Models which may decompose the three variable interaction in r×s×t contingency tables are proposed, the models for the additive and multiplicative definition of no interaction being extended. One of those models makes possible an inferential approach to Iwatsubo's(1974)quantification technique, which is regarded as a statistically description-oriented method. The equivalence of our chi-square criterion to the maximization of the third order correlation coefficientρis shown. Several properties of the new models are derived, including the n.s. conditions that theρvanishes and the exact upper bound ofρ2. Many versions of the models and testing procedures for them are suggested.
A new estimation method for learning progress distribution of self-paced programmed instruction is introduced in order to better evaluate the instructional program. The traditional program evaluation has been based on student performance for frame responses and scores of pre-and post-tests. This paper points out that learning progress distributions in time process should be utilized in order both to evaluate the program construction and to estimate student learning progress, as well as the traditional evaluation methods. First, this paper discusses differences between a self-paced programmed instruction and a group-paced instruction. Second, this paper describes the relation of learning progress distribution to frame response time distribution. Finally, this paper suggests(1)learning progress distribution models and these characteristics, (2)quantitative estimation of student learning progress, and(3)average response time estimation of each frame.
The notion of transformational grammar is originally defined as a sagenerative grammar and has some drawbacks in syntactic analysis. For eliminating these drawbacks, the transformation of forests(instead of trees)monitored by a control variable is proposed.