Traditional stochastic optimization assumes that the probability distribution of uncertainty is known. However, in practice, the probability distribution oftentimes is not known or cannot be accurately approximated. One way to address such distributional ambiguity is to work with distributionally robust optimization (DRO), which minimize the worst-case expected cost with respect to a set of probability distributions. In this talk, we illustrate that not all, but only some scenarios might have an effect on the optimal value, and we formally define this notion for DRO. We also examine the properties of effective scenarios. In particular, we investigate problems where the distributional ambiguity is modeled by the total variation distance with a finite number of scenarios under convexity assumptions. We propose easy-to-check conditions to identify effective and ineffective scenarios for this class of DRO. Computational results show that identifying effective scenarios provides useful insight on the underlying uncertainties of the problem.