Experiment!: Planning, Implementing and Interpreting

12.2 Graphical Analysis

It is much easier to see relationships between variables in diagrams than in the numerical values themselves. The most common graphic tools have been introduced in the earlier chapters of this book and are only be briefly recapitulated here. They include tools for investigating distributions, for instance of residuals, but also tools for studying the relationships between two or more variables. When working with continuous variables, the scatter plot is probably the most popular type of diagram. Depending on the measurement precision it may or may not be illustrative to connect the points in a scatter plot by lines. If the data are noisy a regression line may be a better option. In cases when we are interested in the simultaneous influence of two variables, contour plots are illustrative.

One way to look for patterns and relationships in larger sets of continuous data is to plot all variables simultaneously in a scatter plot matrix. Figure 12.2 shows an example of such a diagram, where five factor variables are aligned along the x-axis and five responses along the y-axis. This graph provides a convenient overview of all the relationships between the variables. Most of the panes do not display any particular patterns. In the two rightmost panes on the top there is no variation in the response at all, except for some noise. It is more difficult to say if there are any effects in the two panes below them, for instance, because the noise is so dominant. Four ...