On Maximally Selected Chi-Square Statistics
James A. Koziol · Biometrics · 1991
Two samples can be compared by selecting a cutpoint and then forming a 2 x 2 table of the numbers of observations above and below the cutpoint in each sample. Miller and Siegmund (1982, Biometrics 38, 1011-1016) investigated asymptotic theory relating to the distribution of the standard chisquare statistic when the cutpoint is selected to maximize its value; in a companion article, Halpern (1982, Biometrics 38, 1017-1023) studied the finite-sample distribution of this maximally selected chi-square statistic via simulation. Exact finite-sample distribution theory, derived from Durbin's (1971, Journal of Applied Probability 8, 431-453; 1973, Distribution Theory for Tests Based on the Sample Distribution Function, Philadelphia: SIAM) combinatorial approach, is presented here.