ANalysis Of VAriance (ANOVA) is a common technique for computing a ranking of the input parameters in terms of their contribution to the output variance. Nevertheless, the variance is not an universal criterion for ranking variables, since non symmetric outputs could require higher order statistics for their description and analysis. In this work, we illustrate how third and fourth-order moments, i.e. skewness and kurtosis, respectively, can be decomposed mimicking the ANOVA approach. It is also shown how this decomposition is correlated to a Polynomial Chaos (PC) expansion leading to a simple strategy to compute each term. New sensitivity indices, based on the contribution to the skewness and kurtosis, are proposed. The outcome of the proposed analysis is depicted by considering several test functions. Moreover, the ranking of the sensitivity indices is shown to vary according to their statistics order. Furthermore, the problem of formulating a truncated polynomial representation of the original function is treated. Both the reduction of the number of dimensions and the reduction of the order of interaction between parameters are considered. In both cases, the impact on the reduction is assessed in terms of statistics, namely the probability density function. Feasibility of the proposed analysis in a real-case is then demonstrated by presenting the sensitivity analysis of the performances of a turbine cascade in an Organic Rankine Cycles (ORCs), in the presence of complex thermodynamic models and multiple sources of uncertainty.