The ground state energy of disordered quantum dots is studied experimentally as a function of dot population. The fluctuations are found to be considerably larger than those predicted by random matrix theory and to display different statistics. Exact diagonalization of the Hamiltonian pertaining to small clusters shows, indeed, that the random matrix statistics holds only for weak Coulomb interactions. As the interaction is made realistic, a crossover to a different statistics, similar to the experimental one, is observed. The statistics crossover is accompanied by appearance of short range spatial correlations in the electron density.