We have measured the differential cross-sections and analyzing powers for (p, 2p) reactions at an incident energy of 392 MeV on 12C, 16O, 40Ca, and 208Pb nuclei, leading to discrete states of the residual nuclei. The data are compared with two kinds of distorted-wave impulse approximation (DWIA) calculations, a standard calculation using a global optical potential and a calculation using wave functions generated in a relativistic Hartree model. The spectroscopic factors deduced from these two calculations agree with those determined in (e, e_p) studies mostly within 15% in the case of the lighter three target nuclei. However, those for the 208Pb target are overestimated compared with the (e, e_p) results. In the heavy target case, the DWIA results are very sensitive to the radius parameter of the bound-state potential and thus a careful treatment is required. Regarding the analyzing powers of the present measurement, we confirmed that the j-dependence is sufficient for practical spectroscopic use.