Deterministic and stochastic methods such as MPM and MAP have been extensively used for successfully solving problems related to image segmentation, restoration, texture analysis and motion estimation. Within this framework, Markov random field (MRF) is the most popular and powerful model used for describing and analyzing images. Nevertheless the question that arises is to know if MRF is able to model real images. In this paper we address the classification of real images into two model families, namely MRF and non-MRF families. Within this mathematical statistical framework, we propose a novel method based on parameter estimation techniques and hypothesis verification. The main steps of the approach are: (1) Estimating transition probabilities of MRF for various partitions of the image. This stage depends on following parameters: number of gray levels denoted by k, number of components in the partition denoted by L and number of the considered partitions denoted by R. We established that L depends on k, the neighborhood system and the size of the initial image. (2) Testing the homogeneity hypothesis over the set of all the transition matrix estimators. When R equals 1, a one-way analysis of variance is applied. When R >= 1, the dependence on the two factors L and R leads to a two-way analysis of the variances. Such a procedure was applied to different simulated images with the presence of exact MRF among them and to real images. Performances on the non supervised classification into MRF and non-MRF families are discussed in terms of accuracy and robustness. Application of the developed procedure to the lossy compression is presented in details.