Sample size determination for procedures of design of experiments and multivariate analysis

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In this research, we dealt with multiple comparison procedures and Mahalanobis Taguchi system(MT system). We investigated their performance from the view points of sample size determination and proposed several new procedures.Firstly, we investigated the following topics about multiple comparison procedures and obtained the following results. (1) We reorganized the known results about sample size determination for Dunnett procedure and proposed an approximation method. (2) We examined the robustness of Max t procedure for underling assumptions and the relation to the sample size. (3) We examined the performance of maximum contrast procedure and also proposed some improved version of it. We think that these results will be useful for users to apply in practical situations and that they will keep users from misusing multiple comparison procedures.Secondly, we investigated the following topics about MT system and obtained the following results.(1) We establish the relation between the distribution of signal-to-noise ratio and doubly noncentral F distribution, which will be able to enhance the theoretical research of Taguchi methods.(2) We clarified the position of MT system in the Taguchi method.(3) We derived a theorem concerning some distance used in MT system.(4) We compared the performance of several procedures under the multicollinearity. These results contribute to the theoretical development of MT system.Furthermore, we investigated model selection methods for other multivariate analysis and obtained useful results.