1992 Volume 19 Issue 1 Pages 75-82
Hayashi's third method of quantification was presented by C. Hayashi in1956as a fore runner of correspondence analysis developed in France. Many artificial data sets for it have been proposed by several authors, Guttman, Iwatsubo and Otsu among others. Almost all of them have the one-dimensional structure with the circular data dealt with by Iwatsubo as the unique exception as far as the author is aware. This paper has two objectives. First, the author presents a two-parameter family of the artificial data sets with the one-dimensional structure which includes two data sets due to Otsu, Case2and Case3, and the Guttman data as special cases. For almost all artificial data sets with the one-dimensional structure, the second axis is interpreted as Guttman's intensity which is anartifact without any substantial meaning. As the second objective, item pattern with the twodimensional structure is presented. Two types are dealt with, square type and triangular type. For the both types, the first axis is interpreted as the length of the two-dimensional structure, while the number of the axis at which the second dimension, the width, appears is not necessarily two but depends indeed on the value of the length.