Discussion of Tanaka's paper.

The theory of quantification is a method of statistical data analysis of categorical data. In other words, this is a kind of data theory and is closely related to optimum scaling method. This method has been mainly developed by Guttman in Israel and Hayashi in Japan. The multidimensional scaling method, which has been recently developed, is considered to be a continuation of the theory of quantification. Tanaka discussed mathematically some of Hayashi's methods of quantification. The present paper, gives an overview of the methods developed by him and other closely related methods and gives the orientation of those methods introduced by Tanaka. Then, as an illustration of exploratory categorical data analysis, the experimental data of Grizzle are analyzed by using the second method of quantification. The data structure is shown heuristically as a spatial configuration of factors in two-dimensional Euclidean space.