  Gaussian comparison inequalities provide a way of bounding probabilities
relating to multivariate Gaussian random vectors in terms of probabilities of
random variables with simpler correlation structures. In this paper, we
establish the partial stochastic dominance result that the cumulative
distribution function of the maximum of a multivariate normal random vector,
with positive intraclass correlation coefficient, intersects the cumulative
distribution function of a standard normal random variable at most once. This
result can be applied to the Bayesian design of a clinical trial in which
several experimental treatments are compared to a single control.
