Introduction

Correspondence Analysis is a widely used multivariate statistical method, mainly applied to categorical data and contingency tables. Its main objective is to transform a multidimensional data table into a graphical representation that clearly displays the associations between rows and columns. It is primarily a descriptive method that allows the researcher to investigate and interpret complex relationships among variables, offering a simplified yet meaningful view of the information.

Basic Theory

The procedure begins with the construction of a contingency table, which is formed by the cross-classification of two categorical variables. Each cell of the table corresponds to the frequency of a particular combination of categories. The chi-square test is used to examine the independence between the two variables. A statistically significant value of the chi-square statistic leads to the rejection of the null hypothesis and indicates that the variables exhibit some form of association. However, this test does not reveal precisely where the deviations from independence occur, which makes a more elaborate analysis necessary.

Correspondence Analysis proceeds by decomposing the table through eigenvalues and eigenvectors. As in Principal Component Analysis, the eigenvalues are interpreted as indicators of variance and represent the proportion of total inertia, that is, the deviation from independence explained by each dimension. In this way, the most important dimensions are selected, and a new low-dimensional space is constructed, where the row and column points of the original table are placed.

Graphical Representation and Interpretation

The most significant contribution of the method is its ability to represent the data in two- or three-dimensional space. In the resulting diagram, points that lie close to each other indicate categories that present similar distribution patterns. This enables researchers to identify groups, similarities, and differences among categories, which would be difficult to detect solely by examining absolute frequencies.

Moreover, the method allows the detection of potential overlaps between categories and reveals underlying structures that are not apparent in the raw data. Through the graphical representation, it becomes possible to arrange the categories along natural axes, uncovering relationships connected to social, economic, or other characteristics.

Results and Potentials

The outcomes of Correspondence Analysis are both multiple and substantial. The analysis highlights strong associations between rows and columns and arranges the categories in a common space that facilitates visual interpretation. Differences between categories become more explicit, while new synthetic dimensions are created that summarize a large part of the original information. In this way, the method goes beyond description and contributes to both condensation and interpretation of data.

Example of Application

The study material presents the example of employment status by gender. The contingency table includes the categories of full-time employment, part-time employment, and unemployment for men and women. Correspondence Analysis leads to the calculation of eigenvalues, which show the percentage of deviation from independence explained by each dimension. The row and column values are converted into scores, which are then displayed in a diagram. The graphical representation reveals, for instance, that women tend to be more closely related to the category of unemployment, while men are more strongly associated with full-time employment, thus highlighting a socially and economically critical differentiation.

Extensions and Uses

Correspondence Analysis is not limited to two-dimensional tables but can also be applied to more complex data structures. This has led to the development of the French school of “Analyse des données,” which employed the method in a wide range of applications. Today, Correspondence Analysis is used in the social sciences, educational research, marketing, biostatistics, and political analysis, as it provides the ability to transform complex tables into comprehensible visual representations. Its main advantage lies in combining statistical evidence with visual interpretation, thereby facilitating the understanding of data even for non-specialists.

Conclusions

Correspondence Analysis constitutes a bridge between descriptive statistics and multidimensional data analysis. It transforms complex contingency tables into graphical representations that reveal associations, differences, and groupings. Its contribution is not limited to visualization but extends to the creation of new variables that summarize the information. Thus, it offers the researcher a flexible and powerful tool for understanding complex categorical data, expanding the possibilities of interpretation and analysis across various fields of research.