The self-consistent Ornstein-Zernike approach (SCOZA) is solved numerically, and its properties in the critical region are investigated for the lattice gas or Ising model in three dimensions. We especially investigate how critical properties depend upon the inverse range of interaction. We find effective critical indices that depend upon this range. However, the SCOZA does not fulfill scaling. Nevertheless, comparing with experimental results for fluids and magnets we find good agreement. Away from the critical point we find that SCOZA yields deviations from scaling that seem similar to experiments.