On the Intergroup Similarity and Specificity : The Study of Intergroup Similarity and Correlation among several College Sport Teams

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  • 集団相互の類似性と特殊性について : 大学運動部集団相互間における類似性と相関関係の検討
  • シュウダン ソウゴ ノ ルイジセイ ト トクシュセイ ニ ツイテ ダイガク ウンドウブ シュウダン ソウゴ カン ニ オケル ルイジセイ ト ソウカン カンケイ ノ ケントウ

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The new statistical devices for determining the intergroup similarity and specificity were discussed and they were applied to seven sport teams of college boys. Started with the geometrical interpretation of product-moment correlation, the determination of the intergroup correlatlon was attempted, and it was found that this could not be applied unless the variables were independent each other. But most of variables treated in the physical fitness measure can not be hypothesized to be independent. Therefore, m dimensional oblique variable space was converted into the m_0 (m_0⦤m) dimensional orthogonal component space, and the coordinates of individuals were determined with their component scores. Then, the team or group coordinates were determined by the centroid vectors of team members' coordinates in this m_0 component space. Then, these team centroid vectors were normalized to be the unit length vectors, so the teams were located on the surface of m_0 dimensional sphere with unity radius. Then, the distances between one team and another were computed. Let the distance be D. The group similarity was evaluted by (1-D/2) and the group specificity by (D/2). While the computation of intergroup correlation was deviced in the component spcace. It was proved that this type of correlation coefficient was more reasonable than one computed under the hypothesis of independency between the variables. And also it was proved to be more reasonable to evaluate the group similarity and specificity with the function of the intergroup distance than the one of correlation computed in the component space. Then, this idea and devices were applied to the seven sport teams of college boys whose variable measures were nine physique items.

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