Common Errors in Statistics (and How to Avoid Them), 4th Edition

MULTIDIMENSIONAL DISPLAYS

Representing several distinct measures for a collection of points is problematic in both text and graphics. The construction of tables for this display is difficult due to the necessity of effectively communicating the array of subtabular information. The same is true in graphical displays, but the distinction of the various quantities is somewhat easier.

Biplots

In principal component analysis, biplots are used to display the contributions of multiple variables in a two-dimensional display. Fewer than 10 variables should be used if the plot is to be readable [Falissard, 2012].

Common errors include all of the following [Gower et al., 2010]:

• Incomplete captions
• Incomplete legends
• Origin not indicated
• Shape/aspect misleading

Biplot scales should always employ the true aspect ratio. The scales of the biplot shown in Figure 10.17 do not. As a result, distances and angles are distorted, making the results impossible to interpret without extensive discussion. Moreover, the four scales (top, bottom, right, and left) measure two different things:

1. The scales at the top and the right give values of variables.

2. The scales at the bottom and the left are unnecessary as they give coordinates of samples in terms of principal components.

FIGURE 10.17. A biplot with multiple faults.

Reproduced with permission from Gower [2003].

Putting the scales in scientific ...