' on the scatterplot. A continuous characteristic of the plotting symbols such as colour, size or angle is often used.

The choice of which of the three variables to represent using the plotting symbol is often arbitrary, but can greatly affect how easily the diagram is interpreted.

Although this kind of scatterplot is easy to draw, it is usually hard to interpret.

Properties of rubber specimens

In an industrial experiment, 30 rubber specimens were rubbed by an abrasive material. The measurements from each specimen were ...

tensile strength
force per unit cross-sectional area required to break the specimen
hardness
rebound height of a steel indenter dropped onto the specimen
abrasion loss
amount of material abraded from the specimen per unit of energy expended in rubbing it.

The two axes of the following scatterplot represent the tensile strength and hardness of the specimens. Abrasion loss is shown by the size of the circle in the scatterplot (the larger circles represent greater abrasion loss).

There is clearly less abrasion loss for harder specimens. There is also evidence that abrasion loss is less for specimens with higher tensile strength. (Consider the specimens with hardness between 60 and 70.)

Select the options Colour and Angle from the popup menu to use different characteristics of the plotting symbols to represent abrasion loss.