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.
Cheese taste test
In an attempt to understand differences in the perceived taste of cheddar cheese, several samples were analysed chemically and were also subjectively rated for taste by a panel of trained tasters. The effect of two chemicals of importance to taste, hydrogen sulphide and lactic acid, are examined in the scatterplot below.
The main axes show the taste rating against hydrogen sulphide, and the size of the circles represents the lactic acid content of the samples (the larger circles represent higher lactic acid content).
There is clearly a higher taste rating for cheese samples with higher hydrogen sulphide content. There is also evidence of a higher taste rating for samples with more lactic acid. (Consider the cheese samples with hydrogen sulphide content of between 3 and 5.)
Select the options Colour and Angle from the popup menu to use different characteristics of the plotting symbols to represent lactic acid.