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 α. A specific feature of the problem is the behavior of the tests ‘inside’ the hypothesis, where F≠G. We also investigate and compare this aspect for the two tests.