Correspondence analysis (CA) is a multivariate statistical technique proposed[1] by Herman Otto Hartley (Hirschfeld)[2] and later developed by Jean-Paul Benzécri.[3] It is conceptually similar to principal component analysis, but applies to categorical rather than continuous data. In a similar manner to principal component analysis, it provides a means of displaying or summarising a set of data in two-dimensional graphical form. Its aim is to display in a biplot any structure hidden in the multivariate setting of the data table. As such it is a technique from the field of multivariate ordination. Since the variant of CA described here can be applied either with a focus on the rows or on the columns it should in fact be called simple (symmetric) correspondence analysis.[4]
It is traditionally applied to the contingency table of a pair of nominal variables where each cell contains either a count or a zero value. If more than two categorical variables are to be summarized, a variant called multiple correspondence analysis should be chosen instead. CA may also be applied to binary data given the presence/absence coding represents simplified count data i.e. a 1 describes a positive count and 0 stands for a count of zero. Depending on the scores used CA preserves the chi-square distance[5][6] between either the rows or the columns of the table. Because CA is a descriptive technique, it can be applied to tables regardless of a significant chi-squared test.[7][8] Although the statistic used in inferential statistics and the chi-square distance are computationally related they should not be confused since the latter works as a multivariate statistical distance measure in CA while the statistic is in fact a scalar not a metric.[9]