In-situ stress magnitude and orientation have long been analyzed separately using classical statistics, despite the fact that stress is a tensor, and it should be analyzed using tensor-related methods. In this paper we investigate the applicability of a two dimensional aleatory model that can handle the stress tensor as a single entity. Firstly, a multivariate normal distribution of tensor components is assumed and the marginal probability functions of the eigen-parameters (principal stresses and rotational angle) derived. Using published in-situ stress data, random stress tensors are generated to compare the distributions of eigen-parameters obtained using classical and tensor statistics. We conclude that for stress magnitude, these two methods give the identical results, whereas for orientation only tensor statistics gives the correct result. Additionally, it is only tensor statistics that is invariant with regard to orientation of the coordinate system. Therefore, we conclude that in practical cases that deal only with stress magnitude, either method can give reliable result, but any analysis involving principal stress orientation requires tensor statistics.