It is common in epidemiologic analyses to summarize continuous outcomes as
falling above or below a threshold. With such a dichotomized outcome, the u
sual chi(2) statistics for association or trend can be used to test for equ
ality of proportions across strata of the study population. However, if the
threshold is chosen to maximize the test statistic, the nominal chi(2) ref
erence distributions are incorrect. In this paper, the asymptotic distribut
ions of maximally selected chi(2) statistics for association and for trend
for the k x 2 table are derived. The methodology is illustrated with data f
rom an AIDS clinical trial. The results of simulation experiments that asse
ss the accuracy of the asymptotic distributions in moderate sample sizes ar
e also reported.