Approximate distribution of the maximum of c−1 x2-statistics (2 × 2) derived from 2 ×C contingency table

In a 2×c contingency table, let X 1 2 be the X 2 -statistic for 2×2 table composed of 1-st column vs. the sum of 2nd, 3rd,... and c th column. Let x 2 2 be the x 2 -statistic roc 2×2 cable composed of 1st plus 2nd columns vs. the sum of 3rd, 4th,` and c th columns. Finally in this way x c−1 2 can be defined by the X 2 -statistic for 2×2 table composed of the sum of the first c-l columns vs. c th column. ln this paper, it is shown that the asymptotic distribution of T=max{x 1 2 ...,X c−1 2 } is expressed in terms of the multi-variate normal probability of c−1 dimensional cube for large sample sizes. Approximately conservative critical point of T is obtained in (2.14). Application to the procedure by Otaka and Jablon [2] for regrouping a 2×c cable, where the columns are ordered with respect to a numerical variable, is stated in relation to Leukemia data at ABCC.