Symmetrical Normalization

How are the brands related to the image attributes? Principal normalization cannot address these relationships. To focus on how the variables are related to each other, use symmetrical normalization. Rather than spread the inertia twice (as in principal normalization), symmetrical normalization divides the inertia equally over both the rows and columns. Distances between categories for a single variable cannot be interpreted, but distances between the categories for different variables are meaningful.

  1. To produce the following solution with symmetrical normalization, recall the Correspondence Analysis dialog box and click Model.
    Figure 1. Model dialog box
    The Correspondence Analysis Model dialog box.
  2. In the Model dialog, select Symmetrical as the normalization method.
  3. Click Continue.
  4. Click OK in the Correspondence Analysis dialog box.

In the upper left of the resulting biplot, brand EE is the only tough, working brand and appeals to men. Brand AA is the most popular and also viewed as the most highly caffeinated. The sweet, fattening brands include BB and FF. Brands CC and DD, while perceived as new and healthy, are also the most unpopular.

Figure 2. Biplot of the brands and the attributes (symmetrical normalization)
Biplot of the brands and the attributes (symmetrical normalization)

For further interpretation, you can draw a line through the origin and the two image attributes men and yuppies, and project the brands onto this line. The two attributes are opposed to each other, indicating that the association pattern of brands for men is reversed compared to the pattern for yuppies. That is, men are most frequently associated with brand EE and least frequently with brand CC, whereas yuppies are most frequently associated with brand CC and least frequently with brand EE.