  Given two independent samples of non-negative random variables with unknown
distribution functions $F$ and $G$, respectively, we introduce and discuss two
tests for the hypothesis that $F$ is less than or equal to $G$ in increasing
convex order. The test statistics are based on the empirical stop-loss
transform, critical values are obtained by a bootstrap procedure. It turns out
that for the resampling a size switching is necessary. We show that the
resulting tests are consistent against all alternatives and that they are
asymptotically of the given size $\alpha$. A specific feature of the problem is
the behavior of the tests `inside' the hypothesis, where $F\not=G$. We also
investigate and compare this aspect for the two tests.
