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

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Abstract
In a 2×c contingency table, let X1 2 be the X2 -statistic for 2×2 table composed of 1-st column vs. the sum of 2nd, 3rd,… and c th column. Let x2 2 be the x2-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 xc−1 2 can be defined by the X2 -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{x1 2…,Xc−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.

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