Quality (in Correspondence Analysis)

The term quality in the context of correspondence analysis pertains to the quality of representation of the respective row point in the coordinate system defined by the respective numbers of dimensions, as chosen by the user. The quality of a point is defined as the ratio of the squared distance of the point from the origin in the chosen number of dimensions, over the squared distance from the origin in the space defined by the maximum number of dimensions (remember that the metric in the typical correspondence analysis is Chi-square). By analogy to Factor Analysis, the quality of a point is similar in its interpretation to the communality for a variable in factor analysis.

Note that the quality measure reported by STATISTICA is independent of the chosen method of standardization, and always pertains to the default standardization (i.e., the distance metric is Chi-square, and the quality measure can be interpreted as the "proportion of Chi-square accounted for" for the respective row, given the respective number of dimensions). A low quality means that the current number of dimensions does not represent well the respective row (or column).

For more information, see the description of the Correspondence Analysis module.