文章基本信息

标题：成分空間による発育発達の分析 : 体格の発育について (第一報)
其他标题：Analysis of Growth and Development in Component Space : On Growth of Physique (Vol.1)
本地全文：下载
作者：田村喜弘 ; 松浦義行 ; 大山良徳等
期刊名称：体育学研究
印刷版ISSN：0484-6710
电子版ISSN：1881-7718
出版年度：1972
卷号：16
期号：5
页码：291-298
DOI：10.5432/jjpehss.KJ00003405381
语种：Japanese
出版社：Japan Society of Physical Education, Health and Sport Sciences
摘要：発育発達は多くの側面をもっているが,それらの諸側面が相互に関連し合いつつ発育発達の過程が展開されるのである.発育発達現象を現象に忠実に分析してゆくには現象のもつあらゆる側面を測定し,この測定変数間の関連性を考慮しつつ,測定変数全体を同時空間の中で取り扱い,経時的変化を考察する事がより有効な方法と考えられる.この立場に立って,測定変数の数に等しい次元の変数空間での考察に直観的考察の利点を生かすため主成分分析を適用して,第1,第2主成分を直交軸とする2次元成分空間をn次元変数空間の近似空間として,この成分空間で発育発達現象を考察する方法を工夫した.この方法を農村地域小学校児童標本に適用し,体格の発育を成分空間における各学年別に95%の所属楕円の経年的変化を考察することによってアプローチした.
其他摘要：The human growth and development has various aspects which are more or less associated with each other. In order to investigate this process of growth and development more precisely, these various aspects must be treated as the associated attributes in the same space. Now, let X be the measure vector (X_1X_2X_3.........X_n), X can be expressed as a point in the n dimensional variable space. Testing the difference between the mean vectors of two groups in deferent growth level is much more efficient than testing the one between the mean values of measures, separately, However, the n dimensional space can not be observed intuitively, so it may restrict the observation. For the purpose to observe the n-dimensional phenomenon intuitively, the two-dimensional component space was approximated to the n dimensional variable space. In order to extract the two components, principal component analysis was applied and, the first and the second principal component were used. Then, (C-C)V^<-1> (C-C)' = X^2 (β)expresses the β% probability ellipse in the component space, where C stands for component score vector, C the mean vector of component score and V the variance covariance matrix of component score in each grade group, so the ellipse of each grade group was computed and drawn in the two dimensional component space. The change of ellipse area, position and the overlapping area between the ellipses of different grade groups were investigated. This approach can not be applied to all the situations. If considerable portion of total variance can be explained by these two components, this technique can be successfully applied. Then, this technique was applied to investigate the physique growth of elementary school sample in some rural area in Kyoto. Then, several interesting findings were extracted, such as described in this paper.