  Sensitivity indices are commonly used to quantify the relative influence of
any specific group of input variables on the output of a computer code. One
crucial question is then to decide whether a given set of variables has a
significant impact on the output. Sobol indices are often used to measure this
impact but their estimation can be difficult as they usually require a
particular design of experiment. In this work, we take advantage of the
monotonicity of Sobol indices with respect to set inclusion to test the
influence of some of the input variables. The method does not rely on a direct
estimation of the Sobol indices and can be performed under classical iid
sampling designs.
