In medical science and biology, there often exist situations for some data where the number of characteristics is about equal to or greater than the one of individuals. In this paper we discuss the hypothesis testing in that case, i.e., the situation where the degrees of freedom of error are so small that usual test procedures in MANOVA can not be applied for given data. We propose a test procedure with a single test statistic. The test statistic is a multiplication of the sequence of test statistics based on principal component analysis proposed by Dempster (1963a, 1963b). We also propose an influential measure of each individual for the result of the test, and a criterion of how many principal components should be incorporated in the test when the degree of hypothesis is only one. The test procedure for multivariate two sample problem is demonstrated with some data sets appeared in literature.
Ambiguous meanings are expressed by means of verbal probabilistic terms rather than numerical ones, and several methods have been developed for measuring the meanings of probability terms directly. We proposed a new indirect method to measure the probability implied by such terms. An indirect measurement was based on the method used by the experiments of Tversky & Fox (1995). We applied the direct and indirect methods to measure the meanings of terms, and validated the new methods. Finally, the differences between the indirect and the direct measurement methods were discussed. We found that in indirect method subjects evaluated the probabilistic terms more literally than in direct method.
The present study analyzed the structure of cross-subject integrated tests designed for joint university entrance examinations in Japan. Recently, basic academic skills of university students are recognized to be at risk. It is because the government curriculum guideline is getting non-academic oriented while the accessibility of higher education in young generation is getting easier. Universities need to seek for a joint entrance examination system that supports standards for university education. Twenty-six item writers from diverse academic fields made 13 pairs for making questions. They created testing items requiring skills in two completely different subject areas, such as the Japanese language and physics. Two test forms were constructed and administrated to approximately 400 university students respectively. The score analyses showed that both turned out to be too difficult for general university candidates. However, according to factor analyses, interdisciplinary testing categorizations like ‘science of mathematics and materials' and ‘science of life and environment’ appeared promising.