Multivariate Statistical Approach to the Relationships between Sexual Maturation and Growth of Physique

Abstract

In this paper the multivariate statistical analysis was applied to investigate the relation-ships between the sexual maturation and growth of physique. The Sample was consisted of 605 junior high school girls, and the items of physique measures were stature, body weight, chest girth and sitting height, and such items were administered April and the survey of menarche July in 1970. The samples were grouped into three groups, A, B, and C; group A consisted of those whose date of menarche was earlier than one standard deviation minus the sample average of the date of menarche, B wasi those who did not belong to A but had had menarch already, and C was those who did not have menarch yet. As far as the 4 items of physical measurements picked out here, the individual physique could be represented in 4 dimensional variable space. In order to visualize this space, the 2 dimensional principal component spaces were approximated to this variable space. This was done with principal component analysis. These two component axises could be interpreted as length component and breadth component, respectively. And these two component contributes to the total variance at 89.21%. Then, the mean vector and variance-covariance matrix of component scores were computed in each group, A, B, and C. Then, these values were put into (X-X)'Σ^<-1> (X-X)=C_0, where X stands for the mean vector and Σ variance-covariance matrix. This quadratic form represents the ellipes in the component space and also distributes as χ^2 with degree of freedom 2. Then, puttingχ^2(df=2,α=0.05) to C_0,these ellipses show the domain to which 95% of each group belong. In other words, these ellipses are good representation of each group in the component space. In all groups, X<Y, where X and Y are coordinate of ellipe center ; so the tendency of Ectomorphy may be inferred. The common domain between group A and C was very small; so it could be concluded that group A was superior in physique in general to group C, but the common domains between group A and B, and B and c were relatively large. That is, as far as the only average of physique items investigated separately, group A is superior to B and C, and group B to C, but such conclusions were found not always right, because the multivariate investigation showed that considerable percentage of group A had the same physique as group B and also group B as group C. However, the unique domain of group C was very large and the coordinates of these points in this domain were very small, so it can be inferred that considerable almount of group C hod the inferior physique.