A direct calculation of moments of the sample variance

A systematic method to deal with the interrelations of systems with multi-index quantities (random variables) is proposed. The method differs of the well-known Polykays. An application of the theoretical results here presented is the calculation of the moments of the sample variance for general populations in a direct way. The main advantage of the proposed methodology is that no conversion formulae and other complicated Polykays rules are needed. However, the proposed method is compatible with Polykays philosophy and conversion formulae and multiplication rules can be derived by using the theoretical results of this work. For practical purposes, two algorithms for the calculation of the moments of the sample variance are proposed.