Collapsed Two-Way Contingency Tables and the Chi-Square Reduction Principle
研究了列联表在合并同质行列后卡方统计量不变的性质，并证明卡方缩减量具有有意义的典型分解，可帮助研究者检测同质行列。
SUMMARY The value of the chi-square statistic for homogeneity of rows and columns in a contingency table remains unchanged if the table is collapsed (grouped) over homogeneous rows and columns. The difference between the chi-square values pertaining to the original table and to the collapsed table (the ‘chi-square reduction‘) is shown to have a meaningful canonical decomposition which can guide the researcher in detecting homogeneous rows and columns. The methodology proposed generalizes an earlier methodology suggested by Gilula for the same problem.