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For two independent groups, let $M_j(x)$ be some conditional measure oflocation for the $j$th group associated with some random variable $Y$, giventhat some covariate $X=x$. When $M_j(x)$ is a robust measure of location, oreven some conditional quantile of $Y$, given $X$, methods have been proposedand studied that are aimed at testing $H_0$: $M_1(x)=M_2(x)$ that deal withcurvature in a flexible manner. In addition, methods have been studied wherethe goal is to control the probability of one or more Type I errors whentesting $H_0$ for each $x \in \{x_1, \ldots, x_p\}$. This paper suggests amethod for testing the global hypothesis $H_0$: $M_1(x)=M_2(x)$ for $\forall x\in \{x_1, \ldots, x_p\}$ when using a robust or quantile location estimator.An obvious advantage of testing $p$ hypotheses, rather than the globalhypothesis, is that it can provide information about where regression linesdiffer and by how much. But the paper summarizes three general reasons tosuspect that testing the global hypothesis can have more power. 2 Data from theWell Elderly 2 study illustrate that testing the global hypothesis can make apractical difference.

ANCOVA: A global test based on a robust measure of location or quantiles when there is curvature