## 7.3 Simple Correpondence Analysis

Analyzed Data: two-way table or contingency table obtained by crossing two categorical variables.

• Rows: analysis of the proximities between the row-profiles.

• Columns: analysis of the proximities between the column-profiles.

The utilized distance in both cases is the chi-squared distance.

#### Interpretation

• Overlapped representation of the row-profiles and the column-profiles.

• Barycentric Property: besides the dilation coefficient $$(1/\sqrt{\lambda})$$, a column-point is located in the barycenter of all the row-categories, weighted by the column-profile. Likewise, a row-point is located in the barycenter of all the column-categories, weighted by the row-profile.

• In the periphery of the cloud, two row-points that are close to each other indicate similar proportions in their column-categories. The same applies to column-points.

• The same rules of the active elements apply to the supplementary rows and columns. A supplementary row is located in a pseudo-barycenter of all the active columns, and viceversa.