Physical ability was extracted as orthogonal factor from variables chosen; physique and muscular strength in this paper. The abilities extracted were estimated with factor score determined by a certain linear combination of variables significant to the factor extracted. Their growth and development was discussed through investigating in the distribution of abilities extracted for each grade under the assumption that ability is distributed as normal. The overlaps in distribution of different grades were evaluated by integral and they were used as one of indicators for growth and development. Then in two dimensional ability space the relative growth and development was discussed through investigating the configuration of ellipses that showed the grade groups in two dimensional space.
We conformed the age and sex-specific onset rates of SLE in three series from the United States, Netherland and Japan to the Weibull distribution. It was shown that all sample distributions were conformed to the distribution except for the first decade of age. In addition, it was observed on the Weibull probability paper that all distributions except the one for the American male SLE were displayed parallelly with nearly the same slope. It was not reasonable to explain the etiology of the disease with the random failure model simply because of a good fit obtained by the Weibull distribution. It was considered however that the fact that there were remarkable similarity on the shape among distributions from the three countries suggested the empirical distribution derived in this paper to be be used as provisional reference until more accurate statistics would be available.
Simple procedures for obtaining the m.l. estimates of multiple correlation, canonical correlation, partial canonical correlation and bi-partial canonical correlation have been derived for situations where the underlying covariance structure is uniform (equal variances and equal positive covariances). It has been shown that for any even-sized p × p symmetric R matrix with intra-class correlation structure, the largest canonical correlation is identically equal to the maximum eccentricity of the p-dimensional correlation ellipsoid. Using an empirical variance convariance matrix based on attribute ratings of coffee, the computational short-cuts in the m.l. estimation of various measures of multivariate relationships have been demonstrated.
This report investigates attribution processes using 68 students in a cooperation-noncooperation modified prisoner's dilemma game. The attribution processes of the subjects were explored in a 2 × 2 factorial design (subject's high or low cooperation and target's high or low cooperation). Experimental results showed that subjects attributed the target's high cooperation significantly less to an internal cause when the subject's own cooperation was high than when it was low. There was no significant difference in the subject's ratings of the internal attribution for the target's low cooperation between the subject's cooperation conditions. When subjects attributed the less to the internal cause, the subjects had a tendency to attribute the cooperation to subject's own cooperation. These results confirmed that an active observer in a social interaction perceives the causes of another person's behavior dependent on observer's own behavior toward the other. Adjective ratings of the target's dispositions gave further evidence.
This paper is concerned with a methodological study of Hayashi's eij-type quantification method (EQ) and development of a new method (PAMSE) of multidimensional scaling (MDS). First we propose procedures to compare EQ with other methods of MDS in terms of the separation of eigenvalues. Secondly we examine a problem of the fit and dimensionality and point out a peculiar property inherent to EQ. Third we propose a new method of MDS, which is developed from EQ, intended principally for dissimilarity data measured on the medium level between ordinal and interval scale levels. Our method is conceptually similar to but fundamentally different from Johnson's in that our index of fit is specially formulated in view of the scale level. The method has been found to work successfully, giving a high degree of the rank correlation between the dissimilarities and the derived distances.
A Bayesian approach to analysis of covariance is proposed, in which it is assumed that the relevant parameters are exchangeable in the sense of De Finetti, i.e., they still have the same prior joint distribution when they are permuted. Actual data analysis shows that this exchangeability assumption results in makred differences in the posterior distributions of effect parameters from analysis using noninformative prior distributions, and hence from the sampling theory results.
“Social preference orders” obtained by voting rules may be evaluated in terms of how individual preferences expressed by voters have been properly reflected in the obtained orders. To represent the degree of reflection of the preferences by voter i, Pi, in a given social order, P, we defined the matching score, tip by the number of those pairs of alternatives the orders of which match for Pi and P>. Then we proposed using the mean and variance of the tip to evaluate outcomes of voting, i.e., social orders, given a profile of individual preferences expressed by voters. A new rule, Varmin rule, is proposed which yields the order that minimizes the variance of these matching scores. Various social orders obtained by a number of voting rules, such as, Majority, Borda, Double Plurality, and Varmin, were evaluated in terms of means and variances of matching scores through a computer simulation of 15, 000 profiles. Results generally indicated as follows: The Majority rule tends to yield rather large variances, although it theoretically yields in largest mean. The Borda rule yielded rather small variances, keeping the means at rather high levels. The Double Plurality rule yielded large variances with unpredictable fluctuations of the means. The Varmin rule yielded too small means, although it theoretically yields the least possible variance. A method to modify social orders to reduce the variances most effectively was proposed (called, “Maximum Covariance Method”), showing that only a small modification of the Majority orders would be sufficient to yield very small variances with only a minor decrease of means.