The probability distributions of the closest neighbour (CN) and farther neighbour (FN) spacings from a given level have been studied for interacting fermion/boson systems with and without spin degree of freedom constructed using an embedded Gaussian orthogonal ensemble (GOE) of one plus random two-body interactions. Our numerical results demonstrate a very good consistency with the recently derived analytical expressions using a 3 × 3 random matrix model and other related quantities by Srivastava et al, J. Phys. A: Math. Theor. 52, 025101 (2019). This establishes conclusively that local level fluctuations generated by embedded ensembles (EE) follow the results of classical Gaussian ensembles.