In this paper, we propose ROBIST, a simple, yet effective, data-driven algorithm for optimization under parametric uncertainty. The algorithm first generates solutions in an iterative manner by sampling and optimizing over a relatively small set of scenarios. Then, using statistical testing, the robustness of the solutions is evaluated, which can be done with a much larger set of scenarios. ROBIST offers a number of practical advantages over existing methods as it is: (i) easy to implement, (ii) able to deal with a wide range of problems and (iii) capable of providing sharp probability guarantees that are easily computable and independent of the dimensions of the problem. Numerical experiments demonstrate the effectiveness of ROBIST in comparison to alternative methods.