With the rapid application of computers, a number of techniques of multivariate analysis have been developed and widely used in the fields of behavioral sciences. Unfortunately, many researchers who are concerned with data analysis often think that it is too difficult to determine the best technique for the given data, since they consider various techniques to be quite varied in its mathematical structure. In view of this, we try to describe various techniques of multivariate analysis in terms projection operator in order toclarify the mutual relationships among various techniques by introducing the conception of generalized coefficient of determination(G.C.D.). As a result, we can prove that coefficients of determination such as correlation ratio, squared multiple correlation and Maharanobis generalized distance are represented as special cases of G.C.D.
The purpose of clinical diagnosis is to determine the most fitting treatment for individual pathological conditions, and the process of diagnosis and treatment is one of feedback control system. In this paper, application of “optimal control theory” to diagnostic process was discussed and one example of computer program was showed. When diagnostic process is regarded as one of control system, medical treatment, pathological internal conditions and clinical findings are replaced to input variables, state variables and output variables respectively, and if the interrelationship of these three variables is quantitatively represented, it becomes to a problem of optimal control theory. As a clinical application, “insulin therapy in diabetic coma” was proposed. Injection of insulin and infusion therapy as input variables, and blood glucose level and insulin level state variables were used respectively, and the iterrelationship was mathematically represented based on the simulation study of blood glucose kinetics. This model was programmed for digital computer. When observed data of blood glucose level and details treatment were entered, the dosis of insulin to be injected now, fitting to the desired blood glucose level after adequate time, is computed.
Multivariate analysis of variance had, for the first time, been applied to the analysis of speech sounds by the author, considering the frequency components of speech spectra as the components of multi-dimensional vectors. In this paper, a divided type of model for mulitivariate analysis of variance was proposed in order to give an answer to the hypothesis that “the influence of the vowel on the following vowel in the vowel-vowel sequence is larger than the influence of the consonant on the following vowel in the consonant-vowel sequence.” One of the geometric representations of the divided type of model was also introduced. As a result, it was found that the way of influence of the preceding phoneme on the vowel is significantly different due to whether the preceding phoneme is a vowel or a consonant.
This paper would point out some problems of the models of Impression formation under the traditional point of view. One of the problems may be stemed from the one-dimensional point of view to the scale. The model, therefore, would be constructed from the multi-dimensional point of view. The other may be in the weight factor, so, in this paper, it would define that the weight is the degree of relevance with respect to the meaning factor of the stimulus word. After these considerations, it would represent a new progressive redundancy model, and that would be firmed by experiment and computer simulation. The feature of this model lies in that it reduces the impression to the common meaning factors and unique meaning factors based on factor analytic method.