The author presented lately an artificial data set for Hayashi's second method of quantification (H2MQ) or categorical discriminant analysis. The data set is simple and has an explicit mathematical solution, though it is not so flexible with respect to generalization as the Guttman data for Hayashi's third method of quantification. In this paper are presented two more data sets for H2MQ, which enjoy similar features as the previous one does. Every set is described in the context of test situation with a few binary questions (items). The previous set consists of 3 groups and is symmetric with respect to the ordering transformation which reverses the ordering of 4 questions. Both of the new ones consist of 4 groups and are symmetric with respect to the interchange transformation which interchanges the two alternative answers for each of 3 questions. The latter has the ordering symmetricity too.
